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有效性约束下的置信度估计AI 解读

We examine the decision theoretic estimated confidence approach proposed by Kiefer, Robinson and Berger, and focus on results under the frequentist validity constraint previously described by Brown and by Berger. Our main result is that the usual constant coverage probability estimator for the usual confidence set of a linear model is admissible under the frequentist validity constraint. Note that it is inadmissible without the frequentist validity constraint when the…

逆回归问题中的序贯置信区域AI 解读

In inverse regression problems (or more generally, the estimation of ratios of regression parameters) and errors-in-variables models, it has been shown by Gleser and Hwang that the length of any confidence interval with positive confidence level is infinite with positive probability. Therefore the confidence sets derived using asymptotic theory, although having correct asymptotic coverage probability, typically have zero confidence level when the sample size is fixed. Is it…

普遍支配与随机支配：最小二乘估计量的 U 可容许性与不可容许性AI 解读

Assume the standard linear model $X_{n \times 1} = A_{n \times p} \theta_{p \times 1} + \varepsilon_{n \times 1},$ where $\varepsilon$ has an $n$-variate normal distribution with zero mean vector and identity covariance matrix. The least squares estimator for the coefficient $\theta$ is $\hat{\theta} \equiv (A'A)^{-1}A'X$. It is well known that $\hat{\theta}$ is dominated by James-Stein type estimators under the sum of squared error loss $|\theta - \hat{\theta}|^2$ when $p \geq 3$…

测量误差及相关模型中有限期望直径置信集的不存在性AI 解读

Confidence intervals are widely used in statistical practice as indicators of precision for related point estimators or as estimators in their own right. In the present paper it is shown that for some models, including most linear and nonlinear errors-in-variables regression models, and for certain estimation problems arising in the context of classical linear models, such as the inverse regression problem, it is impossible to construct confidence intervals for key…

乘性测量误差模型及其美国能源部数据应用AI 解读

In an errors-in-variables model, the predicting variables are observed with errors. Traditionally, the errors are assumed to be additive. In this article, I consider the case in which the error is multiplicative, a situation that arises when analyzing some recent data released by the U.S. Department of Energy. A consistent estimator is provided for regression coefficients β by correcting the asymptotic bias of the least squares estimate. It is shown that , after being…