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通过序贯重心构造随机分布AI 解读

This article introduces and develops a constructive method for generating random probability measures with a prescribed mean or distribution of the means. The method involves sequentially generating an array of barycenters which uniquely defines a probability measure. Basic properties of the generated measures are presented, including conditions under which almost all the generated measures are continuous or almost all are purely discrete or almost all have finite support.…

利用无限维指数族的贝叶斯拟合优度检验AI 解读

We develop a nonparametric Bayes factor for testing the fit of a parametric model. We begin with a nominal parametric family which we then embed into an infinite-dimensional exponential family. The new model then has a parametric and nonparametric component. We give the log density of the nonparametric component a Gaussian process prior. An asymptotic consistency requirement puts a restriction on the form of the prior, leaving us with a single hyperparameter for which we…

对称统计量的经验 Edgeworth 展开AI 解读

In this paper the validity of a one-term Edgeworth expansion for Studentized symmetric statistics is proved. We propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency. As a result we obtain the second-order correctness of the empirical Edgeworth expansion for a very general class of statistics, including $U$-statistics, $L$-statistics and smooth functions of the sample mean. We illustrate the application of the bootstrap…

具有不变性结构的监测问题中误报警平均运行长度AI 解读

Surveillance can be based, in some change-point detection problems, on a sequence of invariant statistics. Gordon and Pollak prove that, under certain conditions, the average run length (ARL) to false alarm of invariance- based Shiryayev–Roberts detection schemes is asymptotically the same as that of the dual classical scheme that is based on the original sequence of observations. In this paper we give alternative conditions under which the two ARLs coincide and demonstrate…

位置 M 估计量的崩溃性质AI 解读

In this article, we consider the asymptotic behavior of three kinds of sample breakdown points. It is shown that for the location $M$-estimator with bounded objective function, both the addition sample breakdown point and the simplified replacement sample breakdown point strongly converge to the gross-error asymptotic breakdown point, whereas the replacement sample breakdown point strongly converges to a smaller value. In addition, it is proved that under some regularity…

近似线性回归中一步 GM 估计量的泛函稳定性AI 解读

This paper provides a comparative sensitivity analysis of one-step Newton–Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by $\varepsilon$-contamination of the model. These bounds yield break-down points and local rates of…

线性模型中的最优稳健检验AI 解读

Robust tests for linear models are derived via Wald-type tests that are based on asymptotically linear estimators. For a robustness criterion, the maximum asymptotic bias of the level of the test for distributions in a shrinking contamination neighborhood is used. By also regarding the asymptotic power of the test, admissible robust tests and most-efficient robust tests are derived. For the greatest efficiency, the determinant of the covariance matrix of the underlying…

SO(N) 上的反卷积密度估计AI 解读

This paper develops nonparametric deconvolution density estimation over $SO(N)$, the group of $N \times N$ orthogonal matrices of determinant 1. The methodology is to use the group and manifold structures to adapt the Euclidean deconvolution techniques to this Lie group environment. This is achieved by employing the theory of group representations explicit to $SO(N)$. General consistency results are obtained with specific rates of convergence achieved under sufficient…

欧氏若尔当代数上格条件独立模型的估计与检验AI 解读

In this paper we generalize the major results of Andersson and Perlman on LCI models to the setting of symmetric cones and give an explicit closed form formula for the estimate of the covariance matrix in the generalized LCI models that we define. To this end, we replace the cone $H_I^+(\mathbb{R})$ sitting inside the Jordan algebra of symmetric real $I \times I$-matrices by the symmetric cone $\Omega$ of an Euclidean Jordan algebra $V$. We introduce the Andersson-Perlman…

缺失数据下广义线性模型的局部线性回归AI 解读

Fan, Heckman and Wand proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions. When the covariate variables are missing at random, we propose a weighted estimator based on the inverse selection probability weights. Distribution theory is derived when the selection probabilities are estimated nonparametrically. We show that the asymptotic variance of the resulting nonparametric estimator of the mean function…

随机截断模型中截断概率的估计AI 解读

Under random truncation, a pair of independent random variables $X$ and $Y$ is observable only if $X$ is larger than $Y$. The resulting model is the conditional probability distribution $H( x, y) =P[X \leq x,Y \leq y|X \geq Y]$. For the truncation probability $\alpha=P[X \geq Y]$, a proper estimate is not the sample proportion but $\alpha_n=\int G_n (s)dF_n(s)$ where $F_n$ and $G_n$ are product limit estimates of the distribution functions $F$ and$G$ of $X$ and$Y$,…

随机截断下的强大数定律AI 解读

The random truncation model is defined by the conditional probability distribution $H (x, y) =P[X\leq x,Y\leq y |X \geq Y] where $X$ and $Y$ are independent random variables. A problem of interest is the estimation of the distribution function $F$ of $X$ with data from the distribution $H$. Under random truncation, $F$ need not be fully identifiable from $H$ and only a part of it, say $F_0$ , is. We show that the nonparametric MLE $F_n$ of $F_0$ obeys the strong law of large numbers in the sense that for any nonnegative, measurable function $…

曲线结构平均的渐近与 Bootstrap 置信界AI 解读

For analyzing samples of curves, Kneip and Gasser proposed a “structural analysis” for estimating an average curve which gives the average amplitude and dynamics of the sample curves. An important step of their method is the estimation of the warping functions in order to eliminate the differences in dynamics between different curves. It is of interest to compute confidence bounds for the structural average curve. First, we derive the necessary asymptotic results to obtain…

加性模型中低维分量的直接估计AI 解读

Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory. In this paper an asymptotic treatment of this estimate is offered for several models. A modification of this…

核与小波曲线估计中的块阈值规则AI 解读

Motivated by recently developed threshold rules for wavelet estimators, we suggest threshold methods for general kernel density estimators, including those of classical Rosenblatt–Parzen type. Thresholding makes kernel methods competitive in terms of their adaptivity to a wide variety of aberrations in complex signals. It is argued that term-by-term thresholding does not always produce optimal performance, since individual coefficients cannot be estimated sufficiently…

k 近邻分类风险的渐近展开AI 解读

The finite-sample risk of the $k$ nearest neighbor classifier that uses a weighted $L^p$-metric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in $mathbb{R}^n$, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal weighted $L^p$-metric, that is, the metric that minimizes the…

通过小波收缩实现极小极大估计AI 解读

We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets, we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients. The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebel- and Besov-type smoothness constraints and asymptotically mini-max over Besov bodies with $p \leq q$. Linear estimates cannot…

Arcing 分类器：附讨论与作者答复AI 解读

Recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error. One of the more effective is bagging. Here, modified training sets are formed by resampling from the original training set, classifiers constructed using these training sets and then combined by voting. Freund and Schapire propose an algorithm the basis of which is to adaptively resample and combine (hence the acronym “arcing”) so…

线性回归模型的验证AI 解读

A new test is proposed in order to verify that a regression function, say $g$, has a prescribed (linear) parametric form. This procedure is based on the large sample behavior of an empirical $L^2$-distance between $g$ and the subspace $U$ spanned by the regression functions to be verified. The asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the $L^2$-distance between the regression…

M_m估计量的Bahadur表示AI 解读

We take a unified approach to asymptotic properties of $M_m$ estimates based on i.i.d. observations defined through the minimization of a real-valued criterion function of one or more variables. Our results are applicable to a host of location and scale estimators found in the literature.

一般条件下L₁回归估计量的极限分布AI 解读

It is well known that $L_1$-estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0. In this paper, we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0.

非平稳自回归模型中残差序贯经验过程的弱收敛AI 解读

This paper establishes the weak convergence of the sequential empirical process $\hat{K}_n$ of the estimated residuals in nonstationary autoregressive models. Under some regular conditions, it is shown that $\hat{K}_n$ converges weakly to a Kiefer process when the characteristic polynomial does not include the unit root 1; otherwise $\hat{K}_n$ converges weakly to a Kiefer process plus a functional of stochastic integrals in terms of the standard Brownian motion. The latter…

长记忆过程的状态空间建模AI 解读

This paper develops a state space modeling for long-range dependent data. Although a long-range dependent process has an infinite-dimensional state space representation, it is shown that by using the Kalman filter, the exact likelihood function can be computed recursively in a finite number of steps. Furthermore, an approximation to the likelihood function based on the truncated state space equation is considered. Asymptotic properties of these approximate maximum likelihood…

截断经验过程的局部渐近正态性AI 解读

Given $n$ iid copies $X_1,\dots, X_n$ of a random element $X$ in some arbitrary measurable space $S$, we are only interested in those observations that fall into some subset $D$ having but a small probability of occurrence. It is assumed that the distribution $P_X$ of $X$ belongs on $D$ to a parametric family $P_X(\cdot\capD) = P_{\vartheta}, \vartheta \epsilon \Theta \subset \mathbb{R}^d$. Nonlinear regression analysis and the peaks-over-threshold (POT) approach in extreme…