Probability and Statistics seminar
Wednesday, 24 January, 3.00-4.00 pm
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Venue: Ramanujan Hall
Speaker: Hira Koul
Affiliation: Professor, Department of Statistics and Probability, Michigan State University
Distinguished Visiting Professor, Department of Mathematics, IIT Bombay
Title: A signed-rank estimator in nonlinear regression models when covariates and errors are dependent
Abstract: This talk will describe the asymptotic uniform linearity of a signed rank statistic of the residuals in a class of nonlinear parametric regression models when regression errors are possibly dependent on the covariates. This result is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent. The latter result in turn is used to derive the asymptotic distribution of this signed rank estimator in the errors in variables linear regression model. The asymptotic relative efficiency of this SR estimator relative to the bias-corrected least squares estimator is shown to increase to infinity, as the measurement error variance increases to infinity, thereby establishing another robustness property of this estimator.