Estimation and hypothesis testing in stochastic regression

Sazak, Hakan Savaş
Regression analysis is very popular among researchers in various fields but almost all the researchers use the classical methods which assume that X is nonstochastic and the error is normally distributed. However, in real life problems, X is generally stochastic and error can be nonnormal. Maximum likelihood (ML) estimation technique which is known to have optimal features, is very problematic in situations when the distribution of X (marginal part) or error (conditional part) is nonnormal. Modified maximum likelihood (MML) technique which is asymptotically giving the estimators equivalent to the ML estimators, gives us the opportunity to conduct the estimation and the hypothesis testing procedures under nonnormal marginal and conditional distributions. In this study we show that MML estimators are highly efficient and robust. Moreover, the test statistics based on the MML estimators are much more powerful and robust compared to the test statistics based on least squares (LS) estimators which are mostly used in literature. Theoretically, MML estimators are asymptotically minimum variance bound (MVB) estimators but simulation results show that they are highly efficient even for small sample sizes. In this thesis, Weibull and Generalized Logistic distributions are used for illustration and the results given are based on these distributions. As a future study, MML technique can be utilized for other types of distributions and the procedures based on bivariate data can be extended to multivariate data.


Inference in multivariate linear regression models with elliptically distributed errors
İslam, Muhammed Qamarul; Yazici, Mehmet (2014-08-01)
In this study we investigate the problem of estimation and testing of hypotheses in multivariate linear regression models when the errors involved are assumed to be non-normally distributed. We consider the class of heavy-tailed distributions for this purpose. Although our method is applicable for any distribution in this class, we take the multivariate t-distribution for illustration. This distribution has applications in many fields of applied research such as Economics, Business, and Finance. For estimat...
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...
Basis in nuclear Frechet spaces
Erkurşun, Nazife; Nurlu, Mehmet Zafer; Department of Mathematics (2006)
Existence of basis in locally convex space has been an important problem in functional analysis for more than 40 years. In this thesis the conditions for the existence of basis are examined. These thesis consist of three parts. The first part is about the exterior interpolative conditions. The second part deals with the inner interpolative conditions on nuclear frechet space. These are sufficient conditions on existence of basis. In the last part, it is shown that for a regular nuclear Köthe space the inner...
Binary regression with stochastic covariates
Oral, E. (2006-01-01)
In binary regression the risk factor X has been treated in the literature as a non-stochastic variable. In most situations, however, X is stochastic. We present solutions applicable to such situations. We show that our solutions are more precise than those obtained by treating X as non-stochastic when, in fact, it is stochastic.
Stochastic optimal control theory: new applications to finance and insurance
Akdoğan, Emre; Yolcu Okur, Yeliz; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2017)
In this study, the literature, recent developments and new achievements in stochastic optimal control theory are studied. Stochastic optimal control theory is an important direction of mathematical optimization for deriving control policies subject to timedependent processes whose dynamics follow stochastic differential equations. In this study, this methodology is used to deal with those infinite-dimensional optimization programs for problems from finance and insurance that are indeed motivated by the real l...
Citation Formats
H. S. Sazak, “Estimation and hypothesis testing in stochastic regression,” Ph.D. - Doctoral Program, Middle East Technical University, 2003.