PARAMETERS ESTIMATION AND HYPOTHESIS TESTING OF CUBIC SEMIPARAMETRIC RECURSIVE BIVARIATE PROBIT REGRESSION MODEL
Abdullah Fahmi (a), Purhadi (b), Jerry Dwi Trijoyo Purnomo (c)

(a) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
(b) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
purhadi[at]statistika.its.ac.id
(c) Department of Statistics, Institut Teknologi Sepuluh Nopember (ITS), Sukolilo, 60111, Indonesia
jerrypurnomo[at]gmail.com

Abstract

The cubic semiparametric recursive bivariate probit regression model is a model that describes the relationship between two response variables in the form of binary categorical data with one or more predictor variables in the form of categorical data and continuous data by considering the endogeneity problem. This endogeneity problem is a model case where endogenous variables can become exogenous variables. A cubic semiparametric recursive bivariate probit regression model to overcome the problem of inconsistent and biased parameter estimates. This study aims to estimate parameters using the Penalized Likelihood Estimation and to test the hypothesis using the likelihood ratio test, which is a simultaneous and partial significance test. Because the log function for the first possible derivative is not in a close form, it uses a numerical iteration method, namely fisher scoring iterations until it convergence.

Keywords: Cubic Semiparametric Recursive Bivariate Probit, Penalized Likelihood Estimation, Fisher Scoring

Topic: Mathematics and Statistics