Edgeworth size corrected W, LR and LM test in the formation of the preliminary test estimator

Article

Khan, Shahjahan, Hoque, Zahirul and Billah, Baki. 2006. "Edgeworth size corrected W, LR and LM test in the formation of the preliminary test estimator." Journal of Statistical Research. 40 (2), pp. 55-64.
Article Title

Edgeworth size corrected W, LR and LM test in the formation of the preliminary test estimator

ERA Journal ID900
Article CategoryArticle
AuthorsKhan, Shahjahan (Author), Hoque, Zahirul (Author) and Billah, Baki (Author)
Journal TitleJournal of Statistical Research
Journal Citation40 (2), pp. 55-64
Number of Pages12
Year2006
Place of PublicationDhaka, Bangladesh
ISSN0020-3165
0256-422X
Web Address (URL)http://www.isrt.ac.bd/images/jsr/v40n2/zahirul.pdf
Abstract

This paper defines the preliminary test estimator (PTE) of the univariate normal mean under the original as well as the Edgeworth size corrected Wald (W), likelihood ratio (LR) and Lagrange multiplier (LM) tests. The bias and mean squared error (MSE) functions of the estimators are derived. The conflicts among the biases and the MSEs of the PTEs
under the three original and the size corrected tests have been obtained. It is found that instead of the original W, LR and LM tests, the use of the Edgeworth size corrected W, LR and LM tests in the formation of the PTEs reduces the conflict among the biases and MSEs of the estimators remarkably.

KeywordsPreliminary test estimator; Wald, likelihood ratio, Lagrange multiplier tests; bias; mean squared error
ANZSRC Field of Research 2020490509. Statistical theory
490501. Applied statistics
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsDepartment of Mathematics and Computing
United Arab Emirates University, United Arab Emirates
Monash University
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Doi, Suhail A. R., Barendregt, Jan J., Khan, Shahjahan, Thalib, Lukman and Williams, Gail M.. 2015. "Advances in the meta-analysis of heterogeneous clinical trials II: the quality effects model." Contemporary Clinical Trials. 45 (A), pp. 123-129. https://doi.org/10.1016/j.cct.2015.05.010
Advances in the meta-analysis of heterogeneous clinical trials I: the inverse variance heterogeneity model
Doi, Suhail A. R., Barendregt, Jan J., Khan, Shahjahan, Thalib, Lukman and Williams, Gail M.. 2015. "Advances in the meta-analysis of heterogeneous clinical trials I: the inverse variance heterogeneity model." Contemporary Clinical Trials. 45 (A), pp. 130-138. https://doi.org/10.1016/j.cct.2015.05.009
Simulation comparison of the quality effects and random effects methods of metaanalysis
Doi, Suhail A. R., Barendregt, Jan J., Khan, Shahjahan, Thalib, Lukman and Williams, Gail M.. 2015. "Simulation comparison of the quality effects and random effects methods of metaanalysis." Epidemiology. 26 (4), pp. 42-44. https://doi.org/10.1097/EDE.0000000000000289
Contribution of Muslims to the regional social harmony, interreligious dialogue and culture
Khan, Shahjahan. 2014. "Contribution of Muslims to the regional social harmony, interreligious dialogue and culture." Harmes, Marcus K. and Batorowicz, Krzysztof (ed.) Peace, Interreligious Dialogue and Culture Seminar 2014. Toowoomba, Australia 13 - 14 Feb 2014 Toowoomba, Australia.
Score test in robust M-procedure
Khan, Shahjahan and Yunus, Rossita M.. 2014. "Score test in robust M-procedure." Journal of Applied Probability and Statistics. 9 (2), pp. 55-75.
Effect of timing of pharmaconutrition (immunonutrition) administration on outcomes of elective surgery for gastrointestinal malignancies: a systematic review and meta-analysis
Osland, Emma, Hossain, Md Belal, Khan, Shahjahan and Memon, Muhammed Ashraf. 2014. "Effect of timing of pharmaconutrition (immunonutrition) administration on outcomes of elective surgery for gastrointestinal malignancies: a systematic review and meta-analysis." Journal of Parenteral and Enteral Nutrition. 38 (1), pp. 53-69. https://doi.org/10.1177/0148607112474825
Classical and Bayesian prediction for multivariate simple regression model
Khan, Shahjahan. 2014. "Classical and Bayesian prediction for multivariate simple regression model." Journal of Applied Probability and Statistics. 9 (1), pp. 67- 78.
Laparoscopic anterior versus posterior fundoplication for gastro-esophageal reflux disease: a meta-analysis and systematic review
Memon, Muhammed Ashraf, Subramanya, Manjunath S., Hossain, Md Belal, Yunus, Rossita Mohamad, Khan, Shahjahan and Memon, Breda. 2015. "Laparoscopic anterior versus posterior fundoplication for gastro-esophageal reflux disease: a meta-analysis and systematic review." World Journal of Surgery. 39 (4), pp. 981-996. https://doi.org/10.1007/s00268-014-2889-0
Laparoscopic vs open repair for incisional hernia
Awaiz, Aiman, Rahman, Foyzur, Hossain, Md Belal, Yunus, Rossita Mohamad, Khan, Shahjahan, Memon, Breda and Memon, Muhammad Ashraf. 2014. "Laparoscopic vs open repair for incisional hernia." Ahmed, Munir (ed.) 13th Islamic Countries Conference on Statistical Sciences (ICCS 2013): Statistics for Better Life. Bogor, Indonesia 18 - 21 Dec 2014 Lahore, Pakistan.
Shrinkage estimation of elliptical regression model under balanced loss function
Arashi, M. and Khan, Shahjahan. 2012. "Shrinkage estimation of elliptical regression model under balanced loss function." Ahmad, Munir (ed.) 12th Islamic Countries Conference on Statistical Sciences (ICCS 2012): Statistics for Everyone and Everywhere. Doha, Qatar 19 - 22 Dec 2012 Lahore, Pakistan.
Linear model inference with non-sample prior information
Khan, Shahjahan, Pratikno, Budi and Yunus, Rossita M.. 2012. "Linear model inference with non-sample prior information." Ahmad, Munir (ed.) 12th Islamic Countries Conference on Statistical Sciences (ICCS 2012): Statistics for Everyone and Everywhere. Doha, Qatar 19 - 22 Dec 2012 Lahore, Pakistan.
Slope estimator for the linear error-in-variables model
Saqr, Anwar and Khan, Shahjahan. 2012. "Slope estimator for the linear error-in-variables model." Ahmad, Munir (ed.) 12th Islamic Countries Conference on Statistical Sciences (ICCS 2012): Statistics for Everyone and Everywhere. Doha, Qatar 19 - 22 Dec 2012 Lahore, Pakistan.
Weighted reduced major axis method for regression model
Saqr, Anwar and Khan, Shahjahan. 2012. "Weighted reduced major axis method for regression model." Ahmad, Munir (ed.) 12th Islamic Countries Conference on Statistical Sciences (ICCS 2012): Statistics for Everyone and Everywhere. Doha, Qatar 19 - 22 Dec 2012 Lahore, Pakistan.
Statistics in planning and development
Khan, Shahjahan. 2013. "Statistics in planning and development." Pakistan Journal of Statistics. 29 (4), pp. 513-524.
Shrinkage estimation under multivariate elliptic models
Arashi, M., Khan, Shahjahan, Tabatabaey, S. M. M. and Soleimani, H.. 2013. "Shrinkage estimation under multivariate elliptic models." Communications in Statistics: Theory and Methods. 42 (11), pp. 2084-2103. https://doi.org/10.1080/03610926.2011.602492
Bayesian prediction of matrix elliptical multivariate models with conjugate prior
Arashi, Mohamed and Khan, Shahjahan. 2012. "Bayesian prediction of matrix elliptical multivariate models with conjugate prior." Ahmed, Munir (ed.) 11th Islamic Countries Conference on Statistical Sciences (ICCSS 2011). Lahore, Pakistan 19 - 22 Dec 2011 Lahore, Pakistan.
Empirical link between economic growth, energy consumption and CO2 emission in Australia
Salahuddin, Mohammad and Khan, Shahjahan. 2013. "Empirical link between economic growth, energy consumption and CO2 emission in Australia." Journal of Developing Areas. 47 (2), pp. 81-92.
Reflection method of estimation for measurement error models
Saqr, Anwar and Khan, Shahjahan. 2012. "Reflection method of estimation for measurement error models." Journal of Applied Probability and Statistics. 7 (2), pp. 71-88.
Meta-analyses of lightweight versus conventional (heavy weight) mesh in inguinal hernia surgery
Memon, M. Ashraf, Khan, S. and Osland, E.. 2012. "Meta-analyses of lightweight versus conventional (heavy weight) mesh in inguinal hernia surgery." Hernia. 16 (5), pp. 497-502. https://doi.org/10.1007/s10029-012-0987-1
Testing base load with non-sample prior information on process load
Khan, Shahjahan and Pratikno, Budi. 2013. "Testing base load with non-sample prior information on process load." Statistical Papers. 54 (3), pp. 605-617. https://doi.org/10.1007/s00362-012-0451-4
Testing of intercept when slope is under suspicion
Pratikno, Budi and Khan, Shahjahan. 2012. "Testing of intercept when slope is under suspicion." Ahmad, Munir (ed.) 11th Islamic Countries Conference on Statistical Sciences (ICCSS 2011). Lahore, Pakistan 19 - 22 Dec 2011 Lahore, Pakistan.
Statistical meta-analysis for ordinal categorical data
Hossain, Md. Belal and Khan, Shahjahan. 2012. "Statistical meta-analysis for ordinal categorical data." Ahmed, Munir (ed.) 11th Islamic Countries Conference on Statistical Sciences (ICCSS 2011). Lahore, Pakistan 19 - 22 Dec 2011 Lahore, Pakistan.
Instrumental variable estimator of the slope parameter when the explanatory variable is subject to measurement error
Saqr, Anwar and Khan, Shahjahan. 2012. "Instrumental variable estimator of the slope parameter when the explanatory variable is subject to measurement error." Ahmed, Munir (ed.) 11th Islamic Countries Conference on Statistical Sciences (ICCSS 2011). Lahore, Pakistan 19 - 22 Dec 2011 Lahore, Pakistan.
Early versus traditional postoperative feeding in patients undergoing resectional gastrointestinal surgery: a meta-analysis
Osland, Emma, Yunus, Rossita Mohamad, Khan, Shahjahan and Memon, Muhammed Ashraf. 2011. "Early versus traditional postoperative feeding in patients undergoing resectional gastrointestinal surgery: a meta-analysis." Journal of Parenteral and Enteral Nutrition. 35 (4), pp. 473-487. https://doi.org/10.1177/0148607110385698
Meta-analysis of D1 versus D2 gastrectomy for gastric adenocarcinoma
Memon, Muhammed Ashraf, Subramanya, Manjunath S., Khan, Shahjahan, Hossain, Md. Belal, Osland, Emma and Memon, Breda. 2011. "Meta-analysis of D1 versus D2 gastrectomy for gastric adenocarcinoma." Annals of Surgery. 253 (5), pp. 900-911. https://doi.org/10.1097/SLA.0b013e318212bff6
The bivariate noncentral chi-square distribution – a compound distribution approach
Yunus, Rossita M. and Khan, Shahjahan. 2011. "The bivariate noncentral chi-square distribution – a compound distribution approach." Applied Mathematics and Computation. 217 (13), pp. 6237-6247. https://doi.org/10.1016/j.amc.2010.12.112
Early enteral nutrition within 24 h of intestinal surgery versus later commencement of feeding: a systematic review and meta-analysis [Letter to the Editor]
Osland, Emma, Yunus, Rossita M., Khan, Shahjahan and Memon, Muhammed Ashraf. 2009. "Early enteral nutrition within 24 h of intestinal surgery versus later commencement of feeding: a systematic review and meta-analysis [Letter to the Editor]." Journal of Gastrointestinal Surgery. 13 (6), pp. 1163-1165. https://doi.org/10.1007/s11605-009-0846-2
Prediction distribution of future regression and residual sum of squares matrices for multivariate simple regression model with correlated normal responses
Khan, Shahjahan. 2006. "Prediction distribution of future regression and residual sum of squares matrices for multivariate simple regression model with correlated normal responses." Journal of Applied Probability and Statistics. 1 (1), pp. 15-30.
Optimal tolerance regions for some functions of multiple regression model with Student-t errors
Khan, Shahjahan. 2006. "Optimal tolerance regions for some functions of multiple regression model with Student-t errors." Journal of Statistics and Management Systems. 9 (3), pp. 699-715.
Meta-analysis of laparoscopic posterior and anterior fundoplication for gastro-oesophageal reflux disease
Subramanya, M. S., Hossain, M. B., Khan, S., Memon, B. and Memon, M. A.. 2010. "Meta-analysis of laparoscopic posterior and anterior fundoplication for gastro-oesophageal reflux disease." Li, Yan, Yang, Jiajia, Wen, Peng and Wu, Jinglong (ed.) 2010 IEEE/ICME International Conference on Complex Medical Engineering (ICME 2010). Gold Coast, Australia 13 - 15 Jul 2010 Piscataway, NJ. United States. https://doi.org/10.1109/ICCME.2010.5558829
M-tests for multivariate regression model
Yunus, Rossita M. and Khan, Shahjahan. 2011. "M-tests for multivariate regression model." Journal of Nonparametric Statistics. 23 (1), pp. 201-218. https://doi.org/10.1080/10485252.2010.503896
Statistical inference
Khan, Shahjahan. 2010. "Statistical inference." Gaber, Mohamed Medhat (ed.) Scientific data mining and knowledge discovery: principles and foundations. Berlin, Germany. Springer. pp. 53-76
Bridging the divide by screencasting in an introductory statistics class at an Australian university
Khan, Shahjahan, Loch, Birgit and McDonald, Christine. 2010. "Bridging the divide by screencasting in an introductory statistics class at an Australian university." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Preliminary results of a meta-analysis evaluating the effect of immunonutrition on outcomes on outcomes of elective gastrointestinal surgery
Osland, Emma, Hossain, Md. Belal, Khan, Shahjahan and Memon, Muhammed A.. 2010. "Preliminary results of a meta-analysis evaluating the effect of immunonutrition on outcomes on outcomes of elective gastrointestinal surgery." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Benefits of early feeding versus traditional nil-by-mouth nutritional postoperative management in gastrointestinal resectional surgery patients: a meta-analysis
Osland, Emma, Yunus, Rossita Mohamad, Khan, Shahjahan and Memon, Muhammed A.. 2010. "Benefits of early feeding versus traditional nil-by-mouth nutritional postoperative management in gastrointestinal resectional surgery patients: a meta-analysis." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Preliminary results of meta-analysis of endoscopic retrograde cholangiopancreatography (ERCP) versus conservative treatment for gall stone pancreatitis
Burstow, Matthew J., Yunus, Rossita M., Khan, Shahjahan, Memon, Breda and Memon, Muhammed A.. 2010. "Preliminary results of meta-analysis of endoscopic retrograde cholangiopancreatography (ERCP) versus conservative treatment for gall stone pancreatitis." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
M-test of two parallel regression lines under uncertain prior information
Khan, Shahjahan and Yunus, Rossita M.. 2010. "M-test of two parallel regression lines under uncertain prior information." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Meta-analysis of laparoscopic posterior and anterior fundoplication for gastro-oesophageal reflux disease
Subramanya, Manjunath S., Hossain, Md. Belal, Khan, Shahjahan, Memon, Breda and Memon, Muhammed Ashraf. 2010. "Meta-analysis of laparoscopic posterior and anterior fundoplication for gastro-oesophageal reflux disease." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Meta-analysis of D1 versus D2 gastrectomy for gastric adenocarcinoma
Subramanya, Manjunath S., Hossain, Md. Belal, Khan, Shahjahan, Memon, Breda and Memon, Muhammed A.. 2010. "Meta-analysis of D1 versus D2 gastrectomy for gastric adenocarcinoma." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Preliminary results of meta-analysis of laparoscopic and open inguinal hernia repair
Burstow, Matthew John, Yunus, Rossita Mohamad, Khan, Shahjahan, Memon, Breda and Memon, Muhammed Ashraf. 2010. "Preliminary results of meta-analysis of laparoscopic and open inguinal hernia repair." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences (ICCSS-10): Statistics for Development and Good Governance. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Increasing the power of the test through pre-test: a robust method
Yunus, Rossita M. and Khan, Shahjahan. 2011. "Increasing the power of the test through pre-test: a robust method." Communications in Statistics: Theory and Methods. 40 (4), pp. 581-597. https://doi.org/10.1080/03610920903350572
M-test for intercept after pre-testing on slope
Yunus, Rossita M. and Khan, Shahjahan. 2010. "M-test for intercept after pre-testing on slope." Journal of Statistical Modeling and Analytics. 1 (1), pp. 45-57.
Increasing power of robust test through pre-testing in multiple regression model
Yunus, Rossita M. and Khan, Shahjahan. 2010. "Increasing power of robust test through pre-testing in multiple regression model." Pakistan Journal of Statistics. 26 (1), pp. 151-170.
Scientific and scholarly contributions of Distinguished Research and Emeritus Professor A K Md Ehsanes Saleh
Khan, Shahjahan. 2009. "Scientific and scholarly contributions of Distinguished Research and Emeritus Professor A K Md Ehsanes Saleh." International Journal of Statistical Sciences. 9, pp. 7-31.
Meta-analysis of randomised clinical trials comparing open and laparoscopic anti-reflux surgery
Peters, Matthew James, Mukhtar, Athar, Yunus, Rossita Mohamad, Khan, Shahjahan, Pappalardo, Juanita, Memon, Breda and Memon, Muhammed Ashraf. 2009. "Meta-analysis of randomised clinical trials comparing open and laparoscopic anti-reflux surgery." The American Journal of Gastroenterology. 104 (6), pp. 1548-1561. https://doi.org/10.1038/ajg.2009.176
Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors
Khan, Shahjahan. 2009. "Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors." Statistical Papers. 50 (3), pp. 511-525. https://doi.org/10.1007/s00362-007-0095-y
Prediction distribution of generalized geometric series distribution and its different forms
Hassan, Anwar and Khan, Shahjahan. 2009. "Prediction distribution of generalized geometric series distribution and its different forms." Pakistan Journal of Statistics. 25 (1), pp. 47-57.
Improved meta analysis using predicted relative risk
Khan, Shahjahan and Hasan, Md Masud. 2008. "Improved meta analysis using predicted relative risk." Chowdhury, Abdul Hannan, Khan, Shahjahan, Ahmed, Nasar U., Rahman, M. Saydur and Kibria, B. M. Golam (ed.) 2008 International Conference on Recent Development in Statistical Sciences. Dhaka, Bangladesh 26 - 27 Dec 2008 Dhaka, Bangladesh.
Estimation of slope for linear regression model with uncertain prior information and student-t error
Khan, Shahjahan and Saleh, A. K. Md. E.. 2008. "Estimation of slope for linear regression model with uncertain prior information and student-t error." Communications in Statistics: Theory and Methods. 37 (16), pp. 2564-2581. https://doi.org/10.1080/03610920802040399
Sine square distribution: a new statistical model based on the sine function
Al-Faris, Rand Q. and Khan, Shahjahan. 2008. "Sine square distribution: a new statistical model based on the sine function." Journal of Applied Probability and Statistics. 3 (1), pp. 163-173.
Meta-analysis of laparoscopic and open distal gastrectomy for gastric carcinoma
Memon, Muhammed Ashraf, Khan, Shahjahan, Yunus, Rossita Mohamad, Barr, Richard and Memon, Breda. 2008. "Meta-analysis of laparoscopic and open distal gastrectomy for gastric carcinoma." Surgical Endoscopy. 22 (8), pp. 1781-1789. https://doi.org/10.1007/s00464-008-9925-9
Estimation in multiple regression model with elliptically contoured errors under MLINEX loss
Arashi, M., Tabatabaey, S. M. M. and Khan, Shahjahan. 2008. "Estimation in multiple regression model with elliptically contoured errors under MLINEX loss." Journal of Applied Probability and Statistics. 3 (1), pp. 23-35.
Prediction distribution for linear regression model with multivariate student-t errors
Rahman, Azizur and Khan, Shahjahan. 2008. "Prediction distribution for linear regression model with multivariate student-t errors." Far East Journal of Theoretical Statistics. 24 (1), pp. 35-48.
Estimation of univariate normal mean using p-value
Kabir, Md Enamul and Khan, Shahjahan. 2007. "Estimation of univariate normal mean using p-value." 9th Islamic Countries Conference on Statistical Sciences (ICCS-IX): Statistics in the Contemporary World - Theories, Methods and Applications. Shah Alam, Malaysia 12 - 14 Dec 2007 Kuala Lumpur, Malaysia.
Test for intercept after pre-testing on slope - a robust method
Yunus, Rossita M. and Khan, Shahjahan. 2007. "Test for intercept after pre-testing on slope - a robust method." Ahmad, Munir, Mohamed, Ibrahim, Osman, Jamil and Ibrahim, Noor Akma (ed.) 9th Islamic Countries Conference on Statistical Sciences (ICCS-IX): Statistics in the Contemporary World - Theories, Methods and Applications. Shah Alam, Malaysia 12 - 14 Dec 2007 Kuala Lumpur, Malaysia.
Observed data based estimator and both observed data and prior information based estimator under asymmetric losses
Hoque, Zahirul, Wesolowski, Jacek and Khan, Shahjahan. 2007. "Observed data based estimator and both observed data and prior information based estimator under asymmetric losses." American Journal of Mathematical and Management Sciences. 27 (1-2), pp. 93-110. https://doi.org/10.1080/01966324.2007.10737690
Shrinkage estimators of intercept parameters of two simple regression models with suspected equal slopes
Khan, Shahjahan. 2008. "Shrinkage estimators of intercept parameters of two simple regression models with suspected equal slopes." Communications in Statistics: Theory and Methods. 37 (2), pp. 247-260. https://doi.org/10.1080/03610920701648961
Preliminary test estimators for the multivariate normal mean based on the modified W, LR and LM tests
Khan, S. and Hoque, Z.. 2003. "Preliminary test estimators for the multivariate normal mean based on the modified W, LR and LM tests." Journal of Statistical Research. 37 (1), pp. 43-55.
Comparison of estimators of means based on p-samples from multivariate Student-t population
Khan, Shahjahan and Saleh, A. K. Md. Ehsanes. 1998. "Comparison of estimators of means based on p-samples from multivariate Student-t population." Communications in Statistics: Theory and Methods. 27 (1), pp. 193-210. https://doi.org/10.1080/03610929808832660
Prediction distribution for linear regression model with multivariate Student-t errors under the Bayesian approach
Rahman, Azizur and Khan, Shahjahan. 2007. "Prediction distribution for linear regression model with multivariate Student-t errors under the Bayesian approach." Ismail, Fudziah, Tarmizi, Rohani, Midi, Habsha, Said, Mohamad and Abbas, Zulkifly (ed.) 3rd International Conference on Research and Education in Mathematics (ICREM3). Kuala Lumpur, Malaysia 10 - 12 Apr 2007 Kuala Lumpur, Malaysia.
Shrinkage estimation of the slope parameters of two parallel regression lines under uncertain prior information
Khan, Shahjahan. 2006. "Shrinkage estimation of the slope parameters of two parallel regression lines under uncertain prior information." Model Assisted Statistics and Applications: an international journal. 1 (3), pp. 193-205.
On the Size Corrected Tests in Improved Estimation
Hoque, Zahirul, Billah, Baki and Khan, Shahjahan. 2005. "On the Size Corrected Tests in Improved Estimation." Calcutta Statistical Association Bulletin. 57 (3-4), pp. 143-160. https://doi.org/10.1177/0008068320050301
Estimation of the parameters of two parallel regression lines under uncertain prior information
Khan, Shahjahan. 2003. "Estimation of the parameters of two parallel regression lines under uncertain prior information." Biometrical Journal: journal of mathematical methods in biosciences. 45 (1), pp. 73-90. https://doi.org/10.1002/bimj.200290017
Estimation of the slope parameter for linear regression model with uncertain prior information
Khan, Shahjahan, Hoque, Zahirul and Saleh, A. K. Md. Ehsanes. 2002. "Estimation of the slope parameter for linear regression model with uncertain prior information." Journal of Statistical Research. 36, pp. 55- 73.
The role of the shape parameter in the estimation of the mean vector in multivariate Student-t population
Khan, Shahjahan. 2004. "The role of the shape parameter in the estimation of the mean vector in multivariate Student-t population." International Journal of Statistical Sciences. 3 (Special issue), pp. 69-89.
Estimation of parameters of the simple multivariate linear model with student-t errors
Khan, Shahjahan. 2005. "Estimation of parameters of the simple multivariate linear model with student-t errors." Journal of Statistical Research. 39 (2), pp. 79-94.
Improved estimation of the mean vector for Student-t model.
Khan, Shahjahan. 2000. "Improved estimation of the mean vector for Student-t model." Communications in Statistics: Theory and Methods. 29 (3), pp. 507-527.
Distribution of sum of squares and products matrices for the generalized multilinear matrix-T model
Khan, Shahjahan. 2002. "Distribution of sum of squares and products matrices for the generalized multilinear matrix-T model." Journal of Multivariate Analysis. 83, pp. 124-140. https://doi.org/10.1006/jmva.2001.2040
Distribution of future location vector and residual sum of squares for multivariate location-scale model with spherically contoured errors
Khan, Shahjahan and Kabir, Md Enamul. 2006. "Distribution of future location vector and residual sum of squares for multivariate location-scale model with spherically contoured errors." Journal of Statistical Theory and Applications. 5 (2), pp. 91-104.
Predictive distribution of regression vector and residual sum of squares for normal multiple regression model
Khan, Shahjahan. 2004. "Predictive distribution of regression vector and residual sum of squares for normal multiple regression model." Communications in Statistics: Theory and Methods. 33 (10), pp. 2423-2443. https://doi.org/10.1081/STA-200031471
Estimation of the intercept parameter for linear regression model with uncertain non-sample prior information
Khan, Shahjahan, Hoque, Zahirul and Saleh, A. K. Md. E.. 2005. "Estimation of the intercept parameter for linear regression model with uncertain non-sample prior information." Statistical Papers. 46 (3), pp. 379-395.