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序贯试验停止后次级过程的推断AI 解读

We consider the following sequential testing problem. A group‐sequential or fully‐sequential test is carried out for a primary parameter, using a score process or an effective score process to eliminate nuisance parameters. After stopping, the possibility of additional parameters is considered, and appropriate tests and estimators are desired that recognise the sequential stopping rule. We formulate an asymptotic multi‐dimensional Gaussian process form of such problems, and…

基于最大似然排序的停止后追加数据序贯检验与估计AI 解读

SUMMARY Often in sequential trials some additional data become available after a stopping boundary has been reached. A method for incorporating such information from overrunning is developed, based on a maximum-likelihood ordering of the sample space after overrunning. This yields a p-value for the primary test and a median-unbiased estimator and confidence intervals for the parameter under test. The context is that of observing a Brownian motion with drift, with either…

序贯检验后次要参数的置信区间AI 解读

Summary In sequential studies, formal interim analyses are usually restricted to a consideration of a single null hypothesis concerning a single parameter of interest. Valid frequentist methods of hypothesis testing and of point and interval estimation for the primary parameter have already been devised for use at the end of such a study. However, the completed data set may warrant a more detailed analysis, involving the estimation of parameters corresponding to effects that…

参数与半参数模型中的渐近一致最强检验AI 解读

Tests of hypotheses about finite-dimensional parameters in a semiparametric model are studied from Pitman's moving alternative (or local) approach using Le Cam's local asymptotic normality concept. For the case of a real parameter being tested, asymptotically uniformly most powerful (AUMP) tests are characterized for one-sided hypotheses, and AUMP unbiased tests for two-sided ones. An asymptotic invariance principle is introduced for multidimensional hypotheses, and AUMP…

分组生存数据边际似然的最大化AI 解读

Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data…

分组生存数据边际似然的最大化AI 解读

Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data…

回归与位移效应的再随机化推断：计算可行的方法AI 解读

An idea due to Quade (1973) is used to develop a method that reduces the computational load for rerandomization inferences in certain situations, and, for experiments carried out with a sufficiently small reference set of randomizations, makes computations entirely feasible. Consider an experimental design for N units for which an experimental plan E is to be chosen randomly from a set of K plans. Plan E will assign treatment dosage dE,u to unit u with postulated additive…

参数—非参数模型中的信息与渐近效率AI 解读

Asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems (for regular estimates) and asymptotic minimax bounds. The methods used involve: (i) the notion of a "Hellinger-differentiable (root-) density", where part of the differentiation is with respect to the nonparametric part of the model, to obtain appropriate scores; and (ii) calculation of the "effective score"…

P值的渐近对数正态性AI 解读

Sufficient conditions for asymptotic lognormality of exact and approximate, unconditional and conditional $P$-values are established. It is pointed out that the mean, which is half the Bahadur slope, and the standard deviation of the asymptotic distribution of the log transformed $P$-value together, but not the mean alone, permit approximation of both the level and power of the test. This provides a method of discriminating between tests that have Bahadur efficiency one. The…

删失数据下生存曲线的置信带AI 解读

For arbitrarily right-censored data, the Kaplan-Meier product-limit estimator Ŝ 0N provides a nonparametric estimate of the survival function S 0 = 1 − F 0 . We provide large-sample simultaneous confidence bands for S 0 , centred at Ŝ 0N . The derivation uses the weak convergence of N½ { Ŝ 0N ( t ) − S 0 ( t )}, on a finite interval, to a Gaussian process, a theorem of Breslow & Crowley (1974), and transforms both the time and space axes of the limiting process to achieve a…

位置参数的最节省样本稳健选择程序AI 解读

Consider samples of size $n$ from each of $k$ symmetric populations, differing only in their location parameters. The decision problem is to select the best population--the one with the largest location parameter--with control on the probability of correct selection (PCS) whenever the largest parameter is at least $\Delta$ units larger than all others, and whenever the common error distribution belongs to a specified neighborhood of the standard normal. It is shown that, if…

与似然比有关的过程的弱收敛AI 解读

Material in Chapter VI of Hajek and Sidak's book is extended to a sequential analysis setting: conditions are given under which a sequence of log-likelihood-ratio processes (log-likelihood-ratios for sequential sampling, represented as jump processes in continuous time) converges weakly to a Wiener process with drift, the drift parameter depending on which hypothesis, in a suitable neighborhood of a null hypothesis, prevails. Conditions for convergence of other "test…

一种贝叶斯无差别先验构造程序AI 解读

In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical…

Stein 两阶段检验的若干序贯对应方法AI 解读

This paper presents several sequential analogs of Stein's two-stage test procedure for testing hypotheses about the mean of a normal population with unknown variance and with specified bounds on the error probabilities. These procedures are modifications of a procedure due to A. G. Baker (1950). When sequential experimentation is feasible, they provide alternatives to the sequential normal test (variance known) or the sequential t -test. If the variance is assumed known, the…