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Analysis of censored data under heteroscedastic transformation regression models with unknown transformation function
Author(s) -
Wang Qihua,
Wang Xuan
Publication year - 2018
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11347
Subject(s) - heteroscedasticity , mathematics , estimator , transformation (genetics) , variance function , statistics , censored regression model , data transformation , regression analysis , function (biology) , asymptotic distribution , computer science , biochemistry , chemistry , database , evolutionary biology , biology , data warehouse , gene
Consider a censored heteroscedastic transformation regression model where both the transformation function and the error distribution function are completely unknown. A method is developed to estimate the transformation function, the regression parameter vector, and the single index parameter vector of the variance function by establishing an expression for the transformation function and two estimating equations for both the parameter vectors. It is shown that the estimator of the transformation function converges weakly to a mean zero Gaussian process, and the parametric estimators are asymptotically normal. All the estimators converge to their true values in probability at a rate proportional to n − 1 / 2 . Simulation studies are conducted to evaluate the finite sample behaviour of the proposed estimators, and a real data analysis is used to illustrate the proposed estimating method. The Canadian Journal of Statistics 46: 233–245; 2018 © 2017 Statistical Society of Canada