M-estimation of multivariate linear regression parameters under a convex discrepancy function
M-estimation of multivariate linear regression parameters under a convex discrepancy function
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发表时间：
1992
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通讯作者：
Z. Bai;Calyampudi R. Rao;Yuehua Wu
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作者：
Z. Bai;Calyampudi R. Rao;Yuehua Wu
关于线性回归参数的 M 估计有大量文献。大多数论文通过选择要最小化的特定差异函数或特定估计方程来处理特殊情况。一些讨论了一般结果，但证明了在严格假设下的结果，这些假设似乎排除了重要的特殊情况。在本文中，在似乎是发展令人满意的渐近理论的必要假设集下，使用凸差异函数发展了 M 估计的一般理论。给出了建立 M 估计分布的渐近正态性的详细证明，并将结果应用于几个特定情况。制定了适当的标准来检验有关回归参数的假设。该问题是在包括单变量情况在内的多变量情况下讨论的。
There is vast literature on M-estimation of linear regression parameters. Most of the papers deal with special cases by choosing particular discrepancy functions to be minimized or particular estimating equations. A few discuss general results, but prove results under heavy assumptions which seem to exclude important special cases. In this paper, a general theory of M-estimation is developed using a convex discrepancy function under what appear to be a necessary set of assumptions to develop a satisfactory asymptotic theory. Detailed proofs are given for establishing the asymptotic normality of the distribution of M-estimates and the results are applied to several particular cases. Appropriate criteria are developed for tests of hypotheses concerning regression parameters. The problem is discussed in the multivariate situation which includes the univariate case.