方差未知的不等式约束回归

许多实际问题中经常会遇到带约束条件的回归问题．方差已知时这种问题的估计量的性质已有很多研究．但在许多实际问题中随机误差的方差可能是未知的．本文给出未知方差的估计量和它的性质，提出方差估计量和参数估计量之间条件独立的概念．有了这些性质，就可以定义t统计量和F统计量，它们是方差未知时做统计推断所必须的．然后说明如何利用这些结果来构造回归参数的置信区间．这里的许多结果对回归分析的其它一些问题（如残差分析，统计诊断）也是很有用的．

Inequality-constrained Regression with Unknown Variance

In many practical problems it is quite often to meet the regression problems with constraints.The properties of the estimators for inequality-constrained problems with known variances have been studied a lot.However,in many practical problems the variances of random errors may be unknown.In this paper we give an estimator of the unknown variance and study its properties.We propose the concept of conditional independence between the estimators of the regression parameter and the unknown variance.With these properties we can define t- and F-statistics,which are necessarily required for making statistical inference in the case with unknown variance.Then we show how these results can be used to construct confidence bounds for the regression parameter.Some results here are also useful for some other important parts of regression analysis,such as residual analysis and diagnostics.