Minimax Linear Predictor under Lipschitz' Type Conditions for the Regression Function

摘要

Regression analysis is one of the most popular and most often used techniques in various fields of statistical data analysis. In some cases, however, regression analysis is very dangerous, and sometimes gives awkward results. Such dangers, which are inherent in regression techniques, are well known, at least well perceived by experienced applied statisticians. But theoretical analysis of such a situation that yields some pitfalls to the careless application of regression analysis is far from satisfactory. Though well trained statisticians can evade such a danger by their good judgment, there is no formal well established technique that may be applied. The purpose of this paper is to derive some method to treat one such difficulty, i.e. the problem of the functional form of the regression.