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SUMMARY This paper describes an approach to Bayesian sensitivity analysis that uses an influence statistic and an outlier statistic to assess the sensitivity of a model to perturbations. The basic outlier statistic is a Bayes factor, whereas the influence statistic depends strongly on the purpose of the analysis. The task of influence analysis is aided by having an interpretable influence statistic. Two alternative divergences, an L 1-distance and a χ2-divergence, are…

连续统回归并不总是连续AI 解读

SUMMARY Continuum regression (CR) is regression of a response y on that linear combination t γ of explanatory variables which maximizes r 2(y, t) var(t)γ, where γ is chosen from a continuum of candidates. CR includes several common methods as special cases: ordinary least squares, principal component regression, partial least squares and a modified ridge regression. We demonstrate that CR, despite its name, can yield a predictor that is a discontinuous function of γ and of…

层级广义线性模型AI 解读

SUMMARY We consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models. The distribution of these components is not restricted to be normal; this allows a broader class of models, which includes generalized linear mixed models. We use a generalization of Henderson's joint likelihood, called a hierarchical or h-likelihood, for inferences from hierarchical generalized linear models. This avoids the…

有限混合模型中的自助法似然比推断AI 解读

SUMMARY Statistical inference using the likelihood ratio statistic for the number of components in a mixture model is complicated when the true number of components is less than that of the proposed model since this represents a non-regular problem: the true parameter is on the boundary of the parameter space and in some cases the true parameter is in a nonidentifiable subset of the parameter space. The maximum likelihood estimator is shown to converge to the subset…

模型增加参数的代价AI 解读

SUMMARY For a general regression model with n independent observations we consider the variance of the estimate of a quantity of interest under two scenarios. One scenario is where all the parameters are estimated from the data; the other scenario is where a subset of the parameters is assumed known at their true values and the remaining parameters are estimated. We focus on quantities of interest which are defined on the scale of the response variable. We show that, under…

广义线性模型残差最大似然估计的条件似然方法AI 解读

SUMMARY Residual maximum likelihood (REML) estimation is often preferred to maximum likelihood estimation as a method of estimating covariance parameters in linear models because it takes account of the loss of degrees of freedom in estimating the mean and produces unbiased estimating equations for the variance parameters. In this paper it is shown that REML has an exact conditional likelihood interpretation, where the conditioning is on an appropriate sufficient statistic…

双重删失当前状态数据的回归AI 解读

SUMMARY Data from settings in which an initiating event and a subsequent event occur in sequence are called doubly censored current status data if the time of neither event is observed directly, but instead it is determined at a random monitoring time whether either the initiating or subsequent event has yet occurred. This paper is concerned with using doubly censored current status data to estimate the regression coefficient in an accelerated failure time model for the…

马尔可夫链蒙特卡洛中样本均值的渐近效率AI 解读

SUMMARY In many cases, a univariate time series derived from a time reversible stationary Markov chain has the property that there is a distribution function on [–1, 1] ([0, 1]) such that, for all non-negative integers l, its lth moment is the lth lag autocorrelation of the time series. We discuss some consequences of this property. Effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary Markov chain are discussed. The…

空间格点数据统计量的方差估计AI 解读

SUMMARY A statistic s() is computed on spatially indexed data {X i: i ∈ D), where D is a finite subset of the integer lattice Z2. We propose a method for estimating the variance (and other moments) of s() by using only the data. The set D may be irregularly shaped, the statistic s() may be arbitrarily complicated and no distributional assumptions (marginal or joint) are necessary. The method uses the statistic computed on overlapping 'subshapes' of D as replicates of s().…

用伪数据方法消除核密度估计的边界效应AI 解读

SUMMARY We suggest a method for boundary correcting kernel density estimators, based on generating pseudodata beyond the extremities of the density's support. The estimator produced in this way enjoys optimal orders of bias and variance right up to the ends of the support, and it may be used with kernels of arbitrary order. Our method is considerably more adaptive than the common data reflection approach, which is not really appropriate for kernels of order 2 or more since…

对数线性与逻辑斯蒂模型的蒙特卡洛精确条件检验AI 解读

SUMMARY The form of the exact conditional distribution of a sufficient statistic for the interest parameters, given a sufficient statistic for the nuisance parameters, is derived for a generalized linear model with canonical link. General results for log-linear and logistic models are given. A Gibbs sampling approach for generating from the conditional distribution is proposed, which enables Monte Carlo exact conditional tests to be performed. Examples include tests for…

基于极端值的参数生存模型检验AI 解读

SUMMARY Hougaard proposed a scaled, exponentially tilted, positive stable distribution for the frailty in survival analysis. This leads to a class of survivor functions which encompasses certain special cases. Some tests based on extreme sample values are proposed for assessing the fit of these submodels within a full model. The tests are applied to some data on the breaking strengths of carbon fibres.

预测更新方法及其在贝叶斯分类中的应用AI 解读

SUMMARY We propose algorithms based on random draws from predictive distributions of unknown quantities (missing values, for instance). This procedure can either be iterative, which is a special variation of the Gibbs sampler, or be sequential, which is a variation of sequential imputation. In the latter case one can update the posterior distribution with new observations easily. The methods proposed have intuitive statistical implications and can be generalized to…

稀疏数据下广义线性模型的拟合优度评估AI 解读

SUMMARY Approximations to the first three moments of Pearson's statistic are obtained for non-canonical generalized linear models, extending the results of McCullagh. A first-order modification to Pearson's statistic is proposed which induces local orthogonality with the regression parameters, resulting in substantial simplifications and increased power. Accurate and easily computed approximations to the moments of the modified Pearson statistic conditional on the estimated…

拟似然与 EM 算法的推广AI 解读

SUMMARY This paper is concerned with situations in which there are missing or otherwise incomplete data and the full likelihood may not be available. Extensions of the EM algorithm are developed to deal with estimation via general estimating functions and in particular the quasi-score. The E-step is replaced by projecting the quasi-score and the M-step requires the solution of an estimating equation. The standard EM algorithm can be obtained as a particular case if the…

贝叶斯线性充分性与专家后验评估系统AI 解读

SUMMARY Data arising in the form of expert assessments are received by a decision maker. The decision maker is required to estimate a set of unknown quantities, and receives expert assessments at varying levels of accuracy, on samples of the quantities of interest. We present a Bayes linear analysis of this problem. In the absence of other assessments, the decision maker will accept as his or her current estimate of any single quantity the most accurate received assessment…

使用交叉验证的小波收缩AI 解读

SUMMARY Wavelets are orthonormal basis functions with special properties that show potential in many areas of mathematics and statistics. This paper concentrates on the estimation of functions and images from noisy data by using wavelet shrinkage. A modified form of twofold cross-validation is introduced to choose a threshold for wavelet shrinkage estimators operating on data sets of length a power of 2. The cross-validation algorithm is then extended to data sets of any…

非线性小波回归中平滑、阈值与截断参数的选择AI 解读

SUMMARY Concise asymptotic theory is developed for non-linear wavelet estimators of regression means, in the context of general error distributions, general designs, general normalizations in the case of stochastic design, and non-structural assumptions about the mean. The influence of the tail weight of the error distribution is addressed in the setting of choosing threshold and truncation parameters. Mainly, the tail weight is described in an extremely simple way, by a…

分层有限总体中的准线性贝叶斯估计AI 解读

SUMMARY In this paper a Bayesian least squares approximation is proposed for descriptive inference in a finite population when a categorical auxiliary variable is known. A hierarchical model II analysis of variance is assumed. The solution consists of a projection on the vector of group totals and on the between and within sums of squares. The approximation can be seen as a normal approximation of the joint distribution of the statistic and of the parameter of interest,…

多项分布协方差矩阵的谱分解AI 解读

SUMMARY This paper gives information about the spectral decomposition of the covariance matrices of a multinomial. It is a note to the paper of Tanabe and Sagae which gives fascinating information about the Cholesky decomposition of the covariance matrices of multinomial distributions.

多项与泊松对数线性模型的比较AI 解读

SUMMARY We introduce a method for comparing multinomial and Poisson log-linear models which affords an explicit description of their equivalences and differences. The method involves specifying the model in terms of constraint equations, rather than the more common freedom equations. The Poisson and multinomial large sample distributions of log-linear model parameter estimators are derived and compared within this constraint equation context; reparameterizations are thereby…

SUMMARY A version of the sequential probability ratio test for testing simultaneously a set of nested hypotheses is developed. This procedure is then applied to define a sequential procedure of sampling at the inner level of the two nested levels of resampling required by Monte Carlo construction of an iterated bootstrap percentile method confidence interval. The sequential resampling scheme reduces very significantly the computational demands of construction of the iterated…

Cramér–von Mises统计量的精确分布与渐近分布AI 解读

SUMMARY It is shown that an asymptotically precise one-term correction to the asymptotic distribution function of the classical Cramér-von Mises statistic approximates the exact distribution function remarkably closely for sample sizes as small as 7 or even smaller. This correction can be quickly evaluated, and hence it is suitable for the computation of practically exact p-values when testing simple goodness of fit. Similar findings hold for Watson's rotationally invariant…

离散与连续重复测量中随机化后协变量的处理AI 解读

SUMMARY Adjusting for covariates observed post randomization is a difficult issue in randomized clinical trials. One approach is to enter these covariates as time-dependent covariates in a general linear model. However, this approach fails to account for interactions between the primary end point and confounding variable as they evolve over time. In this paper, we adopt the view that, since the confounder is observed following randomization, it should be treated as an…