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单调性的非参数贝叶斯检验AI 解读

This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to…

半参数优势比模型迭代算法收敛性的一则说明AI 解读

This paper points out an error in Davidov and Iliopoulos's (Biometrika100, 778–80) proof of convergence of an iterative algorithm for the proportional likelihood ratio model. It is shown that the iterative algorithm increases the likelihood in each iteration and converges under mild additional conditions when the odds ratio function is bounded.

时间序列非线性序列依赖的熵检验AI 解读

We propose tests for nonlinear serial dependence in time series under the null hypothesis of general linear dependence, in contrast to the more widely studied null hypothesis of independence. The approach is based on combining an entropy dependence metric, which possesses many desirable properties and is used as a test statistic, with a suitable extension of surrogate data methods, a class of Monte Carlo distribution-free tests for nonlinearity, and a smoothed sieve…

分量最大值发生时点与多元最大稳定分布似然推断偏差AI 解读

Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, |$d$|-dimensional likelihood inference is usually precluded due to the large number of terms in the likelihood. However, some studies have noted bias when performing high-dimensional inference that incorporates such event information, particularly when dependence is…

依赖型现状数据的筛最大似然回归分析AI 解读

Current status data occur in contexts including demographic studies and tumorigenicity experiments. In such cases, each subject is observed only once and the failure time of interest is either left- or right-censored (Kalbfleisch & Prentice, 2002). Many methods have been developed for the analysis of such data (Huang, 1996; Sun, 2006), most of which assume that the failure time and the observation time are independent completely or given covariates. In this paper, we present…

通过自适应基函数抽样高效计算平滑样条AI 解读

Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be…

稳健协方差代入方法的注意事项AI 解读

The sample covariance matrix, which is well known to be highly nonrobust, plays a central role in many classical multivariate statistical methods. A popular way of making such multivariate methods more robust is to replace the sample covariance matrix with some robust scatter matrix. The aim of this paper is to point out that multivariate methods often require that certain properties of the covariance matrix hold also for the robust scatter matrix in order for the…

高通量筛查中假阳性数量的有效估计AI 解读

This paper develops tail estimation methods to handle false positives in multiple testing problems where testing is done at extreme significance levels and with low degrees of freedom, and where the true null distribution may differ from the theoretical one. We show that the number of false positives, conditional on the total number of positives, has an approximately binomial distribution, and we find estimators of the distribution parameter. We also develop methods for…

基于协方差的生物通路分析AI 解读

The use of high-throughput data to study the changing behavior of biological pathways has focused mainly on examining the changes in the means of pathway genes. In this paper, we propose instead to test for changes in the co-regulated and unregulated variability of pathway genes. We assume that the eigenvalues of previously defined pathways capture biologically relevant quantities, and we develop a test for biologically meaningful changes in the eigenvalues between classes.…

有限混合模型的阶数选择：完全似然还是观测似然信息准则？AI 解读

Choosing the number of components in a finite mixture model is a challenging task. In this article, we study the behaviour of information criteria for selecting the mixture order, based on either the observed likelihood or the complete likelihood including component labels. We propose a new observed likelihood criterion called aicmix, which is shown to be order consistent. We further show that when there is a nontrivial level of classification uncertainty in the true model,…

滞回自回归时间序列模型AI 解读

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its…

高维数据的异常值检测AI 解读

Outlier detection is an integral component of statistical modelling and estimation. For high-dimensional data, classical methods based on the Mahalanobis distance are usually not applicable. We propose an outlier detection procedure that replaces the classical minimum covariance determinant estimator with a high-breakdown minimum diagonal product estimator. The cut-off value is obtained from the asymptotic distribution of the distance, which enables us to control the Type I…

充分降维中的诊断方法AI 解读

Sufficient dimension reduction in regression aims to reduce the predictor dimension by replacing the original predictors with some set of linear combinations of them without loss of information. Numerous dimension reduction methods have been developed based on this paradigm. However, little effort has been devoted to diagnostic studies within the context of dimension reduction. In this paper we introduce methods to check goodness-of-fit for a given dimension reduction…

乘法区域模型中带基准约束的经验贝叶斯方法与风险评估AI 解读

The paper develops hierarchical empirical Bayes and benchmarked hierarchical empirical Bayes estimators of positive small area means under multiplicative models. The usual benchmarking requirement is that the small area estimates, when aggregated, should equal the direct estimates for the larger geographical areas. However, while estimating positive small area parameters, the conventional squared error or weighted squared error loss subject to the usual benchmark constraint…

利用非归一化模型进行重污染下的稳健估计AI 解读

Contamination caused by outliers is inevitable in data analysis, and robust statistical methods are often needed. In this paper we develop a new approach for robust data analysis on the basis of scoring rules. A scoring rule is a discrepancy measure to assess the quality of probabilistic forecasts. We propose a simple method of estimating not only parameters in the statistical model but also the contamination ratio, i.e., the ratio of outliers. The outliers are detected…

用于不连续曲线估计与统计推断的跳跃信息准则AI 解读

Nonparametric regression analysis when the regression function is discontinuous has many applications. Existing methods for estimating a discontinuous regression curve usually assume that the number of jumps in the regression curve is known beforehand, which is unrealistic in some situations. Although there has been research on estimation of a discontinuous regression curve when the number of jumps is unknown, the problem remains mostly open because such research often…

大规模同时推断中稀疏模式的层次识别AI 解读

We study how to separate signals from noisy data accurately and determine the patterns of the selected signals. Controlling the inflation of false positive errors is important in large-scale simultaneous inference but has not been addressed in the pattern recognition literature. We develop a decision-theoretic framework and formulate the sparse pattern recognition problem as a simultaneous inference problem with multiple decision trees. Oracle and adaptive classifiers are…

面向统计应用的 Davis–Kahan 定理变体AI 解读

The Davis–Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between certain population and sample eigenvalues. We present a variant of this result that depends only on a population eigenvalue separation condition, making it more natural and convenient for direct application in statistical contexts, and…

随机效应元分析AI 解读

Meta-analysis is widely used to compare and combine the results of multiple independent studies. To account for between-study heterogeneity, investigators often employ random-effects models, under which the effect sizes of interest are assumed to follow a normal distribution. It is common to estimate the mean effect size by a weighted linear combination of study-specific estimators, with the weight for each study being inversely proportional to the sum of the variance of the…

用验证信息准则确定降维模型的结构维数AI 解读

A crucial component of performing sufficient dimension reduction is to determine the structural dimension of the reduction model. We propose a novel information criterion-based method for this purpose, a special feature of which is that when examining the goodness-of-fit of the current model, one needs to perform model evaluation by using an enlarged candidate model. Although the procedure does not require estimation under the enlarged model of dimension k+1, the decision as…

稀疏函数型数据的有效降维AI 解读

We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space, via functional cumulative slicing. Our theoretical study reveals a bias-variance trade-off associated with the regularizing truncation and…

包络方法与降秩回归AI 解读

We incorporate the nascent idea of envelopes (Cook et al., Statist. Sinica20, 927–1010) into reduced-rank regression by proposing a reduced-rank envelope model, which is a hybrid of reduced-rank and envelope regressions. The proposed model has total number of parameters no more than either of reduced-rank regression or envelope regression. The resulting estimator is at least as efficient as both existing estimators. The methodology of this paper can be adapted to other…

二元复发事件过程的依赖结构：推断与估计AI 解读

Bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest. There has been much research on regression analysis for such data, but little has been done to measure the dependence between recurrent event processes. We propose a time-dependent measure, termed the rate ratio, to assess the local dependence between two types of recurrent event processes. We model the rate ratio as a…

由 Möbius 变换诱导的环面分布AI 解读

We propose a five-parameter bivariate wrapped Cauchy distribution as a unimodal model for toroidal data. It is highly tractable, displays numerous desirable properties, including marginal and conditional distributions that are all wrapped Cauchy, and arises as an appealing submodel of a six-parameter distribution obtained by applying Möbius transformation to a pre-existing bivariate circular model. Method of moments and maximum likelihood estimation of its parameters are…