Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
227
views
0
downloads
Cite This
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
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.