Estimation and hypothesis testing in multivariate linear regression models under non normality

Date

2017-01-01

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

77
views

0
downloads

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 modified maximum likelihood estimation method that provides the estimator, called modified maximum likelihood estimator (MMLE), in closed form. These estimators are shown to be unbiased, efficient, and robust as compared to the widely used least square estimators (LSEs). Also, the tests based upon MMLEs are found to be more powerful than the similar tests based upon LSEs.

Subject Keywords

Statistics and Probability

URI

https://hdl.handle.net/11511/44081

Journal

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

DOI

https://doi.org/10.1080/03610926.2016.1183789

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

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.
Representation of Multiplicative Seasonal Vector Autoregressive Moving Average Models Yozgatlıgil, Ceylan (Informa UK Limited, 2009-11-01) Time series often contain observations of several variables and multivariate time series models are used to represent the relationship between these variables. There are many studies on vector autoregressive moving average (VARMA) models, but the representation of multiplicative seasonal VARMA models has not been seriously studied. In a multiplicative vector model, such as a seasonal VARMA model, the representation is not unique because of the noncommutative property of matrix multiplication. In this articl...
Estimation in the simple linear regression model with one-fold nested error Ülgen, Burçin Emre; Güven, Bilgehan; Department of Statistics (2005) In this thesis, estimation in simple linear regression model with one-fold nested error is studied. To estimate the fixed effect parameters, generalized least squares and maximum likelihood estimation procedures are reviewed. Moreover, Minimum Norm Quadratic Estimator (MINQE), Almost Unbiased Estimator (AUE) and Restricted Maximum Likelihood Estimator (REML) of variance of primary units are derived. Also, confidence intervals for the fixed effect parameters and the variance components are studied. Finally, ...
Marginalized transition random effect models for multivariate longitudinal binary data İlk Dağ, Özlem (Wiley, 2007-03-01) Generalized linear models with random effects and/or serial dependence are commonly used to analyze longitudinal data. However, the computation and interpretation of marginal covariate effects can be difficult. This led Heagerty (1999, 2002) to propose models for longitudinal binary data in which a logistic regression is first used to explain the average marginal response. The model is then completed by introducing a conditional regression that allows for the longitudinal, within-subject, dependence, either...

Citation Formats

M. Q. İslam, “Estimation and hypothesis testing in multivariate linear regression models under non normality,” COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, pp. 8521–8543, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44081.