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未知方差下一元或二元正态总体均值常用置信集的可容许性AI 解读

Summary In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi. This solves a long-standing open problem in mathematical statistics, and this has important implications on the performance of modern inference procedures post model selection or post shrinkage, particularly in situations where the number of parameters is larger than the sample…

致编辑的信：关于“两比例之差的最小单侧置信区间构造”的评论AI 解读

Letter to the Editor: Some comments on "On construction of the smallest one-sided confidence interval for the difference of two proportions" by Weizhen Wang [arXiv:1002.4945].

模型选择后置信区间的大样本最小覆盖概率AI 解读

We give a large-sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a “conservative” (or “overconsistent”) model selection procedure. We derive an upper bound for the large-sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the Akaike information criterion as well as various pretesting procedures.…

线性回归中的变量选择AI 解读

Shibata (1981, Biometrika 68, 45–54) considers data-generating mechanisms belonging to a certain class of linear regressions with errors that are independent and identically normally distributed. He compares the variable selection criteria AIC (Akaike information criterion) and BIC (Bayesian information criterion) using the following type of comparison. For each fixed possible data–generating mechanism, these criteria are compared as the data length increases. The results of…

变量选择后回归中的有效置信区间AI 解读

We consider a linear regression model with regression parameters (θ 1 ,...,θ p ) and error variance parameter σ 2 . Our aim is to find a confidence interval with minimum coverage probability 1 − α for a parameter of interest θ 1 in the presence of nuisance parameters (θ 2 ,...,θ p ,σ 2 ). We consider two confidence intervals, the first of which is the standard confidence interval for θ 1 with coverage probability 1 − α. The second confidence interval for θ 1 is obtained…

模型选择对置信区域与预测区域的影响AI 解读

Pötscher (1991, Econometric Theory 7, 163–181) has recently considered the question of how the use of a model selection procedure affects the asymptotic distribution of parameter estimators and related statistics. An important potential application of such results is to the generation of confidence regions for the parameters of interest. It is demonstrated that a great deal of care must be exercised in any attempt at such an application. We also consider the effect of model…

利用样本自相关估计时间序列参数AI 解读

SUMMARY Consider a scalar linear process {xt} whose spectral density is σ 2 k(λ, θ 0) where σ2 is the innovation variance and k(⋅,θ0)∈{k(⋅,θ):θ∈S⊂ℝq}. We introduce a class of estimators of θ0 based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is…