Improved estimation for linear models under different loss functions

PhD Thesis


Hoque, Zahirul. 2004. Improved estimation for linear models under different loss functions. PhD Thesis Doctor of Philosophy. University of Southern Queensland.
Title

Improved estimation for linear models under different loss functions

TypePhD Thesis
Authors
AuthorHoque, Zahirul
SupervisorKhan, Shahjahan
Institution of OriginUniversity of Southern Queensland
Qualification NameDoctor of Philosophy
Number of Pages187
Year2004
Abstract

This thesis investigates improved estimators of the parameters of the linear regression models with normal errors, under sample and non-sample prior information about the value of the parameters. The estimators considered are the unrestricted estimator (UE), restricted estimator (RE), shrinkage restricted estimator (SRE), preliminary test estimator (PTE), shrinkage preliminary test estimator (SPTE), and shrinkage estimator (SE). The performances of the estimators are investigated with respect to bias, squared error and linex loss. For the analyses of the risk functions of the estimators, analytical, graphical and numerical procedures are adopted. In Part I the SRE, SPTE and SE of the slope and intercept parameters of the simple linear regression model are considered. The performances of the estimators are investigated with respect to their biases and mean square errors. The efficiencies of the SRE, SPTE and SE relative to the UE are obtained. It is revealed that under certain conditions, SE outperforms the other estimators considered in this thesis. In Part II in addition to the likelihood ratio (LR) test, the Wald (W) and Lagrange multiplier (LM) tests are used to define the SPTE and SE of the parameter vector of the multiple linear regression model with normal errors. Moreover, the modified and size-corrected W, LR and LM tests are used in the definition of SPTE. It is revealed that a great deal of conflict exists among the quadratic biases (QB) and quadratic risks (QR) of the SPTEs under the three original tests. The use of the modified tests reduces the conflict among the QRs, but not among the QBs. However, the use of the size-corrected tests in the definition of the SPTE almost eliminates the conflict among both QBs and QRs. It is also revealed that there is a great deal of conflict among the performances of the SEs when the three original tests are used as the preliminary test statistics. With respect to quadratic bias, the W test statistic based SE outperforms that based on the LR and LM test statistics. However, with respect to the QR criterion, the LM test statistic based SE outperforms the W and LM test statistics based SEs, under certain conditions. In Part III the performance of the PTE of the slope parameter of the simple linear regression model is investigated under the linex loss function. This is motivated by increasing criticism of the squared error loss function for its inappropriateness in many real life situations where underestimation of a parameter is more serious than its overestimation or vice-versa. It is revealed that under the linex loss function the PTE outperforms the UE if the nonsample prior information about the value of the parameter is not too far from its true value. Like the linex loss function, the risk function of the PTE is also asymmetric. However, if the magnitude of the scale parameter of the linex loss is very small, the risk of the PTE is nearly symmetric.

Keywordslinear model, unrestricted estimator (UE), restricted estimator (RE), shrinkage restricted estimator (SRE), preliminary test estimator (PTE), shrinkage preliminary test estimator (SPTE), and shrinkage estimator (SE)
ANZSRC Field of Research 2020490501. Applied statistics
Permalink -

https://research.usq.edu.au/item/9xxwv/improved-estimation-for-linear-models-under-different-loss-functions

Download files


Published Version
Hoque_2004_whole.pdf
File access level: Anyone

  • 2289
    total views
  • 457
    total downloads
  • 2
    views this month
  • 0
    downloads this month

Export as

Related outputs

The effect of laparoscopic vertical sleeve gastrectomy and laparoscopic roux-en-Y gastric bypass on gastroesophageal reflux disease: An updated meta-analysis and systematic review of 5-year post-operative data from randomized controlled trials.
Memon, Muhammed Ashraf, Osland, Emma, Yunus, Rossita Mohamad, Hoque, Zahirul, Alam, Khorshed and Khan, Shahjahan. 2024. "The effect of laparoscopic vertical sleeve gastrectomy and laparoscopic roux-en-Y gastric bypass on gastroesophageal reflux disease: An updated meta-analysis and systematic review of 5-year post-operative data from randomized controlled trials." Surgical Endoscopy: surgical and interventional techniques. https://doi.org/10.1007/s00464-024-11303-x
Gastroesophageal reflux disease following laparoscopic vertical sleeve gastrectomy and laparoscopic roux-en-Y gastric bypass: meta-analysis and systematic review of 5-year data
Memon, Muhammed A, Osland, Emma, Yunus, Rossita M, Alam, Khorshed, Hoque, Zahirul and Khan, Shahjahan. 2024. "Gastroesophageal reflux disease following laparoscopic vertical sleeve gastrectomy and laparoscopic roux-en-Y gastric bypass: meta-analysis and systematic review of 5-year data." Diseases of the Esophagus. 37 (3), pp. 593-617. https://doi.org/10.1093/dote/doad063
Modelling the Association between Vitamin D Deficiency and Incidence of Covid-19 Infection Adjusting for the Confounders and Unobserved Heterogeneity
Hoque, Zahirul, Hossain, Shahadut, Hasan, Masud, Hoque, Irfanul and Haque, Afrozul. 2023. "Modelling the Association between Vitamin D Deficiency and Incidence of Covid-19 Infection Adjusting for the Confounders and Unobserved Heterogeneity." Journal of Applied Probability and Statistics. 18 (1), pp. 19-33.
Differences in levels of E. coli contamination of point of use drinking water in Bangladesh
Hasan, Md. Masud, Hoque, Zahirul, Kabir, Enamul and Hossain, Shahadut. 2022. "Differences in levels of E. coli contamination of point of use drinking water in Bangladesh." PLoS One. 17 (5), pp. 1-12. https://doi.org/10.1371/journal.pone.0267386
Response-based multiple imputation method for minimizing the impact of covariate detection limit in logistic regression
Hossain, Shahadut, Hoque, Zahirul and Wesolowski, Jacek. 2021. "Response-based multiple imputation method for minimizing the impact of covariate detection limit in logistic regression." Communications in Statistics: Theory and Methods. 50 (2), pp. 371-386. https://doi.org/10.1080/03610926.2019.1635699
Preliminary Test Methodology in View of Asymmetry with Elliptically Contoured Distribution
Arashi, M. and Hoque, Z.. 2020. "Preliminary Test Methodology in View of Asymmetry with Elliptically Contoured Distribution." Journal of Applied Probability and Statistics. 15 (1), pp. 101-112.
Shrinkage Estimator of Regression Model Under Asymmetric Loss
Hoque, Zahirul, Wesolowski, Jacek and Hossain, Shahadut. 2018. "Shrinkage Estimator of Regression Model Under Asymmetric Loss." Communications in Statistics: Theory and Methods. 47 (22), pp. 5547-5557. https://doi.org/10.1080/03610926.2017.1397169
Performance of preliminary test estimator under linex loss function
Hoque, Zahirul, Khan, Shahjahan and Wesolowski, Jacek. 2009. "Performance of preliminary test estimator under linex loss function." Communications in Statistics: Theory and Methods. 38 (2), pp. 252-261. https://doi.org/10.1080/03610920802192471
James-Stein estimators for the mean vector of a multivariate normal population based on independent samples from two normal populations with common covariance structure
Khan, Shahjahan and Hoque, Zahirul. 2002. "James-Stein estimators for the mean vector of a multivariate normal population based on independent samples from two normal populations with common covariance structure." Pakistan Journal of Statistics. 18 (3), pp. 359-381.
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.
A better alternative to non-parametric approaches for adjusting for covariate measurement errors in logistic regression.
Hossain, Shahadut, Hoque, Zahirul and Hasan, A. H. M. Saidul. 2016. "A better alternative to non-parametric approaches for adjusting for covariate measurement errors in logistic regression." Communications in Statistics: Simulation and Computation. 45 (8), pp. 2659-2677. https://doi.org/10.1080/03610918.2014.917675
Education and Health for Human Security in MMCs: Achievements and the Third Sector Interventions
Hossain, Shahadut and Hoque, Zahirul. 2015. "Education and Health for Human Security in MMCs: Achievements and the Third Sector Interventions ." Hasan, Samiul (ed.) Human Security and Philanthropy: Islamic Perspectives and Muslim Majority Country Practices. United States. Springer. pp. 263-288
Improved Estimation in regression with Varying Penalty
Hoque, Zahirul and Hossain, Shahadut. 2012. "Improved Estimation in regression with Varying Penalty." Journal of Statistical Theory and Practice. 6, pp. 260-273. https://doi.org/10.1080/15598608.2012.673878
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
Edgeworth size corrected W, LR and LM test in the formation of the preliminary test estimator
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.
On the Size Corrected Tests in Improved Estimation
Hoque, Z., Billah, B. and Khan, S.. 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 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. https://doi.org/10.1007/bf02762840
Improved Estimation in Linear Dynamic Regression Model
Hoque, Zahirul and Gerlach, Richard. 2005. "Improved Estimation in Linear Dynamic Regression Model." Journal of Applied Statistical Science. 17 (2), pp. 309-314.
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.