Sampling Performance of Some Joint One-Sided Preliminary Test Estimators under Squared Error Loss

Abstract

IN MANY AREAS OF SCIENCE, when drawing conclusions concerning a set of phenomena, individual or linear combinations of parameters are assumed to be nonnegative, nonpositive, or to lie between upper and lower bounds. Likewise, many functions are assumed to be monotonic, convex, or quasiconvex. Consequently, questions naturally arise as to the correctness of the assumptions and, within the context of statistical inference, how to evaluate the evidence against these assumptions and to use the data at hand to seek the appropriate statistical model and the corresponding method of estimation. Within the context of the general linear statistical model, multivariate analogues of one-sided (inequality hypotheses) tests have been explored by Bartholomew (1959), Kudo (1963), Osterhoff (1969), Barlow, et al. (1972), Yancey, Judge, and Bock (1981), Yancey, Bohrer, and Judge (1982), Gourieroux, Holly, and Montfort (GHM) (1982), Judge and Yancey (1986), Wolak (1987) and Shapiro (1988). In general, the likelihood ratio framework has been used in developing a test statistic and determining acceptance and rejection regions. In order to facilitate the interpretation of these test results in econometric practice, in this paper we evaluate, under a squared error loss (SEL) measure, the risk characteristics of the preliminary test (PT) estimators that evolve when, based on the data at hand, an estimation decision is taken as a result of the outcomes of two one-sided multivariate hypothesis tests.