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存在干扰参数时后验分位数的频率学有效性：高阶渐近分析AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior quantiles of θ1, treating θ2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o(n−1).

效力曲线形状先验约束下的非参数贝叶斯生物测定AI 解读

We consider the problem of implementing nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve (for example, to be convex, concave or ogive). Sampling based approaches to calculating posterior features of interest are detailed and illustrated. Extensions to prior constraints on hazard rates are outlined.

使零假设极限分布渐近正态的拟合优度统计量修正AI 解读

SUMMARY The Cramér-von Mises class of test statistics for the one-sample goodness-of-fit problem is based on the weighted L2-distance of the distribution from its empirical counterpart. It is well known that the root π standardized norm has a degenerate limiting distribution under the null hypothesis, and the π standardized norm has a nondegenerate limiting distribution that is not normal and depends on identifying the principal components for every weight function. Usually…

两状态过程的拟合优度检验AI 解读

Binary data in which successive outcomes may be dependent frequently arise in a medical and social sciences context. A simple model for such data is a homogeneous 2-state Markov chain. Under this model one would usually treat the first observation in each sequence, Y1, as fixed. In the case of panel data this may constitute a substantial loss of information. In this paper we propose goodness-of-fit tests for the 2-state Markov model under several likely alternative…

基于 MINQUE 理论的亲子与同胞相关估计AI 解读

We derive easily computable expressions for MINQUE estimators of covariance parameters in an unbalanced family data structure used to study traits. These estimators are strongly consistent and asymptotically normal. Simple expressions for limiting sample variances and covariances of MINQUE estimators are provided.

利用辅助信息估计有限总体分布函数的核方法AI 解读

This paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population. A method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable. The resulting estimator compares favourably with existing estimators in terms of efficiency, conditional behaviour and robustness. The…

重新审视残差方差的非参数估计AI 解读

Several difference-based estimators of residual variance are compared for finite sample size. Since the introduction of a rather simple estimator by Gasser, Sroka & Jennen-Steinmetz (1986) other proposals have been made. Here the one given by Hall, Kay & Titterington (1990) is of particular interest. It minimizes the asymptotic variance. Unfortunately it has severe problems with finite sample bias, and the estimator of Gasser et al. (1986) proves still to be a good choice. A…

分类协变量观测不完整时的逻辑回归：三种方法比较AI 解读

A logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates. Three different approaches allowing the use of this information are compared: maximum likelihood estimation, pseudo maximum likelihood estimation, and probability imputation. The first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically…

验证抽样下病例对照研究的逻辑回归分析AI 解读

This paper proposes an analysis of case-control data under a double-sampling scheme, when covariates are missing or measured with error at the first stage of sampling and are validated at the second stage in a subsample. The method combines risk information from both samples. It is derived under the assumptions that (i) the prospective disease incidence model is of logistic form, (ii) the proxy or partial information takes on finitely many values, and (iii) the error is…

多元 M 估计中经验似然与经验鞍点近似的关系AI 解读

By comparing the expansions of the empirical log-likelihood ratio and the empirical cumulant generating function calculated at the saddlepoint, we investigate the relationship between empirical likelihood and empirical saddlepoint approximations. This leads to a nonparametric approximation of the density of a multivariate M-estimator based on the empirical likelihood and, on the other hand, it provides nonparametric confidence regions based on the empirical cumulant…

存在干扰参数时的局部辅助性AI 解读

Approximate ancillarity in the presence of a nuisance parameter is considered. A theory of approximate S-ancillarity, based on the concept of local ancillarity introduced by Cox (1980), is developed. First- and second-order local S-ancillarity are considered in detail and these results are applied to several examples. These examples indicate that, although first-order local S-ancillarity is a weak condition, second-order local S-ancillarity is too strong a requirement for…

通过 ECM 算法进行最大似然估计：一般框架AI 解读

Two major reasons for the popularity of the EM algorithm are that its maximum step involves only complete-data maximum likelihood estimation, which is often computationally simple, and that its convergence is stable, with each iteration increasing the likelihood. When the associated complete-data maximum likelihood estimation itself is complicated, EM is less attractive because the M-step is computationally unattractive. In many cases, however, complete-data maximum…

一般乘法截距风险模型下病例对照数据的前瞻式分析AI 解读

We show that, under a general multiplicative-intercept model for risk, case-control data can be analyzed by maximum likelihood as if they had arisen prospectively, up to an unidentifiable multiplicative constant which depends on the relative sampling fractions. This generalizes earlier work of Anderson (1972, 1979), by showing that not only the point estimates but also the standard errors based on the observed information matrix are correct when the prospective likelihood is…

lq球对称模型中的稳健贝叶斯推断AI 解读

The class of multivariate lq-spherical distributions is introduced and defined through their isodensity surfaces. We prove that, under a Jeffrey's type improper prior on the scale parameter, posterior inference on the location parameters is the same for all lq-spherical sampling models with common q. This gives us perfect inference robustness with respect to any departures from the reference case of independent sampling from the exponential power distribution.

部分可交换性与调查抽样推断AI 解读

The role of the sampling mechanism for Bayesian inference on symmetric functions of a finite population is examined under partial design and partial label information. A new definition of partial exchangeability is proposed, together with a corresponding property of the sampling mechanism. These properties provide conditions under which certain symmetries in priors or designs can protect against lack of symmetry in others, in the sense of Scott & Smith (1973).

点过程约化二阶矩测度的渐近最优估计AI 解读

A modification of the rigid motion correction estimator for the reduced second moment measure of a stationary, isotropic point process is shown to possess an asymptotic optimality property as the observation region grows. Furthermore, a modification of the translation correction estimator for stationary, anisotropic point processes has a similar optimality property.

含脉冲连续过程采样时间序列的状态空间建模AI 解读

A non-Gaussian time series model useful for describing the dynamics of endocrinological data is introduced by using a state-space representation. This model is applicable even when the data are sparsely sampled in comparison with time lengths of pulses. Likelihood-based methods of inference for the model are developed. By fitting the present model to partially observed hormonal time series data, we can estimate the locations and heights of the peaks of the pulses as well as…

受限权重下序约束推断相关分布的界AI 解读

SUMMARY Level probabilities, which are central to the theory of testing order restricted hypotheses, are intractable in some applications. Thus, approximations for them and the associated distributions are of considerable importance. The level probabilities depend on weights which in some situations are monotonic. For the simple linear and simple tree orderings, we study the improvements in the equal-weights and pattern approximations which arise when the weights are…

用于多项分布额外变异建模的有限混合分布AI 解读

We propose a new distribution to model categorical data exhibiting overdispersion when the overdispersion is believed to be caused by clumped sampling. The proposed distribution is a finite mixture of multinomial random variables. The finite mixture representation facilitates computation of the maximum likelihood estimator. For large cluster sizes, we derive an approximation for the Fisher information matrix of the model, and an explicit expression for the joint asymptotic…

修正剖面似然与 Cox–Reid 调整剖面似然的关系AI 解读

An adjustment to the profile likelihood proposed by Cox & Reid (1987) when the parameters are orthogonal is shown to agree with modified profile likelihood in a number of instances in which the parameters are not orthogonal. Several examples of the phenomenon are given. In the case of composite transformation models with invariant parameter as the parameter of interest, it is shown that the Cox-Reid adjustment agrees with modified profile likelihood in a large-deviation…

利用参考先验消除干扰参数AI 解读

The problem of eliminating nuisance parameters is tackled from different points of view. Standard likelihood techniques, such as profile likelihood and its modifications, are compared with a Bayesian analysis based on reference priors (Berger & Bernardo, 1992a). Examples are considered to illustrate what happens in multiparameter problems. In particular the frequentist coverage probabilities of the credible sets derived from the reference priors are shown to be better than…

累积和、冯·诺伊曼与基于平滑的拟合优度检验的共同框架AI 解读

Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the von Neumann (1941) test, while that of Buckley is based on a functional of cusums. These tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas. Fourier analysis is used to qualitatively compare the Munson & Jernigan and Buckley tests…

利用先验信息的非参数样条回归AI 解读

SUMMARY By using prior information about the regression curve we propose new nonparametric regression estimates. We incorporate two types of information. First, we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation. The regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty. We discuss in particular growth and…

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…