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利用平滑间隔函数分析提升算法AI 解读

We introduce a useful tool for analyzing boosting algorithms called the “smooth margin function,” a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, “coordinate ascent boosting” and “approximate coordinate ascent boosting,” which are similar to Freund and Schapire’s AdaBoost algorithm and Breiman’s arc-gv algorithm. We give convergence rates to the maximum margin solution for both of our…

纵向研究中随机效应协方差矩阵的估计AI 解读

Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an estimator be improved by incorporating the within cluster correlation structure into the estimation procedure, but also the within cluster correlation structure can sometimes provide valuable insights in practical problems. For example, it…

粗化预测变量下非参数回归的加速收敛AI 解读

We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while one has available a sample (W1, Y1), …, (Wn, Yn) of independent and identically distributed data, representing observations with precisely measured predictors, where E(Yi|Wi)=g(Wi), instead of the smooth regression function g, the target…

非线性加性自回归模型的样条回拟合核平滑AI 解读

Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the “curse of dimensionality.” Under rather weak conditions, we propose spline-backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high-dimensional time series, and theoretically…

讨论：变量数远大于样本量时的 Dantzig 选择器统计估计AI 解读

Professors Candès and Tao are to be congratulated for their innovative and valuable contribution to high-dimensional sparse recovery and model selection.The analysis of vast data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale studies.Many of these data sets exhibit sparsity where most of the data corresponds to noise and only a small fraction is of interest.The needs of this research have excited much…

未知连接函数的一般非参数回归模型的速率最优估计AI 解读

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that…

控制广义 FWER 与广义 FDR 的逐步上升程序AI 解读

In many applications of multiple hypothesis testing where more than one false rejection can be tolerated, procedures controlling error rates measuring at least k false rejections, instead of at least one, for some fixed k≥1 can potentially increase the ability of a procedure to detect false null hypotheses. The k-FWER, a generalized version of the usual familywise error rate (FWER), is such an error rate that has recently been introduced in the literature and procedures…

Correction to The Annals of Statistics (2006) 34, 1013--1044 [URL: http://projecteuclid.org/euclid.aos/1151418250]

协变量含测量误差时多项式模型的适用性检验AI 解读

A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, the true covariates are not directly observed, and conventional bootstrap methods for testing are not applicable. We develop a new approach, in which deconvolution methods are used…

降维方向估计的构造性方法AI 解读

In this paper we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression estimation methods [e.g., J. Amer. Statist. Assoc. 86 (1991) 328–332, J. Amer. Statist. Assoc. 86 (1991) 316–342, J. Amer. Statist. Assoc. 87 (1992) 1025–1039], the new methods require no strong assumptions on the design of…

局部影响分析中的扰动选择与影响度量AI 解读

Cook’s [J. Roy. Statist. Soc. Ser. B 48 (1986) 133–169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is…

稀疏正态混合模型的估计与置信集AI 解读

For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In particular, Ingster and Donoho and Jin have considered a sparse normal means testing problem, in which they described the precise demarcation or detection boundary. Meinshausen and Rice have shown that it is even possible to estimate consistently…

神经脉冲序列概率模型的若干理论结果AI 解读

This article contains two main theoretical results on neural spike train models, using the counting or point process on the real line as a model for the spike train. The first part of this article considers template matching of multiple spike trains. P-values for the occurrences of a given template or pattern in a set of spike trains are computed using a general scoring system. By identifying the pattern with an experimental stimulus, multiple spike trains can be deciphered…

k 单调密度估计：极限分布理论与样条联系AI 解读

We study the asymptotic behavior of the Maximum Likelihood and Least Squares Estimators of a k-monotone density g0 at a fixed point x0 when k>2. We find that the jth derivative of the estimators at x0 converges at the rate n−(k−j)/(2k+1) for j=0, …, k−1. The limiting distribution depends on an almost surely uniquely defined stochastic process Hk that stays above (below) the k-fold integral of Brownian motion plus a deterministic drift when k is even (odd). Both the MLE and…

回应讨论：当变量数远大于样本量时的 Dantzig 选择器统计估计AI 解读

First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation.The comments all underlie the importance and timeliness of the topics discussed in our paper, namely, accurate statistical estimation in high dimensions.We would also like to thank the editors for this opportunity to comment briefly on a few issues raised in the discussions.Of special interest is the diversity of perspectives, which include…

比较回归方法时交叉验证的一致性AI 解读

Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for kernel smoothing). However, little is known about consistency of cross validation when applied to compare between parametric and nonparametric methods or within nonparametric methods. We show that under some conditions, with an appropriate…

通过距离相关度量与检验依赖关系AI 解读

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation…

讨论：Lasso、L2Boosting 与 Dantzig 三种相关方法AI 解读

We would like to congratulate the authors for their thought-provoking and interesting paper.The Dantzig paper is on the timely topic of high-dimensional data modeling that has been the center of much research lately and where many exciting results have been obtained.It also falls in the very hot area at the interface of statistics and optimization: ℓ 1 -constrained minimization in linear models for computationally efficient model selection, or sparse model estimation (Chen,…

回归场景中的条件密度估计AI 解读

Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association between the predictor and the response is relatively simple. More detailed information about the association can be provided by the conditional density of the response given the predictor. For the first time in the literature, this article…

Dantzig 选择器：变量数远大于样本量时的统计估计AI 解读

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n≪p, and the zi’s are i.i.d. N(0, σ2). Is it possible to estimate β reliably based on the noisy data y? To estimate β, we introduce a new estimator—we call it the Dantzig selector—which is a…

阈值统计估计的最优立方根渐近界AI 解读

This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the estimation errors to be large on a scale determined by the inverse cube root of the sample size. As corollaries, we obtain probabilistic bounds for the prediction error in a classification problem. The key to the proof is an entropy estimate. The…

从离散含噪数据估计 Hurst 参数AI 解读

We estimate the Hurst parameter H of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of H more difficult since relevant information is mostly contained in the high frequencies of the signal. We quantify the difficulty of the statistical problem in a min-max sense: we prove that the rate n−1/(4H+2) is optimal for estimating H and propose rate optimal estimators…

正则模型中修正带符号似然比统计量近似的高阶渐近正态性AI 解读

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n−1, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as (θ̂, a), where θ̂ is the maximum likelihood estimator of the parameter θ of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics…

基于变换的鞅估计函数AI 解读

An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. This method involves the construction of classes of transform-based martingale estimating functions that fit into the general framework of quasi-likelihood. In the parametric…