Multiple linear regression model under nonnormality

Date

2004-10-01

Author

İslam, Muhammed Qamarul

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

57
views

0
downloads

We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.

Subject Keywords

Statistics and Probability

URI

https://hdl.handle.net/11511/38500

Journal

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

DOI

https://doi.org/10.1081/sta-200031519

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Minimum variance quadratic unbiased estimation for the variance components in simple linear regression with onefold nested error Gueven, Ilgehan (Informa UK Limited, 2006-01-01) The explicit forms of the minimum variance quadratic unbiased estimators (MIVQUEs) of the variance components are given for simple linear regression with onefold nested error. The resulting estimators are more efficient as the ratio of the initial variance components estimates increases and are asymptotically efficient as the ratio tends to infinity.
The limiting distribution of the F-statistic from nonnormal universes Gueven, Bilgehan (Informa UK Limited, 2006-12-01) We consider a linear regression model with an unbalanced 1-fold nested error structure, where group effect and error are from nonnormal universes. The limiting distribution of the F-statistic in this model is derived, as the sample size is large and group sizes take values from a finite set of distinct integers. The result is used to approximate the F-distribution quantile and to test the significance of the random effect variance component. Results are also applicable to the F-statistic in the one-way rand...
Estimation and hypothesis testing in multivariate linear regression models under non normality İslam, Muhammed Qamarul (Informa UK Limited, 2017-01-01) This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariate t-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modifie...
Regression analysis with a dtochastic design variable Sazak, HS; Tiku, ML; İslam, Muhammed Qamarul (Wiley, 2006-04-01) In regression models, the design variable has primarily been treated as a nonstochastic variable. In numerous situations, however, the design variable is stochastic. The estimation and hypothesis testing problems in such situations are considered. Real life examples are given.
Multiple linear regression model with stochastic design variables İslam, Muhammed Qamarul (Informa UK Limited, 2010-01-01) In a simple multiple linear regression model, the design variables have traditionally been assumed to be non-stochastic. In numerous real-life situations, however, they are stochastic and non-normal. Estimators of parameters applicable to such situations are developed. It is shown that these estimators are efficient and robust. A real-life example is given.

Citation Formats

M. Q. İslam, “Multiple linear regression model under nonnormality,” COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, pp. 2443–2467, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38500.