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重复微阵列时间进程数据的多元经验贝叶斯统计量AI 解读

In this paper we derive one- and two-sample multivariate empirical Bayes statistics (the MB-statistics) to rank genes in order of interest from longitudinal replicated developmental microarray time course experiments. We first use conjugate priors to develop our one-sample multivariate empirical Bayes framework for the null hypothesis that the expected temporal profile stays at 0. This leads to our one-sample MB-statistic and a one-sample T̃2-statistic, a variant of the…

最优子集选择、高维统计学习的持续性与 l1 约束优化AI 解读

Let (Y, X1, …, Xm) be a random vector. It is desired to predict Y based on (X1, …, Xm). Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the problem of best subset selection, and study it in the context m=nα, α>1, where n is the number of observations. We investigate procedures that are based on empirical risk minimization. It is shown, that in common cases, we should aim to find the…

统计学习的风险界AI 解读

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov’s analysis of the risk of an ERM under margin type conditions by using concentration inequalities for conveniently weighted empirical processes. This allows us to deal with ways of measuring the “size” of a class of classifiers other than entropy with bracketing as in Tsybakov’s work. In…

二次泛函的最优自适应估计AI 解读

Adaptive estimation of a quadratic functional over both Besov and Lp balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and Lp balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate adaptive over the entire range of Besov and Lp balls in the sense that it attains…

加性模型的一种简便平滑后拟合方法AI 解读

In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya–Watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting. Each component is estimated with the same asymptotic accuracy as if the other components were known.

基于投影深度的多维截尾均值AI 解读

As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The…

从 ε 熵到 KL 熵：最小信息复杂度密度估计分析AI 解读

We consider an extension of ɛ-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators. Consequences of the new inequality will be presented. In particular, we show that this technique can lead to improvements of some classical results concerning the convergence…

函数型线性回归中的预测AI 解读

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical interest in the slope centers on its application for the purpose of prediction, rather than on its significance in its own right. We show that the problems of slope-function estimation, and of prediction from an estimator of the slope function,…

泊松过程的逆问题AI 解读

In this paper we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization, we find that our method combines the well-known theoretical advantages of wavelet–vaguelette decompositions for inverse problems in terms of optimally adapting to the unknown smoothness of the solution, together with the remarkably simple closed-form expressions of Galerkin inversion…

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…

关于纵向条件百分位图的讨论意见AI 解读

I will use the terms "reference centiles" or "centile charts," as the setting that I consider here is more general than that of "growth charts."Longitudinal reference centiles over some measure of time (typically age) are almost always implemented repeatedly on the same individual.In this kind of setting the notion of conditional or adaptive centile charts is very appealing, particularly when the within-individual variability is much less than that between individuals.While…

关于条件生长曲线方法的讨论AI 解读

Overview.Wei and He are to be congratulated on an innovative and important article.The conditional approach to growth charts described in their article is important in a practical sense, and the use of quantile regression is both natural and well motivated.We look forward to further application of their idea to actual practice, because the concept of "falling behind" in one's growth cycle has two meanings: the usual standard growth chart, and the conditional growth chart…

能否估计模型选择后估计量的条件分布？AI 解读

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion such as AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based…

多元非参数回归中的分量选择与平滑AI 解读

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The “COSSO” is a method of regularization with the penalty functional being the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. The COSSO provides a unified framework for several recent proposals for model selection in linear models and smoothing spline ANOVA models.…

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…

状态空间模型中的有效似然估计AI 解读

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root…

尾部 copula 过程的加权近似及二元极值条件检验AI 解读

Consider n i.i.d. random vectors on ℝ2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which…

重尾分布高分位数的置信域AI 解读

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.

扩散过程与Itô过程的方差分析AI 解读

Itô processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such Itô processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the…

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range dependent data. The results are applied to isotonic regression, isotonic regression after kernel smoothing, estimation of convex regression functions, and estimation of monotone and convex density functions. Various pointwise limit…

纹理合成与随机场的非参数重抽样AI 解读

This paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields. The motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields. We give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a…

嵌套误差回归模型中均方预测误差的非参数估计AI 解读

Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and mean-squared prediction error is the main way in which prediction performance is measured. In this paper we suggest a new approach to estimating mean-squared prediction error. We introduce a matched-moment, double-bootstrap algorithm, enabling…

非参数自回归与非参数回归的渐近等价性AI 解读

It is proved that nonparametric autoregression is asymptotically equivalent in the sense of Le Cam’s deficiency distance to nonparametric regression with random design as well as with regular nonrandom design.

风险包络方法与不适定逆问题的投影正则化AI 解读

We study a standard method of regularization by projections of the linear inverse problem Y=Af+ε, where ε is a white Gaussian noise, and A is a known compact operator with singular values converging to zero with polynomial decay. The unknown function f is recovered by a projection method using the singular value decomposition of A. The bandwidth choice of this projection regularization is governed by a data-driven procedure which is based on the principle of risk hull…