On Large-Sample Estimation and Testing in Parametric Models
以研究生教材水平,系统介绍参数模型的大样本估计与假设检验理论,包括信息界、正则估计、高效估计,以及似然比、Wald、Rao等检验的渐近等价性,适合经济学等领域的学者快速把握核心方法。
Summary Large-sample theory of estimation and of hypothesis testing is developed, at an intermediate (graduate textbook) level. Attention is confined to parametric models. Local analysis ('moving parameter') methods are used. For estimation, an information bound is found for the large-sample variance of regular estimates, regularity being a kind of large-sample unbiasedness. And near solution of the score equations yields estimates achieving these bounds. Regular estimates and efficient estimates are characterized. For hypothesis testing, various classical tests-including likelihood ratio, Wald, and Rao-are shown to be asymptotically equivalent, and efficient within a class of quadratic form (QF) tests. A Neyman-Rao, or effective scores, test is introduced; it too is equivalent to the classical tests. Regular (asymptotically similar, and with no local power against changes in nuisance parameters) QF tests, and efficient tests, are characterized. Many of the results are not entirely new; but the organization and presentation are.