日期精度：到日 5104 篇 · 到月 0 篇 · 到年 0 篇
贝叶斯阶数识别的误差界及其混合模型应用
The efficiency of two Bayesian order estimators is studied. By using nonparametric techniques, we prove new underestimation and overestimation bounds. The results apply to various models, including mixture models. In this case, the errors are shown to be O(e−an) and $O((\log n)^{b}/\sqrt{n})$ (a, b>0), respectively.
半参数变换模型的估计
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the…
This paper provides closed-form expansions for the transition density and likelihood function of arbitrary multivariate diffusions.The expansions are based on a Hermite series, whose coefficients are calculated explicitly by exploiting the special structure afforded by the diffusion hypothesis.Because the transition function for most diffusion models is not known explicitly, the expansions of this paper can help make maximum-likelihood a practical estimation method for…
排序与 U 统计量的经验最小化
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule for deciding, among two instances, which one is “better,” with minimum ranking risk. Since the natural estimates of the risk are of the form of a U-statistic, results of the theory of U-processes are required for…
使用辅助数据的 GMM 模型半参数效率
We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be…
高维广义线性模型与 Lasso
We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.
未知均值对非参数回归方差函数估计的影响
Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results indicate that, contrary to the common practice, it is not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean when the mean function is not smooth. Instead it is more desirable to…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without it. However, if additional data are available, then it is possible to estimate consistently the unknown error density. Data are seldom available directly on the transformation, but repeated, or replicated, measurements increasingly are…
Rodeo：稀疏、贪心的非参数回归
We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large. The method—called rodeo (regularization of derivative expectation operator)—conducts a sequence of hypothesis tests to threshold derivatives,…
删失数据的高崩溃点稳健回归
In this paper, we propose a class of high breakdown point estimators for the linear regression model when the response variable contains censored observations. These estimators are robust against high-leverage outliers and they generalize the LMS (least median of squares), S, MM and τ-estimators for linear regression. An important contribution of this paper is that we can define consistent estimators using a bounded loss function (or equivalently, a redescending score…
强依赖下 higher criticism 检验的性质
The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each problem can be solved by conducting a large number of simultaneous hypothesis tests, the properties of which are readily accessed under the assumption of independence. In this paper we address the case of dependent data, in the context of…
贝叶斯层级模型中 Gibbs 采样器的稳定性
We characterize the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence can be uniform, geometric or subgeometric depending on the relative tail behavior of the error distributions, and on the parametrization chosen. Our theory is applied to characterize the convergence of the Gibbs sampler on latent Gaussian…
依赖情形下的错误发现控制
A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses. The dependence can be useful to characterize the spatial structure of the null hypotheses. Asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large-sample…
调查中的内生事后分层：使用样本拟合模型分类
Post-stratification is frequently used to improve the precision of survey estimators when categorical auxiliary information is available from sources outside the survey. In natural resource surveys, such information is often obtained from remote sensing data, classified into categories and displayed as pixel-based maps. These maps may be constructed based on classification models fitted to the sample data. Post-stratification of the sample data based on categories derived…
多类删失数据下两样本半参数模型的加权经验似然
In this article, the weighted empirical likelihood is applied to a general setting of two-sample semiparametric models, which includes biased sampling models and case-control logistic regression models as special cases. For various types of censored data, such as right censored data, doubly censored data, interval censored data and partly interval-censored data, the weighted empirical likelihood-based semiparametric maximum likelihood estimator (θ̃n, F̃n) for the underlying…
具有长记忆设计与误差的异方差回归模型渐近推断
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple linear regression model, the first-order asymptotic distribution of the least square estimator of the slope parameter is observed to be degenerate. However, in the second order, this estimator is n1/2-consistent and asymptotically normal for…
混合收敛速率的渐近分析
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the complete limiting behavior of the estimator. The asymptotic analysis depends on a…
广义加性模型中的平滑回拟合
Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting generalized additive models is proposed. It aims to maximize a smoothed likelihood. The additive functions are estimated by solving a system of nonlinear integral equations. An iterative algorithm based on smooth backfitting is developed…
推广 Simes 检验与 Hochberg 逐步上升程序
In a multiple testing problem where one is willing to tolerate a few false rejections, procedure controlling the familywise error rate (FWER) can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k-FWER, the probability of falsely rejecting at least k null hypotheses, for some fixed k>1. Simes’ test for testing the intersection null hypothesis is generalized to control the k-FWER weakly, that is, under the…
多元检验统计量随机场及其形状分析应用
Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main…
大型协方差矩阵的正则化估计
This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (log p)/n→0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned families of covariance matrices. We also introduce an analogue of the Gaussian white…
扩散过程模型设定检验
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized L2-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test on smoothing bandwidth…
贪婪算法的逼近与学习
We consider the problem of approximating a given element f from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward stepwise projection algorithm. For all these algorithms, we prove convergence results for a variety…
半参数回归建模中的变量选择
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise…