Regression Analysis (Ashish Sen and Muni Srivastava)
Regression Analysis (Ashish Sen and Muni Srivastava)
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回归分析（Ashish Sen 和 Muni Srivastava）
DOI：
10.1137/1034042
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
K. Berk
中科院分区：
文献类型：
--
作者：
K. Berk
是对集合之外的任何简单替代价值的最有力的考验。最后，如果没有其他方法，可以通过与统计对数-2\f25-2\f25 L-2到-2\f25 X2-2的渐近分布相关的相同作者的结果来执行所需的计算。总之，L可以作为一个完整的估计系统的基石，它的许多性质都是有吸引力的，并且可以直接在计算机上编程，而不需要闭合形式的解。加文·J·S·罗斯的这本书讨论了最大似然估计的非线性估计，从一个问题的不同参数化是可能的，并且它们应该被转换以适应手头的目的。在目前的情况下使用这一想法有一些限制。上面提到的最大似然估计的变换性质表明，原则上特定参数集的估计不会受到变换、估计然后再变换回来的影响。人们可以很好地想象，在实践中，在精度或速度方面可能会有计算优势。然而，作者认为这是显而易见的：他没有引用任何定理。(更广泛地说，我猜测中等经验的用户在尝试使用MLE时发现的最大障碍是难以相信计算估计的正确性。因此，我希望看到数值分析问题的明确理论发展，从其他问题中解脱出来。)这本书的目标读者没有说明。一个完全的初学者可能会因为一些解释上的错误、理论上的不准确和粗心大意而受到阻碍。在2.1.4中的一个例子中，常规方法(A)得到估计(2.549，9.956)，而参数变换(E)“改善(A)中优化算法的性能”得到0(2.549，9.956)。也许改进在于融合的时间，但我们没有得到进一步的信息。在1.2.1中，最大似然估计被认为是“一致的，因为随着样本量的增加，渐近趋于0。”同样在1.2.1中，随着样本量的增加，最大似然估计的离散度“达到”CramerRao下限，这意味着“在大样本中，非最大似然估计的方差不能大于最大似然估计。”在这里，“更小”或“几乎更小”的意思是“更大”。尽管如此，对非线性估计有一定了解并希望探索参数转换观点的用户可能使用数值算法组(NAG)子例程库中的最大似然程序--将在本书中找到丰富的信息和建议。如果用户想要更全面地介绍非线性估计的可能性和意义，并且愿意阅读一本冗长的教科书，那么《Seber and Wild》这本书可能会更好地满足他们的需求。另一种方法是由Bates和Watts描述的。
of Neyman and Pearson, is a most powerful test against any simple alternative value outside the set. Finally, the required calculations can be performed, if in no other way, by the same authors’ result relating the asymptotic distribution of the statistic -2 log L to X2. Altogether, L can be used as the cornerstone of a complete system of estimation, many of whose properties are attractive and which can be directly programmed on a computer without needing a closed-form solution. The book by Gavin J. S. Ross discusses nonlinear estimation by MLE from the point of view that different parameterizations of a problem are possible and that they should be transformed to suit the purpose at hand. There are some limitations to using this idea in the present context. The transformation property of the MLE, mentioned above, suggests that in principle an estimate of a particular parameter set cannot be affected by transforming, estimating, and then transforming back again. One can well imagine that in practice there might be a computational advantage in accuracy or speed. However, the author takes this as obvious: he does not cite any theorems. (More generally, I would guess that the greatest obstacle that the moderately sophisticated user finds in trying to use MLE is difficult in believing in the correctness of the computed estimates. Therefore, I would have liked to have seen a clear theoretical development of the numerical analysis issues as such, disentangled from the other issues.) The intended audience for the book is not stated. A complete beginner might be hindered by some expository glitches, imprecision in theoretical matters, and carelessness. In an example in 2.1.4, the conventional method (a) yields estimates (2.549, 9.956), while parameter transformation (e) "to improve the performance of the optimization algorithm in (a)" leads to 0 (2.549, 9.956). Perhaps the improvement lay in the time to convergence, but we are given no further information. In 1.2.1 MLE’S are said to be "consistent in the sense that as the sample size increases, tends asymptotically to 0." Also in 1.2.1, as sample size increases the dispersion of the MLE "attains" the CramerRao lower bound, meaning "that in large samples nOn-MLES cannot have a greater variance than the MLE." Here, "smaller" or "practically smaller" is meant for "greater." Nonetheless, a user having some familiarity with nonlinear estimation and wishing to explore the parameter transformation point of viewmperhaps using the Maximum Likelihood Program in the Numerical Algorithms Group (NAG) subroutine library--will find in this book a wealth of information and suggestions. A user seeking a more general introduction to the possibilities and meaning of nonlinear estimation and willing to tackle a lengthy textbook might be better served by the book [1] of Seber and Wild. Another approach is described [2] by Bates and Watts.