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广义回归残差的经验分布函数AI 解读

Generalised residuals, as defined by Cox and Snell, may be thought of as residuals from generalised regression. Under regularity conditions on the regression and on the estimator of the unknown parameters, the asymptotic behaviour of the empirical distribution of these residuals is determined. The addition of a random adjustment to the maximum likelihood estimator leads to the familiar Brownian bridge as the limit.

关于Prescott归一化残差上界的一则说明AI 解读

Prescott (1977) has given an inequality for linear functions of normed residuals. Here we give an alternative simpler proof and derive analogous bounds for normed residuals of other kinds, such as the Theil blus residuals.

关于 Prescott 标准化残差上界的一则说明AI 解读

Prescott (1977) has given an inequality for linear functions of normed residuals. Here we give an alternative simpler proof and derive analogous bounds for normed residuals of other kinds, such as the Theil blus residuals.

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…

渐近最优的随机化回答程序AI 解读

An abstract general model of multiway randomized response procedures is investigated, with the aim of minimizing the variance matrix while bounding the risk to which respondents are subjected. A general result on the structure of possible optimal designs is obtained, an improved result is derived for the three-way case, and a complete answer is found for the dichotomous case.

若干位置参数估计量的渐近相对效率AI 解读

Summary If, by analogy with means and medians, one computes that value such that the sum of the absolute pth powers of the sample deviations about that point takes on its minimum, one obtains an estimate of the central value of a symmetric distribution. Such estimates, for p ≥ 1 and under reasonable conditions, are known to be asymptotically normal as the sample size becomes large, and here the asymptotic relative efficiency of any pair is obtained, both for the general case…

Summary Cox and Snell have introduced a definition of residuals, in a situation more general than the usual linear hypothesis. They have also discussed briefly the distribution of these residuals, and the complementary aspect of transforming them so that they have (approximately) the same distribution as the random variables which they are effectively estimating. Here it is shown how a complete discussion can be given.

非平稳过程的谱概念AI 解读

Summary Following a brief general description of the attitude adopted here to statistical models and definitions, a study of the problem of defining a spectrum for non-stationary processes is made. The approach is to determine first what one would wish to use such a spectrum for, and then attempt to discover whether this is possible. By the nature of the case no conclusive answer is possible, but the tentative conclusion drawn is that it is not.

摘要暂缺

分位数估计的若干问题AI 解读

Summary The problem of estimating quantiles in the context where restriction to particular parametric families is inappropriate is considered, for simple random sampling and stratified sampling. For the former type of sampling the distribution-free procedures are obtained and the admissible estimators identified, and certain other questions are dealt with. In the stratified sampling situation similar problems are considered, less successfully.

描述简单队列与水坝的随机游走的一项性质AI 解读

Summary A so-called duality principle, which has been given by previous authors for simple queues and dams, is here shown to be valid in more general circumstances. The conditions under which the result, relating the stationary distribution of one random walk with absorption probabilities in another, is applicable are investigated.