A Link-Free Regression Method
Regression analysis is one of the most useful tools in statistical analysis. Usually, regression analysis requires specifying the link function for the model. The popular link functions used widely include the linear link function, the logistic link function, and the probit link function. However, in many applications, the functional form and the link function might not be known precisely. Therefore, the usual regression analysis based on a specific link function might not perform well. In this paper, the authors propose a new regression method, the slicing regression, which does not require specifying the link function in advance. The method is based on the inverse regression: the authors regress the predictor variables on the outcome variable, then relate the inverse regression result to the forward regression model that they are actually interested in. The slicing regression is shown to have desirable statistical properties, including consistency and asymptotic normality. The theory is illustrated with a simulation study.