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分位数回归的贝叶斯经验似然AI 解读

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal;…

基于新型有序回归模型的老年人功能状态预测AI 解读

The functional mobility of the elderly is a very important factor in aging research, and prognostic information is valuable in making clinical and health care policy decisions. We develop a predictive model for the functional status of the elderly based on data from the Second Longitudinal Study of Aging (LSOA II). The functional status is an ordinal response variable. The ordered probit model has been moderately successful in analyzing such data; however, its reliance on…

高效随机化自适应设计AI 解读

Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer–Rao lower bounds on the allocation variances for any allocation proportions, including optimal allocation proportions. The allocation probability functions of proposed procedures are discontinuous. The existing large sample theory for adaptive designs relies on…

基于奇异值分解的可变剪接检测AI 解读

Altered alternative splicing has been identified as an important factor in tumorigenesis. The Affymetrix exon tiling array is designed for detecting alternative splicing events in a transcriptome-wide fashion; however, there are currently few analysis tools that are well studied for effective detection of alternative splicing events. We propose a new screening procedure based on singular value decomposition (SVD) of the residual matrix from a robust additive model fit to…

基于约束典型相关与变量筛选的降维AI 解读

The “curse of dimensionality” has remained a challenge for high-dimensional data analysis in statistics. The sliced inverse regression (SIR) and canonical correlation (CANCOR) methods aim to reduce the dimensionality of data by replacing the explanatory variables with a small number of composite directions without losing much information. However, the estimated composite directions generally involve all of the variables, making their interpretation difficult. To simplify the…

通过幂变换构建线性分位数回归AI 解读

In this article we consider the linear quantile regression model with a power transformation on the dependent variable. Like the classical Box–Cox transformation approach, it extends the applicability of linear models without resorting to nonparametric smoothing, but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations. We propose an estimation procedure and establish its consistency and…

A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252–260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252–260]. The present paper proves the conjecture…

广义部分线性模型中的稳健估计AI 解读

In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by yi|(xi, ti)∼F(⋅, μi) with μi=H(η(ti)+xiTβ), for some known distribution function F and link function H. It is shown that the estimates of β are root-n consistent and asymptotically normal. Through a Monte Carlo study, the performance of these estimators is compared with that of the classical ones.

条件生长图模型讨论的作者回复AI 解读

First of all, we would like to thank all the discussants for their encouragement of and insightful comments on our work.We are especially appreciative of their unique perspectives brought to the topic of conditional growth charts.The discussants raised a number of interesting questions from statistical as well as clinical points of view, some of which are broader and deeper than what we will be able to address fully in this rejoinder.Our rejoinder will focus on the issues…

条件生长曲线图AI 解读

Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions. The model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers, and it is…

分组数据下的稳健与有效估计AI 解读

The minimum Hellinger distance estimator is known to have desirable properties in terms of robustness and efficiency. We propose an approximate minimum Hellinger distance estimator by adapting the approach to grouped data from a continuous distribution. It is easier to compute the approximate version for either the continuous data or the grouped data. Given certain conditions on the model distribution and reasonable grouping rules, the approximate minimum Hellinger distance…

聚类数据广义部分线性模型的稳健估计AI 解读

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated…

Stahel–Donoho 估计量与多元数据的深度加权均值AI 解读

The depth of multivariate data can be used to construct weighted means as robust estimators of location. The use of projection depth leads to the Stahel-Donoho estimator as a special case. In contrast to maximal depth estimators, the depth-weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature. We also confirm through a finite-sample study that the Stahel-Donoho estimator achieves a…

摘要暂缺

马尔可夫链边际自助法AI 解读

Markov chain marginal bootstrap (MCMB) is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of M estimators of linear regression. The MCMB method distinguishes itself from the usual bootstrap methods in two important aspects: it involves solving only one-dimensional equations for parameters of any dimension and produces a Markov chain rather than a (conditionally) independent…

半参数混合模型的影响诊断与异常值检验AI 解读

Summary Semiparametric mixed models are useful in biometric and econometric applications, especially for longitudinal data. Maximum penalized likelihood estimators (MPLEs) have been shown to work well by Zhang and co-workers for both linear coefficients and nonparametric functions. This paper considers the role of influence diagnostics in the MPLE by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric…

回归与多变量位置最大深度估计量的渐近分布AI 解读

We derive the asymptotic distribution ofthe maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and the limiting distribution is characterized through a max–min operation of a continuous process. The same techniques can be used to obtain the limiting distribution of some other depth estimators including Tukey’s deepest point based on half-space depth. Results for the special case of…

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…

单调 B 样条平滑AI 解读

Estimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated. Built on the ideas of Koenker, Ng, and Portnoy and Ramsay, we propose monotone B-spline smoothing based on L 1 optimization. This method inherits the desirable properties of spline approximations and the computational…

摘要暂缺

M 估计量的一般 Bahadur 表示及其在非随机设计线性回归中的应用AI 解读

We obtain strong Bahadur representations for a general class of M-estimators that satisfies $\Sigma_i \psi (x_i, \theta) = o(\delta_n)$, where the $x_i$'s are independent but not necessarily identically distributed random variables. The results apply readily to M-estimators of regression with nonstochastic designs. More specifically, we consider the minimum $L_p$ distance estimators, bounded influence GM-estimators and regression quantiles. Under appropriate design…

线性模型中影响有界且具有高崩溃点的检验程序AI 解读

Three classes of testing procedures based on one-step high breakdown point bounded influence estimators, for testing subhypotheses in linear models are developed. These are drop-in-dispersion, Wald-type, and score-type tests. The asymptotic distributions of these testing procedures are obtained under the null hypothesis and under contiguous alternatives. Their stability properties are studied in terms of their influence functions and breakdown points. It is shown that the…

摘要暂缺

污染偏差的下界：全局极小极大与局部线性估计AI 解读

We study how robust estimators can be in parametric families, obtaining a lower bound on the contamination bias of an estimator that holds for a wide class of parametric families. This lower bound includes as a special case the bound used to establish that the median is bias minimax among location equivariant estimators, and it is tight or nearly tight in a variety of other settings such as scale estimation, discrete exponential families and multiple linear regression. The…