Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Economic Research Unit (ERU-Kolkata)


Mukherjee, Robin (ERU-Kolkata; ISI)

Abstract (Summary of the Work)

This thesis attempta to cansider and provids solutions to viat nay be broadly decribed na Bone problems of speciification and satatistical inforence in single equation lineur regression models. It co sists of three parte, each having several chepters. The firat part in devoted to sme problems connec ted vith the use of the wall-imown Bor-Cox (BC) tranaformation of variablee in single equetion ragreanion nodels. In the other two parts we exanine an autocorrelated linear regreasion nodel from a rather unconventional angle. Precisely, we consider the problema which arise when the error tem in an autocorre lated linear regression nodel is viewed as doconponed into two additive camponanta, one of which may arise due to nisspecification while the other nay be the true disturbance. The second part deals with the analysis of much situstions in large sanples and the third part die cusses the ronul ta of a Monte Carlo experiment comparing the performances of different catinatora in small samples. There are four chapters in the first part of viich the first Chapter is devoted to oritioaiAy revieving the literature on the Box-Cox tranaformation. Box and Cox (1964) proposed a fanly of power tran formations of the dependunt veriable (y) in a regrassion nodel defined as ii A 0 In y if A-0. They ansumed that there exiats a A for which the tranaformed dependant variable i.e.,(x)willl be a linear function of the regressors (or similarly of the tranafomed regressors) and that the disturbance tem in the tranafomed lincar regression will be honosoedastio and nomal. They algo suegested naxinun 1Likelihood (ML) mothod of astination for much transfomed 1inear regression nodels. Subsequently, a mnber of studiee have been nade in order to exanine the robustiess of the MI proc edure suggested by Box and Cox and/ar generalising the 30 tranafomation by ino crporating the problems of heteroscedasticity, sutoaorrelation and nonnomality. There are al80 same studies on the use of the BC transforne- tion in simultanecus equatione yatams and in applied econometric work. Our review gives an account of these studies and notes their important linitations,partioularly those which are relevant to our reacaroh. We have also indicated the ralationahip betveen the BC tranefomation vith truncated nomnlity of the disturbano es and Tobin'a limited dependent variable aodel in this chapter. In Chapter 2, tve conaider the problem of heteroacedaaticity in the coutext ui the lox-Cox tranefomation. It has beon shown by Zarmbka (1974) that the ML mothod of estin tion guggestud by Box and Cox is not robust to heterogcedasticity. This led Zarambka (1974), later Eey and Lahiri (1970) and Lahiri and Egy (1991) to try to incorpo- rate heterogo edaetioity in the BC model. For this purpose Zarenbica assumed.


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