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两阶段结果依赖抽样下逻辑回归参数的最大似然估计AI 解读

Summary Outcome-dependent sampling increases the efficiency of studies of rare outcomes, examples being case—control studies in epidemiology and choice–based sampling in econometrics. Two-phase or double sampling is a standard technique for drawing efficient stratified samples. We develop maximum likelihood estimation of logistic regression coefficients for a hybrid two-phase, outcome–dependent sampling design. An algorithm is given for determining the estimates by repeated…

重复测量剂量—反应关系的随机效应阈值模型AI 解读

Summary A random threshold model for dose--response designs with repeated measurements is introduced. Inference procedures for this model are discussed. The framework of generalized linear models is used to propose a quasi-likelihood inference procedure. The feasibility of this approach is illustrated with the analysis of food science data concerning a forced choice sensory experiment.

不完全观测下的传染病过程估计AI 解读

Summary The construction of estimating equations by martingale methods is generalized to yield estimators with explicit expressions for the parameters of the birth-and-death and the general epidemic processes when only partial observations are available. (For the birth-and-death process the death process is observed but the number of births is observed only at the end and for the general epidemic process only the removal process is observed.) For large populations, the use…

不完整分类数据的简便拟合算法AI 解读

Summary A popular approach to estimation based on incomplete data is the EM algorithm. For categorical data, this paper presents a simple expression of the observed data log-likelihood and its derivatives in terms of the complete data for a broad class of models and missing data patterns. We show that using the observed data likelihood directly is easy and has some advantages. One can gain considerable computational speed over the EM algorithm and a straightforward variance…

标准化统计量分布函数的估计AI 解读

Summary For estimating the distribution of a standardized statistic, the bootstrap estimate is known to be local asymptotic minimax. Various computational techniques have been developed to improve on the simulation efficiency of uniform resampling, the standard Monte Carlo approach to approximating the bootstrap estimate. Two new approaches are proposed which give accurate yet simple approximations to the bootstrap estimate. The second of the approaches even improves the…

可忽略性、充分性与辅助性AI 解读

Summary This paper explores the relationship between ignorability, sufficiency and ancillarity in the coarse data model of Heitjan and Rubin. Bayes or likelihood ignorability has a natural relationship to sufficiency, and frequentist ignorability an analogous relationship to ancillarity. Weaker conditions, termed observed likelihood sufficiency, observed specific sufficiency and observed ancillarity, expand the concepts to models where the coarsening mechanism is sometimes,…

平面点子集的 Procrustes 形状分析AI 解读

Summary Consider a set of points in the plane randomly perturbed about a mean configuration by Gaussian errors. In this paper a Procrustes statistic based on the shapes of subsets of the points is studied, and its approximate distribution is found for small variations. We derive various properties of the distribution including the first two moments, a central limit result and a scaled χ2–-approximation. We concentrate on the independent isotropic Gaussian error case,…

相关噪声数据的小波阈值估计AI 解读

Summary Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level-dependent soft threshold to the coefficients in the wavelet transform. A variety of threshold choices is proposed, including one based on an unbiased estimate of mean-squared error. The practical performance of the method is demonstrated on examples, including data from a neurophysiological context. The theoretical properties of the estimators are investigated…

Gibbs 采样器的更新方案、相关结构、分块与参数化AI 解读

Summary In this paper many convergence issues concerning the implementation of the Gibbs sampler are investigated. Exact computable rates of convergence for Gaussian target distributions are obtained. Different random and non-random updating strategies and blocking combinations are compared using the rates. The effect of dimensionality and correlation structure on the convergence rates are studied. Some examples are considered to demonstrate the results. For a Gaussian image…

Procrustes 估计量的一致性AI 解读

Summary Lele has shown that the Procrustes estimator of form is inconsistent and raised the question about the consistency of the Procrustes estimator of shape. In this paper the consistency of estimators of form and shape is studied under various assumptions. In particular, it is shown that the Procrustes estimator of shape is consistent under the assumption of an isotropic error distribution and that consistency breaks down if the assumption of isotropy is relaxed. The…

加权平均生存检验统计量：删失生存数据的一类距离检验AI 解读

Summary A class of test statistics is introduced which is sensitive against the alternative of stochastic ordering in the two-sample censored data problem. The test statistics for evaluating a cumulative weighted difference in survival distributions are developed while taking into account the imbalances in base-line covariates between two groups. This procedure can be used to test the null hypothesis of no treatment effect, especially when base-line hazards cross and…

混合谱时间序列的半参数贝叶斯推断AI 解读

Summary A Bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms. The periodic terms may have known or unknown frequencies. The advantage of our approach is that different features of the data—such as the regression parameters, the spectral density, unknown frequencies and missing observations—are combined in a…

通过最小化多步预测误差拟合时间序列模型：频域方法AI 解读

Summary This paper brings together two topics in the estimation of time series forecasting models: the use of the multistep-ahead error sum of squares as a criterion to be minimized and frequency domain methods for carrying out this minimization. The methods are developed for the wide class of time series models having a spectrum which is linear in unknown coefficients. This includes the IMA(1, 1) model for which the common exponentially weigh-ted moving average predictor is…

基于预测的选择准则之最优性与估计量收敛速度AI 解读

Summary Several estimators of squared prediction error have been suggested for use in model and bandwidth selection problems. Among these are cross-validation, generalized cross-validation and a number of related techniques based on the residual sum of squares. For many situations with squared error loss, e.g. nonparametric smoothing, these estimators have been shown to be asymptotically optimal in the sense that in large samples the estimator minimizing the selection…

乘性误差平滑回归模型中的变量变换AI 解读

Summary We consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation, i.e. with multiplicative errors. Kernel-based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation. Comparisons are based on the mean-squared error (MSE) or mean integrated squared error (MISE), calculated in the original units. Even when the data are…

基于相关随机效应模型的同质性广义得分检验AI 解读

Summary We present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing. In these models each subject has a particular random effect, but the random effects between subjects are correlated. We derive the general form of the score statistic for testing that the random effects have a variance equal to 0. We apply this result to both parametric and semi-parametric models. In both cases…

回归残差的迭代部分和与连续性约束下的变点检验AI 解读

Summary Iterated partial sum sequences of regression least squares residuals are defined and large sample properties of sequences of stochastic processes defined by these iterated partial sums are discussed. Also, finite sample properties of the iterated partial sum sequences are obtained. These include a property of least squares residuals of polynomial fits to equispaced data, namely the iterated partial sums sum to 0 provided that the order of iteration is not greater…

生存数据混合回归模型中的参数正交性AI 解读

Summary The implications of parameter orthogonality for the robustness of survival regression models are considered. The question of which of the proportional hazards or the accelerated life families of models would be more appropriate for analysis is usually ignored, and the proportional hazards family is applied, particularly in medicine, for convenience. Accelerated life models have conventionally been used in reliability applications. We propose a one-parameter family…

基于“标准化”最优性准则的实验设计AI 解读

Summary We introduce a new class of ‘standardized' optimality criteria which depend on ‘standardized' covariances of the least squares estimators and provide an alternative to the commonly used criteria in design theory. Besides a nice statistical interpretation the new criteria satisfy an extremely useful invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces.

Summary Observational data are often analysed as if they had resulted from a controlled study, and yet the tacit assumption of randomness can be crucial for the validity of inference. We take some simple statistical models and supplement them by adding a parameter θ which reflects the degree of non-randomness in the sample. For a randomized study θ is known to be 0. We examine the profile log-likelihood for θ and the sensitivity of inference to small non-zero values of θ.…

考虑边界的密度导数乘积积分估计AI 解读

Summary Integrated squared density derivatives are important to the plug-in type of bandwidth selector for kernel density estimation. Conventional estimators of these quantities are inefficient when there is a non-smooth boundary in the support of the density. We introduce estimators that utilize density derivative estimators obtained from local polynomial fitting. They retain the rates of convergence in mean-squared error that are familiar from non-boundary cases, and the…

多元线性回归中的多响应预测AI 解读

Summary We look at the problem of predicting several response variables from the same set of explanatory variables. The question is how to take advantage of correlations between the response variables to improve predictive accuracy compared with the usual procedure of doing individual regressions of each response variable on the common set of predictor variables. A new procedure is introduced called the curds and whey method. Its use can substantially reduce prediction…

伪似然比检验统计量的渐近行为AI 解读

SUMMARY This paper concerns the asymptotic distribution of the likelihood ratio statistic T for testing H 0: θ = θ 0 based on the pseudolikelihood L(θ,ϕ^), where ϕ^ is a simple estimator of ϕ. We show that the asymptotic distribution of T under H 0 is a weighted sum of independent χ 1 2-variables where the weights involve the asymptotic joint covariance matrix of ϕ^ and the score function for θ. Some sufficient conditions are provided for the limiting distribution to be χ 2.…

删失时间存在误差时指数分布删失数据的估计AI 解读

SUMMARY The problem of estimating the parameter of the negative exponential distribution with censored data may be complicated by a lack of complete knowledge of the censoring times. The effect of ignoring these errors in the censoring times rather than using a complete maximum likelihood estimation approach is investigated and it is shown that the loss in efficiency is generally small for the inverted gamma model considered in this paper. The theory is supplemented by some…