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裂区设计中的随机化因果推断AI 解读

Under the potential outcomes framework, we propose a randomization based estimation procedure for causal inference from split-plot designs, with special emphasis on $2^{2}$ designs that naturally arise in many social, behavioral and biomedical experiments. Point estimators of factorial effects are obtained and their sampling variances are derived in closed form as linear combinations of the between- and within-group covariances of the potential outcomes. Results are compared…

运用有限总体抽样工具改进复杂实验的因果推断AI 解读

This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization…

具有频率学有效性的后验可信集：经验型似然的高阶渐近理论AI 解读

With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest posterior density. These asymptotics, in turn, characterise members of the class that allow approximate frequentist validity of such sets. It is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here.

基于经验差异统计量的置信区间期望长度AI 解读

We consider a very general class of empirical discrepancy statistics that includes the Cressie–Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order asymptotics for expected lengths of associated confidence intervals are investigated. An explicit formula is worked out and its use for comparative purposes is discussed. It is seen that the empirical likelihood ratio statistic, which enjoys interesting second-order power…

具有最大估计容量的分块正规部分因子设计AI 解读

In this paper, the problem of constructing optimal blocked regular fractional factorial designs is considered. The concept of minimum aberration due to Fries and Hunter is a well­accepted criterion for selecting good unblocked fractional factorial designs. Cheng, Steinberg and Sun showed that a minimum aberration design of resolution three or higher maximizes the number of two­factor interactions which are not aliases of main effects and also tends to distribute these…

具有近似频率学有效性的贝叶斯预测AI 解读

We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering both posterior quantiles and highest predictive density regions with reference to a future observation. The resulting priors are shown to be invariant under reparameterization. The role of Jeffreys’ prior in this regard is also investigated. It is further shown that, for any…

通常似然与调整似然所对应的置信区间AI 解读

Summary In the presence of nuisance parameters, we drive an explicit higher order asymptotic formula to compare the expected lengths of confidence intervals given by likelihood ratio statistics arising from the usual profile likelihood and various adjustments thereof. Highest posterior density regions, with approximate frequentist validity, are also included in the study.

具有近似频率学有效性的扰动椭球与最高后验密度区域AI 解读

SUMMARY This paper considers, in the multiparameter case, perturbed ellipsoidal and highest posterior density regions with both Bayesian and frequentist validity up to o(n −1).

二阶 Pitman 接近性与 Pitman 可容许性AI 解读

Motivated by the first-order Pitman closeness of best asymptotically normal estimators and some recent developments on higher-order asymptotic efficiency of estimators, a second-order asymptotic theory is developed for comparison of estimators under the Pitman closeness criterion, covering both the cases without and with nuisance parameters. The notion of second-order Pitman admissibility is also developed.

调整似然与条件似然：功效性质及Bartlett型调整AI 解读

SUMMARY Under contiguous alternatives the adjusted likelihood ratio (ALR) test is seen to have the same power properties as the conditional likelihood ratio test up to the third order of comparison. In particular, an optimum property of the ALR test in terms of second-order local maximinity follows. It is also seen that the ALR statistic admits a Bartlett-type adjustment.

存在干扰参数时后验分位数的频率学有效性：高阶渐近分析AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior quantiles of θ1, treating θ2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o(n−1).

存在干扰参数时后验分位数的频率学有效性：高阶渐近分析AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior quantiles of θ1, treating θ2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o(n−1).

条件似然比检验与通常似然比检验的比较AI 解读

SUMMARY This paper compares, under contiguous alternatives, the conditional likelihood ratio test of Cox and Reid with the usual likelihood ratio test on the basis of second-order power. It is seen that although the power of the former is identical, up to the second order, with that of the likelihood ratio test with known nuisance parameter, it does not hold with the latter. This provides a justification for the use of the conditional likelihood ratio test, rather than the…

似然比与条件似然比检验的贝叶斯及频率学派 Bartlett 修正AI 解读

SUMMARY This paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio and the conditional likelihood ratio (CLR) statistics differ by o(1). It is seen that, except for sample points with negligible probability, the CLR statistic has a posterior distribution for which a posterior Bartlett correction exists. This observation leads to an alternative proof of the existence of a frequentist Bartlett correction for the CLR…

Cox–Reid 条件似然比统计量的 Bartlett 型调整AI 解读

This paper explicitly derives a Bartlett-type adjustment for the conditional likelihood ratio statistic of Cox & Reid via that for the usual likelihood ratio statistic.

Cox–Reid 条件似然比统计量的 Bartlett 型调整AI 解读

SUMMARY This paper explicitly derives a Bartlett-type adjustment for the conditional likelihood ratio statistic of Cox & Reid via that for the usual likelihood ratio statistic.

存在线性趋势时有限总体均值的最优估计AI 解读

Postulating different superpopulation models for a finite population with linear trend, we suggest optimal sampling strategies for estimating the finite population mean within some classes of unbiased strategies.

存在线性趋势时有限总体均值的最优估计AI 解读

Postulating different superpopulation models for a finite population with linear trend, we suggest optimal sampling strategies for estimating the finite population mean within some classes of unbiased strategies.

一般相关模型下有限总体总量的最优估计AI 解读

Restricting attention to fixed size sampling designs and linear unbiased estimators of a finite population total, we give methods for finding estimators with minimum model expected variance and the optimal strategy under a general correlated superpopulation model. Some techniques popular in the theory of optimal experiments help in the derivation. Several earlier optimality results are deduced as special cases.

一般相关模型下有限总体总量的最优估计AI 解读

Restricting attention to fixed size sampling designs and linear unbiased estimators of a finite population total, we give methods for finding estimators with minimum model expected variance and the optimal strategy under a general correlated superpopulation model. Some techniques popular in the theory of optimal experiments help in the derivation. Several earlier optimality results are deduced as special cases.

摘要暂缺

方差分量估计的最优设计AI 解读

The design problem for the estimation of variance components by the method of unweighted squares of means, under a multifactor random effects model, is considered. First it is shown that with the numbers of levels of the factors fixed, a balanced design, if it exists, is optimal. Next the numbers of levels are also treated as decision variables and the derivation of minimax designs is indicated.

可分解与仿射可分解的方差平衡设计AI 解读

This paper introduces the notion of affine (μ1, …, μ1)-resolvability and explores the interrelations between: (a) affine (μ1…, μ1)-resolvability, (b) variance-balance, and (c) the relation b = v+t−1, where b is the number of blocks. It is seen that, while (a) and (b) imply (c), and (b) and (c) imply (a), the relation (a) and (c) imply (b) is not in general true. A necessary and sufficient condition under which (a) and (c) imply (b) has been derived and certain nonexistence…

响应面斜率估计的二阶与三阶极小极大设计AI 解读

Designs for estimating the slope of a response surface are considered. Minimization of the variance of the estimated slope maximized over all points in the factor space is taken as the optimality criterion. Optimal designs under the minimax criterion are derived for second- and third-order polynomial regression over spherical regions.