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广义刀切法：有限样本与子样本规模AI 解读

This paper is concerned with bias-reduction properties of that generalized jackknife which pertains to a single-estimator, single-sample situation. Jackknifing is a technique for reducing bias by exploiting the dependence of the bias on sample size. In practice, this is carried out by reestimating the unknown parameter(s) with only part of the sample and combining the new and original estimates suitably weighted to produce cancellation in their biases. The size of the…

平衡三阶段嵌套随机效应模型中方差分量估计量的均方误差比较AI 解读

Various estimators of variance components for the balanced three-stage nested random effects model are compared under standard assumptions of normality and independence of random effects, using MSE as the measure of performance. Several results are proven, demonstrating the inequality relationships on MSE of the unbiased, restricted maximum likelihood and maximum likelihood, and several modifications of the unbiased and maximum likelihood estimators as introduced here,…

非标准随机区组设计中精度不等的多重比较AI 解读

A multiple comparison technique for simultaneous inference in the nonstandard randomized block design models considered by Graybill [3] and Scheffé [11] is developed. Its computation and properties are discussed in terms of a clinical trial. The technique involving a number of independent tests with possibly unequal sizes, not the well-known Bonferroni tests [5], is appropriate when most contrasts between the treatments are of interest, but a few of the comparisons are of…

平衡不完全区组模型参数的同时置信区间AI 解读

Inferences concerning the variance ratios of a random linear model are important in genetics and other areas of scientific investigation. For example, in genetics, the heritability parameters are functions of the variance ratios of a random model. This paper derives simultaneous confidence intervals for all or certain subsets of the parameters of a balanced incomplete random model. This procedure is based on the mean squares of the analysis of variance, and the mean squares…

正态总体分位数的置信带AI 解读

Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic,…

由贝叶斯检验规则导出的区间估计AI 解读

Given a family of rules for the three-decision testing problems of locating a scalar parameter θ relative to θ0, with decisions θ < θ0, θ = θ0 and θ > θ0, and given a sample x, the set S(x) = {θ0: decide θ = θ0) (usually an interval) is an intuitively appealing set estimate of θ. This paper considers the optimality of S(x) for the case in which the testing rules are Bayes. The main result is that when the losses for the testing problems have a particular structure, S(x) is…

检验两个协方差平稳时间序列的独立性：单变量残差互相关方法AI 解读

A two-stage method is proposed for investigating the independence of two covariance-stationary time series. It involves, first, fitting univariate models to each of the series, and then cross-correlating the two residual series thereby obtained. The asymptotic distribution of such a set of lagged residual cross-correlations is established to be of a very simple form under the null hypothesis of the two series' independence. A Monte Carlo study verifies the applicability of…

误差协方差矩阵未知时线性模型中最小二乘法的最优性AI 解读

Optimal properties of the least-squares coefficient estimator in the linear model with scalar error covariance matrix are shown to carry over to the case where the error covariance matrix has a distribution in a class which includes distributions proposed as representing vague prior information.

贝叶斯回归中的缺失变量（二）AI 解读

We are concerned with the problem of parameter estimation in normal regression when some of the observations are missing. A Bayesian approach with vague prior distributions is taken. No assumption is made about the independent variables for which no observations are missing, but the missing components are assumed to be normally distributed with a mean that can depend on the other variables. Joint estimators of the parameters are obtained as the joint mode of the posterior…

回归中的类别控制AI 解读

We assume a normal linear regression model. Among k independent variables, only x k are controllable, and the others are exogenous. The categorical control problem is: given the values of the exogenous variables, how should we control x k so that y lies within a preassigned target interval (c 1, c 2)? The answer is to determine an interval (or union of intervals) on the x k -axis, the “regulation interval.” We require that the probability that the dependent variable falls…

两个残差方差均已知时线性结构关系的一则注记AI 解读

This article provides an alternative derivation of a maximum likelihood solution, due to Birch [1], which simplifies the algebra and characterizes Birch's solution as a special case of a result, due to Dolby [2], that has application to a variety of more complex structural models, including factor analysis.

关于 Birnbaum 似然原则理论的一则注记AI 解读

The principles of sufficiency and conditionality are shown by Birnbaum [1] to imply the principle of likelihood. But in his formulation it is necessary to adopt in the continuous case, a definition of sufficiency which differs from the conventional definition. The objections against the new definition are set out and it is shown that the conventional definition can be adhered to by taking into consideration that in practice there is always a finite limit to the accuracy with…

临床试验中应答及应答持续时间的截断几何模型AI 解读

For treatment comparisons in clinical cancer trials, the data often indicate absence or presence of response along with duration of response when it occurs. Response length is frequently truncated by death, loss of followup information, study termination, or other causes, and is usually a discrete variable (days, weeks, or months). A mixture of a binomial and truncated geometric probability is studied as an appropriate statistical model. Maximum likelihood estimators are…

Bartlett 方差齐性检验的精确临界值AI 解读

Consider n normal populations. Random samples of equal size m are taken from each population. It is desired to use the Bartlett procedure to test at level α the hypothesis of equal variances. A method is presented to provide exact critical values of the Bartlett test statistic. Computed exact critical values are tabulated for various (n, d, α), where d = m - 1 denotes the common number of degrees of freedom.

多元指数分布的参数估计AI 解读

Parameter estimation for a (k + 1)-parameter version of the k-dimensional multivariate exponential distribution (MVE) of Marshall and Olkin is investigated. Although not absolutely continuous with respect to Lebesgue measure, a density with respect to a dominating measure is specified, enabling derivation of a likelihood function and likelihood equations. In general, the likelihood equations, not solvable explicitly, have a unique root which is the maximum likelihood…

完整样本或尾部删失样本下 Logistic 分布参数的线性估计AI 解读

In this paper we present the asymptotically best linear unbiased estimators for the location and scale parameters of the logistic distribution based on samples where there may be Type 2 censoring in the tails. Given the amount of censoring, the weights of the estimators can be expressed in simple closed forms. Comparisons of these with the best linear unbiased estimators and the Cramer-Rao lower bounds demonstrate that they have good efficiency even for small samples.

分位数区间的无分布置信区间AI 解读

Wilks [6] introduced distribution-free confidence intervals based on order statistics for quantile intervals. For the rth and sth order statistics in a sample of size n (1 ≤ r < s ≤ n), upper and lower bounds and an exact expression for the confidence coefficient are derived. Numerical examples comparing the bounds and the exact solution are provided. A connection with distribution-free tolerance intervals is indicated.

长尾对称分布下置信区间的稳健性AI 解读

A variety of 95-percent confidence interval procedures have been examined in some detail using Monte Carlo techniques. These estimators were tried on simulated samples of sizes 10 and 20 from a spectrum of distributions ranging from the Gaussian to the long-tailed Cauchy. The robustness of an estimator is measured by both the closeness of its level to the 5-percent goal (robustness of validity) and its expected length as compared to its competitors (robustness of…

多元 Student-t 误差回归模型的贝叶斯与非贝叶斯分析AI 解读

The linear multiple regression model is analyzed assuming the error vector has a multivariate Student-t distribution with zero location vector and scalar dispersion matrix; the multivariate Cauchy and normal distributions are special cases. It is found that the usual least squares coefficient estimate is the maximum likelihood estimate and the mean of the posterior distribution under a diffuse prior distribution. Inferences based on usual t- and F-statistics are shown valid…

OLS 与 BLUS 残差用于模型设定误差检验的进一步结果AI 解读

This paper considers the test RESET, which is a test for specification error in a linear regression model. It makes a modification in the test based on OLS residuals, and shows that the modified test is equivalent to a test based on BLUS residuals.

多元平稳时间序列创新广义方差的估计AI 解读

Recently there has been renewed interest in the nonparametric estimate of the innovation variance of a stationary time series. Empirical evidence has shown that some smoothing of the periodogram improves the estimate. This paper attempts to clarify the smoothing question and extends the results to the estimation of the innovation generalized variance of a multivariate stationary time series.

整数值单调函数的最小二乘拟合AI 解读

Least-squares monotone regression (also known as least-squares isotone regression) is being used increasingly. Recently, an application arose in which the fitted values are restricted to be integers. We prove that a very simple procedure yields the optimum monotonic fit subject to this restriction, or to the more general restriction that the fitted values lie in some specified closed set. This procedure is to perform unrestricted monotone regression, and then to round off…

非线性方程组的最大似然与迭代 Aitken 估计AI 解读

For nonlinear equation systems, the properties of the MLE commonly have been deduced from related but inapplicable results in the statistical and econometric literature. Under specific regularity conditions, we build on the nonlinear GLS results of Malinvaud to derive the large-sample properties of the MLE and the limiting distribution of the asymptotic likelihood ratio statistic. We discuss iterative convergence conditions under which the iterated Aitken estimator locates a…

一般定性响应模型的最大似然、最小卡方与非线性加权最小二乘估计AI 解读

This article deals with the general qualitative response model involving several polytomous variables. An extension of Berkson's minimum chi-square estimator to this model is defined and shown to be not always asymptotically efficient, and the conditions under which it is so are derived. It is also shown that the nonlinear weighted least squares method proposed by Walker and Duncan [11] is equivalent to the method of scoring.