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用于改进贝叶斯推断参数化的诊断图AI 解读

A major problem with the Bayesian analysis of statistical models is that the computation of posterior and predictive summaries typically requires the numerical evaluation of complicated multivariate integrals. The accuracy and efficiency of these computations are usually sensitive to the choice of parameterization for the statistical model. This paper describes a graphical method which can be used both for assessing a proposed parameterization and choosing a new improved…

由置信区间进行贝叶斯与似然计算AI 解读

Recently there has been considerable progress on setting good approximate confidence intervals for a single parameter θ in a multi-parameter family. Here we use these frequentist results as a convenient device for making Bayes, empirical Bayes and likelihood inferences about θ. A simple formula is given that produces an approximate likelihood function Lx†(θ) for θ, with all nuisance parameters eliminated, based on any system of approximate confidence intervals. The…

最大似然估计的偏差缩减AI 解读

It is shown how, in regular parametric problems, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function. In exponential families with canonical parameterization the effect is to penalize the likelihood by the Jeffreys invariant prior. In binomial logistic models, Poisson log linear models and certain other generalized linear models, the Jeffreys prior penalty function can be imposed in…

分形维数盒计数估计量的表现AI 解读

Box-counting estimators are popular for estimating fractal dimension. However, very little is known of their stochastic properties, despite increasing statistical interest in their application. We show that, if the irregular curve to which the estimators are applied is modelled by a Gaussian process, concise formulae may be developed for asymptotic bias and variance of box-counting estimators. These formulae point to critical differences between a native form of the…

因果型空间自回归过程估计量的偏差AI 解读

We study the asymptotic distribution of Yule-Walker and least squares estimators for twodimensional causal autoregressive processes observed on a rectangular part of a lattice. An explicit expression for the asymptotic bias of Yule-Walker estimators is obtained. It is shown that this bias disappears if we use the so-called unbiased sample autocovariance function or least squares estimators.

病例对照研究中逻辑回归的稳健估计AI 解读

Consider a logistic regression model under case-control sampling. Prentice & Pyke (1979) showed that the logistic slope estimates with case-control sampling may be estimated from a standard prospective logistic regression program and that the resulting standard errors are asymptotically correct. Since logistic regression estimates are nonrobust, we propose and analyze robust estimates of the slope parameters. We focus specifically on estimates which downweight observations…

基于标记过程的一致预测规则框架AI 解读

Recently interest has developed regarding the statistical properties and uses of marker processes in the context of the analysis of failure time data or survival analysis. A marker process is a stochastic process that acts as a time dependent covariate that is internal to the unit under study in the language of Kalbfleisch & Prentice (1980). As such the sample path of the process up to a certain point in time may carry information about the subsequent hazard for failure.…

纵向二元响应的似然分析方法AI 解读

In this paper, we discuss a likelihood-based method for analysing correlated binary responses based on a multivariate model. It is related to the pseudo-maximum likelihood approach suggested recently by Zhao & Prentice (1990). Their parameterization results in a simple pairwise model, in which the association between responses is modelled in terms of correlations, while the present paper uses conditional log odds-ratios. With this approach, higher-order associations can be…

多中心临床试验二元数据的分析AI 解读

We develop several methods for estimating the treatment effect difference defined as the overall log-odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response. A simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions.

状态空间模型的扰动平滑器AI 解读

This paper develops a method to evaluate the smoothed estimator of the disturbance vector in a state space model together with its mean squared error matrix. This disturbance smoother also leads to an efficient smoother for the state vector. Applications include a method to calculate auxiliary residuals for unobserved components time series models and an EM algorithm for estimating covariance parameters in a state space model.

有限总体经验似然估计与辅助信息的有效利用AI 解读

SUMMARY In finite population inference problems, auxiliary population information is often available. We show in this paper that the empirical likelihood method can be naturally applied to such problems to make effective use of the auxiliary information. We prove that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information. A Bahadur-type representation for empirical likelihood sample quantiles is given.…

非线性回归中的杠杆值、局部影响与曲率AI 解读

The connections between measures of leverage, statistical curvature, and the local influence of a mean-shift perturbation are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a commonly-used linear approximation are found to be connected to the effective residual curvature of the nonlinear model. The local influence of a mean-shift perturbation in the model function is seen to be closely related to the Jacobian leverage.

流行型备择下的变点检验AI 解读

The purpose of this paper is to discuss the tests to detect an epidemic alternative in the mean value of a sequence of independent normal variables. Various test statistics, such as the likelihood ratio, the score-like statistic, Levin & Kline's statistic, the semilikelihood ratio, and the recursive residual, are studied. The large deviation approximations to the significance levels and powers are developed by integrating approximations to conditional boundary crossing…

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混合比例已知时正态混合模型中的检验AI 解读

The aim of this paper is to study the behaviour of the likelihood ratio test statistic in mixture models when the proportions of the distributions are known a priori. The results depend on the value of the proportion, the dimenstionality of the problem and whether or not the variance of the distributions is known.

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热卡插补调查数据的 Jackknife 方差估计AI 解读

Hot deck imputation is commonly employed for item nonresponse in sample surveys. It is also a common practice to treat the imputed values as if they are true values, and then compute the variance estimates using standard formulae. This procedure, however, could lead to serious underestimation of the true variance, when the proportion of missing values for an item is appreciable. We propose a jackknife variance estimator for stratified multistage surveys which is obtained by…

核密度估计的自动带宽选择器AI 解读

To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross-validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. It is proposed to select the cut-off frequency by a generalization…

混合分布误设对混合效应 Logistic 模型拟合的影响AI 解读

Mixed-effects logistic models are often used to analyze binary response data which have been gathered in clusters, or groups. Responses are assumed to follow a logistic model with in clusters, with an intercept which varies across clusters according to a specified probability distribution G. In this paper we examine the performance of mixed-effects logistic regression analysis when a main component of the model, the mixture distribution, is misspecified. We show that, when…

线性回归模型中变量选择后的推断AI 解读

We explore the impact of variable selection on statistical inferences in linear regression models. In particular, the generalized final prediction error criterion of Shibata (1984) is considered and it is found, among other things, that inferences on the regression coefficients are impaired by the variable selection procedure. Most notably, the size of the nominal confidence sets tend to be inflated if they are derived based on the selected model. On the other hand, variable…

生存与计划处死实验中约束极大似然估计的显式解AI 解读

Regulatory agencies routinely base conclusions regarding carcinogenicity of compounds tested in long-term animal studies on tests which are known to be biased under conditions of treatment lethality and tumour lethality. The recognition of these biases has led to a variety of proposed approaches which rely on survival and sacrifice data. Williams & Portier (1992) derived analytic expressions for maximum likelihood estimators of the tumour incidence rate and discrete death…

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