Nonnormal regression. I. Skew distributions

Date

2001-01-01

Author

İslam, Muhammed Qamarul
Yildirim, F

Metadata

Show full item record

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

Item Usage Stats

174
views

0
downloads

In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we derive modified likelihood estimators which have explicit algebraic forms and are, therefore, easy to compute. We show that these estimators are remarkably efficient, and robust. We develop hypothesis testing procedures and give a real life example.

Subject Keywords

Robustness, Maximum Likelihood;, Modified Maximum Likelihood, Least Squares, Weibull, Generalised Logistic

URI

https://hdl.handle.net/11511/48452

Journal

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

DOI

https://doi.org/10.1081/sta-100104347

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Statistical inference from complete and incomplete data Can Mutan, Oya; Tiku, Moti Lal; Department of Statistics (2010) Let X and Y be two random variables such that Y depends on X=x. This is a very common situation in many real life applications. The problem is to estimate the location and scale parameters in the marginal distributions of X and Y and the conditional distribution of Y given X=x. We are also interested in estimating the regression coefficient and the correlation coefficient. We have a cost constraint for observing X=x, the larger x is the more expensive it becomes. The allowable sample size n is governed by a...
Non-normal bivariate distributions: estimation and hypothesis testing Qunsiyeh, Sahar Botros; Tiku, Moti Lal; Department of Statistics (2007) When using data for estimating the parameters in a bivariate distribution, the tradition is to assume that data comes from a bivariate normal distribution. If the distribution is not bivariate normal, which often is the case, the maximum likelihood (ML) estimators are intractable and the least square (LS) estimators are inefficient. Here, we consider two independent sets of bivariate data which come from non-normal populations. We consider two distinctive distributions: the marginal and the conditional dist...
Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations Akkaya, Ayşen (2001-01-01) The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] who give solutions for a simple AR(I) model
Inference of Autoregressive Model with Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions Bayrak, Ozlem Tuker; Akkaya, Ayşen (2018-12-01) In classical autoregressive models, it is assumed that the disturbances are normally distributed and the exogenous variable is non-stochastic. However, in practice, short-tailed symmetric disturbances occur frequently and exogenous variable is actually stochastic. In this paper, estimation of the parameters in autoregressive models with stochastic exogenous variable and non-normal disturbances both having short-tailed symmetric distribution is considered. This is the first study in this area as known to the...
Robust estimation in multiple linear regression model with non-Gaussian noise Akkaya, Ayşen (2008-02-01) The traditional least squares estimators used in multiple linear regression model are very sensitive to design anomalies. To rectify the situation we propose a reparametrization of the model. We derive modified maximum likelihood estimators and show that they are robust and considerably more efficient than the least squares estimators besides being insensitive to moderate design anomalies.

Citation Formats

M. Q. İslam and F. Yildirim, “Nonnormal regression. I. Skew distributions,” COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, pp. 993–1020, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48452.