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局部最大似然估计与推断AI 解读

Summary Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local…

超额质量与 Dip 峰态检验的校准AI 解读

Summary Nonparametric tests of modality are a distribution-free way of assessing evidence about inhomogeneity in a population, provided that the potential sub populations are sufficiently well separated. They include the excess mass and dip tests, which are equivalent in univariate settings and are alternatives to the bandwidth test. Only very conservative forms of the excess mass and dip tests are available at presently, however, and for that reason they are generally not…

混合效应模型的快速EM类算法实现AI 解读

Summary The mixed effects model, in its various forms, is a common model in applied statistics. A useful strategy for fitting this model implements EM-type algorithms by treating the random effects as missing data. Such implementations, however, can be painfully slow when the variances of the random effects are small relative to the residual variance. In this paper, we apply the ‘working parameter’ approach to derive alternative EM-type implementations for fitting mixed…

二元分位数平滑样条AI 解读

Summary It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as nonparametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used…

多元贝叶斯变量选择与预测AI 解读

Summary The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high…

赤池信息准则统一化的一则札记AI 解读

Summary To measure the distance between a robust function evaluated under the true regression model and under a fitted model, we propose generalized Kullback–Leibler information. Using this generalization we have developed three robust model selection criteria, AICR*, AICCR* and AICCR, that allow the selection of candidate models that not only fit the majority of the data but also take into account non-normally distributed errors. The AICR* and AICCR criteria can unify most…

具有次序约束的多元极值AI 解读

Summary Multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction. The approach extends the multivariate threshold methodology of Coles and Tawn, Joe and co-workers and Smith and co-workers. The results are illustrated by an analysis of extreme rainfalls of different durations, and by a study of the problem of linking a long series of daily rainfall extremes with a partially…

两阶段层级模型中的三目标估计AI 解读

Summary The beauty of the Bayesian approach is its ability to structure complicated models, inferential goals and analyses. To take full advantage of it, methods should be linked to an inferential goal via a loss function. For example, in the two-stage, compound sampling model the posterior means are optimal under squared error loss. However, they can perform poorly in estimating the histogram of the parameters or in ranking them. ‘Triple-goal’ estimates are motivated by the…

基于经验分布函数的两两序列独立性检验AI 解读

Summary Built on Skaug and Tjøstheim's approach, this paper proposes a new test for serial independence by comparing the pairwise empirical distribution functions of a time series with the products of its marginals for various lags, where the number of lags increases with the sample size and different lags are assigned different weights. Typically, the more recent information receives a larger weight. The test has some appealing attributes. It is consistent against all…

含离群值抽样调查的偏差校准估计AI 解读

Summary We discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers. We clarify the motivation for Chambers's bias-calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters. We then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the…

调查数据的有限信息似然分析AI 解读

Summary Analysts of survey data are often interested in modelling the population process, or superpopulation, that gave rise to a ‘target’ set of survey variables. An important tool for this is maximum likelihood estimation. A survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst. In this circumstance, sample inclusion probabilities, which are typically available, provide information which…

小区域估计中贝叶斯与频率学派的误差度量AI 解读

Summary This paper compares analytically and empirically the frequentist and Bayesian measures of error in small area estimation. The model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables. When the variance components are known, then, under a uniform prior for the regression coefficients and normality of the error…

自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

工业时间序列中可能不连续出现的异常值检测AI 解读

Summary A method for robust estimation and multiple outlier detection in time series generated by autoregressive integrated moving average processes in industrial environments is developed. The procedure is based on reweighted maximum likelihood estimation using Huber or redescending weights and, therefore, generalizes the well-established robust M-estimation procedures used in the regression framework. When the scalar process is non-stationary, the computations required can…

利用改进的 Akaike 信息准则选择非参数回归的平滑参数AI 解读

Summary Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the…

辛普森悖论与贝叶斯因子AI 解读

Summary A counter-example presented by Lindley to Aitkin’s posterior Bayes factor is examined. The paradoxical feature of the counter-example is found to be a simple case of Simpson’s paradox.

已知总样本量时偏倚与截断数据的半参数似然推断AI 解读

Summary Biased and truncated data arise in many practical areas. Many efficient statistical methods have been studied in the literature. This paper discusses likelihood-based inferences for the two types of data in the presence of auxiliary information of known total sample size. It is shown that this information improves inference about the underlying distribution and its parameters in which we are interested. A semiparametric likelihood ratio confidence interval technique…

相似分布的非参数验证与拟合优度评估AI 解读

Summary In this paper the problem of assessing the similarity of two cumulative distribution functions F and G is considered. An asymptotic test based on an α-trimmed version of Mallows distance Γα(F, G) between F and G is suggested, thus demonstrating the similarity of F and G within a preassigned Γα(F, G) neighbourhood at a controlled type I error rate. The test proposed is applied to the validation of goodness of fit and for the nonparametric assessment of bioequivalence.…

可分非参数模型中积分估计与回拟合估计的优化解释AI 解读

Summary We provide an optimization interpretation of both back-fitting and integration estimators for additive nonparametric regression. We find that the integration estimator is a projection with respect to a product measure. We also provide further understanding of the back-fitting method.

一般协方差结构线性模型的残差AI 解读

Summary A general theory is presented for residuals from the general linear model with correlated errors. It is demonstrated that there are two fundamental types of residual associated with this model, referred to here as the marginal and the conditional residual. These measure respectively the distance to the global aspects of the model as represented by the expected value and the local aspects as represented by the conditional expected value. These residuals may be…

变量含测量误差的多项式回归AI 解读

Summary A polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients, assuming hypothetically the latent true regressor variable to be known, and then adjusting for the errors. If normality of the error variables can be assumed, the estimator can be simplified considerably. Only the variance of the errors in the regressor variable and its covariance with…

贝叶斯自助法与可交换抽球方案族的扩展AI 解读

Summary A Bayesian bootstrap for a finite population with censored observations is introduced. It is shown to reduce to the finite population Bayesian bootstrap if there is no censoring and to reduce to the censored data Bayesian bootstrap for a large population. A class of general urn schemes for simulating exchangeable sequences of variables is introduced which is connected to the bootstrap method.

混合效应平滑样条方差分析AI 解读

Summary We propose a general family of nonparametric mixed effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a…

多元位置的自适应变换—逆变换估计AI 解读

Summary An affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied. The work is primarily motivated by earlier work on different versions of the multivariate median and their properties. We explore an issue related to efficiency and equivariance that was originally raised by Bickel and subsequently investigated by Brown and Hettmansperger. Our estimate has better asymptotic performance than the vector…