Order-Restricted Inferences in Linear Regression
本文研究了在回归函数随预测变量单调变化这一先验知识下，如何进行统计推断，并以单变量简单线性回归为例，讨论了参数估计的直观性及现有知识的不足。
Abstract Regression analysis constitutes a large portion of the statistical repertoire in applications. In cases where such analysis is used for exploratory purposes with no previous knowledge of the structure, one would not wish to impose any constraints on the problem. But in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure. An important example of this occurs when the experimenter has a strong belief that the regression function changes monotonically with some or all of the predictor variables in a region of interest. The analyses needed for statistical inferences under such constraints are nonstandard. Considering the present body of knowledge developed for unconstrained regression, it will be an enormous task to derive the analogs of even a small fraction of this for the restricted case. In this article we initiate the study with simple linear regression on a single variable. The estimators of the regression parameters may be intuitively obvious in this case, but, as discussed, very little else is.