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亲代与子代相关性的估计AI 解读

When families have different numbers of offspring, Srivastava (1984) provided an easily computable estimator as an alternative to the maximum likelihood estimator of parent-offspring correlation. Some properties of this estimator are discussed vis-à-vis with those of ensemble and pairwise estimators. Further, we derive the small sample distribution of Srivastava's estimator under the assumption of null parent-offspring correlation. In the process, we demonstrate that a…

ARMA模型的阶数识别AI 解读

We present a new powerful method for determining the order of ARMA (p, q) models having small sets of observations. The procedure is based on an autoregressive order determination criterion and on linear estimation methods. Simulated data are used to demonstrate the capabilities of the approach.

可变带宽曲线估计量的偏差AI 解读

A major difficulty in understanding the properties of variable bandwidth methods (Breiman, Meisel & Purcell, 1977; Abramson, 1982) is that extremely lengthy and complex algebra is needed to assess the influence of bias. Indeed, the complexity is so great that it has forced investigators to use computer algebraic manipulation to determine formulae for bias. In this note we completely eliminate these algebraic obstacles by presenting a simple easy-to-use formula which gives…

修正 Weibull 模型中的若干非正则检验AI 解读

Certain tests on the parameters of a modified Weibull distribution are considered. Nonregular asymptotic behaviour of likelihood-based test statistics is observed. Competing tests, based on extreme order statistics, are investigated and comparisons are made of power functions.

指数分布第二类删失数据的相对信息损失AI 解读

This paper uses information theory to quantify information loss in Type II censored samples drawn from an exponential distribution. Indexes of information loss for the maximum likelihood estimation and for Bayesian analysis are defined. Properties of the proposed information measures as functions of the sample size, the exponential parameter, and the parameters of the prior distribution are studied. It is shown that the relative loss of information in Type II censoring may…

共同优势比的一类渐近有效非迭代估计器AI 解读

A new class of noniterative estimators of a common odds ratio is presented. It is shown that the principle of construction leads to asymptotically optimal estimators, that is estimators which are consistent, asymptotically normally distributed and asymptotically efficient.

均值变化极大似然检验的渐近分布AI 解读

For the maximum likelihood tests for a change in the mean of independent random variables, it is proved that the limit distribution is a double exponential, i.e. Gumbel, distribution. Our results also explain why the maximum likelihood methods are very powerful on the tails.

关于剩余寿命的一则札记AI 解读

Two further characterizations are given of a family of survival distributions introduced by Hall & Wellner (1984). The second result involves a new family of semiparametric models requiring proportional mean residual life.

比率策略的渐近极小极大性AI 解读

The use of simple random sampling together with ratio estimation is of fundamental importance in survey sampling practice. From a theoretical point of view the ratio estimator has been justified by Bayesian methods (Ericson, 1969) and by superpopulation methods (Royall, 1970). But these methods do not yield a rigorous justification of simple random sampling at the same time. We use the minimax principle in an asymptotic version to justify both simple random sampling and…

核回归估计中的权重选择AI 解读

For kernel regression estimation a weighting scheme due to Nadaraya and Watson has been associated with random design, and a convolution type weighting scheme with fixed design. Based on integrated mean square error, none of the estimators is uniformly optimal in either design. However, the convolution type weights are minimax optimal. Further advantages of this estimator can be seen in the structure of the bias.

多响应回归分析中的近似推断AI 解读

We present an approximate inference procedure for the multiresponse regression model. This can be used to determine approximate confidence regions or intervals and to formulate diagnostic tools such as standardized residuals and influence measures. The overall approximation is based on approximations at two stages. At the first stage, the multiresponse regression model is replaced by a generalized least-squares model using the estimated variance-covariance matrix of the…

多元极值分布的建模AI 解读

Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the dependence between the margins. This paper extends to more than two variables the models and results for the bivariate case obtained by Tawn (1988). Two new families of physically motivated parametric models for the dependence structure are presented and are illustrated with an application to trivariate extreme sea…

Lawley–Hotelling 迹准则的正态近似AI 解读

Significance points of the Lawley-Hotelling trace criterion for a linear hypothesis can be approximated by using the normal distribution with correct first two moments.

非参数回归中的方差估计AI 解读

A simple explicit estimator of variance in nonparametric regression is suggested, based on the mean square of a sequence of residuals. The estimator is valid for general error distributions, has elementary bias and variance properties, and is optimal to both first and second orders.

允许长程依赖的一类随机场模型AI 解读

In this note it is shown how a convenient class of random field models with rational spectral densities can be augmented to incorporate the possibility of long range dependence.

To study time-dependent characteristics of a population, we may sample the same population at regular intervals. A basic problem is how the sample should be selected at different time periods. Here we consider successive sampling with partial replacement of units on two occasions from a Bayesian point of view. Bayes estimators and optimal designs for such priors will be obtained. In one situation, the whole survey, i.e. the first sample and the second sample, is planned…

利用辅助信息估计调查数据的分布函数与分位数AI 解读

SUMMARY Ratio and difference estimators of a population distribution function under a general sampling design are obtained, using auxiliary population information. The relative mean errors and relative mean square errors of these estimators and a model-based estimator of Chambers & Dunstan (1986) are compared through a simulation study. The advantages of the design-based estimators over the model-based estimator under model misspecifications, especially for large samples,…

边际齐性模型设计矩阵的构造AI 解读

Suppose that a homogeneous group of n subjects is observed on T occasions. Each subject has one of K levels of response at each of the T occasions. The cross-classification of the recorded responses over time forms a KT contingency table. This paper discusses the design matrix for the marginal homogeneity model, which assumes that the first-order marginal probabilities at each time are equal. The marginal homogeneity model is a linear model for the vector of cell…

基于似然的显著性检验的条件性质AI 解读

This paper considers the conditional properties of the unconditional significance tests based on standardized versions of the maximum likelihood estimate and the score statistic for the case of a simple null hypothesis and a one-parameter model. The properties of the tests are assessed by considering the conditional level of the test given the observed value of a statistic that is locally ancillary near the null model. It is shown that for the test based on the maximum…

非正态线性回归：高维显著性水平的一个例子AI 解读

Analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals, giving an unnormed density on Rk, where k is the number of parameters. To obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability, thus requiring integration in k dimensions. In this paper a conditional approach to evaluating the observed level of significance is developed, and an importance sampling technique is…

删失生存数据中风险率变化的非参数分析：变点模型的替代方案AI 解读

As a nonparametric estimator for the point of the most rapid change of a hazard rate we propose the location of an extremum of a nonparametric estimate of the derivative, or equivalently, of a zero of a nonparametric estimate of the second derivative. Using the kernel method for the nonparametric estimation of derivatives of the hazard rate, the asymptotic local limiting distribution and uniform consistency are applied to prove consistency and to find the limiting…

伯努利变量序列中变化区段的定位AI 解读

The theory underlying inferences about a single change point in a sequence of independent Bernoulli variables is extended to the two change points problem where the distance between the two change points is known, namely a changed segment. Both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations. The…

Logistic 回归中的连续性校正残差AI 解读

In choosing residuals for logistic regression the two primary candidates are Pearson or linear residuals and deviance residuals; an asymptotic bias correction can be used with the latter. Residuals can also be computed after the arc sine or the Anscombe transformation, and there are residuals which approximate an outlier score statistic (Williams, 1984). Recently Pierce & Schafer (1986) proposed correcting for continuity before computing residuals. They first studied the…

Barndorfi-Nielsen & Cox (1979) introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector. This approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states. It is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a…