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采用广义g先验的完全贝叶斯因子AI 解读

For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner’s g-prior which allows for p > n. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.

回归变量数增长时高斯回归的 Bernstein–von Mises 定理AI 解读

This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of regressors increases with the sample size. Two kinds of Bernstein–von Mises theorems are obtained in this framework: nonparametric theorems for the parameter itself, and semiparametric theorems for functionals of the parameter. We apply them…

稀疏备择下的整体检验：方差分析、多重比较与 higher criticismAI 解读

Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the alternative, the response only depends upon the order of p1−α of those, 0 ≤ α ≤ 1.…

高斯变分近似的渐近正态性与有效推断AI 解读

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent…

对称独立成分模型中基于符号秩的半参数有效推断AI 解读

We consider semiparametric location-scatter models for which the p-variate observation is obtained as X = ΛZ + μ, where μ is a p-vector, Λ is a full-rank p × p matrix and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Λ. On the basis of n i.i.d. copies of X, we develop, under a…

高维回归分析中的因子模型与变量选择AI 解读

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression by using a factor approach: it is assumed that the predictor vector can be decomposed into a sum of two uncorrelated random components reflecting common factors and specific variabilities of the explanatory variables. It is shown that the…

自适应推断与置信带AI 解读

The problem of existence of adaptive confidence bands for an unknown density f that belongs to a nested scale of Hölder classes over ℝ or [0, 1] is considered. Whereas honest adaptive inference in this problem is impossible already for a pair of Hölder balls Σ(r), Σ(s), r ≠ s, of fixed radius, a nonparametric distinguishability condition is introduced under which adaptive confidence bands can be shown to exist. It is further shown that this condition is necessary and…

概率预测的评价AI 解读

Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient’s positive response to treatment. Scoring rules have long been used to assess the efficacy of the forecast probabilities after observing the occurrence, or nonoccurrence, of the predicted events. We develop herein a statistical theory for scoring rules and propose an alternative approach to the evaluation…

分布函数的反卷积估计AI 解读

The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density belonging to the Sobolev class, and the error density is ordinary smooth. We develop rate optimal estimators based on direct inversion of empirical characteristic function. We also derive minimax affine estimators of the distribution function…

离散采样函数数据的均值函数最优估计：相变AI 解读

The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs. Minimax rates of convergence are established and easily implementable rate-optimal estimators are introduced. The analysis reveals interesting and different phase transition phenomena in the two cases. Under the common design, the…

含噪低秩矩阵补全的核范数惩罚与最优收敛率AI 解读

This paper deals with the trace regression model where n entries or linear combinations of entries of an unknown m1 × m2 matrix A0 corrupted by noise are observed. We propose a new nuclear-norm penalized estimator of A0 and establish a general sharp oracle inequality for this estimator for arbitrary values of n, m1, m2 under the condition of isometry in expectation. Then this method is applied to the matrix completion problem. In this case, the estimator admits a simple…

网络模型的矩方法与度分布AI 解读

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all…

In this article, the problem of semi-parametric inference on the parameters of a multidimensional Lévy process Lt with independent components based on the low-frequency observations of the corresponding time-changed Lévy process $L_{\mathcal{T}(t)}$, where $\mathcal{T}$ is a nonnegative, nondecreasing real-valued process independent of Lt, is studied. We show that this problem is closely related to the problem of composite function estimation that has recently gotten much…

自回归筛自助法的有效范围AI 解读

We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is…

参数还是非参数？模型选择的参数性指数AI 解读

In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); Akaike’s information criterion (AIC) performs well in an asymptotic efficiency when the true model is infinite dimensional (nonparametric scenario). But there is little work that addresses if it is possible and how to…

ARMA–GARCH/IGARCH 模型的全局自加权与局部准最大指数似然估计AI 解读

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA–GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given…

粗糙微分方程的参数估计AI 解读

We construct the “expected signature matching” estimator for differential equations driven by rough paths and we prove its consistency and asymptotic normality. We use it to estimate parameters of a diffusion and a fractional diffusions, that is, a differential equation driven by fractional Brownian motion.

组稀疏性下的预言不等式与最优统计推断AI 解读

We consider the problem of estimating a sparse linear regression vector β* under a Gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern, namely the set of variables is partitioned into prescribed groups, only few of which are relevant in the estimation process. This group sparsity assumption suggests us to consider the Group Lasso method as a means to estimate β*. We establish oracle…

高维回归的稀疏拉普拉斯收缩估计量AI 解读

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic associated with a graph as the penalty function. We call it the sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave penalty for encouraging sparsity and Laplacian quadratic penalty for promoting smoothness among…

Pickands 依赖函数的新估计量与极值依赖检验AI 解读

We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function A*(t), which minimizes a weighted L2-distance between the logarithm of the copula C(y1−t, yt) and functions of the form A(t)log(y) is derived. If the unknown copula is an extreme-value copula, the function A*(t) coincides with Pickands dependence function. Moreover, even if this is not the…

连续字典下的随机展开：Lévy 自适应回归核AI 解读

This article describes a new class of prior distributions for nonparametric function estimation. The unknown function is modeled as a limit of weighted sums of kernels or generator functions indexed by continuous parameters that control local and global features such as their translation, dilation, modulation and shape. Lévy random fields and their stochastic integrals are employed to induce prior distributions for the unknown functions or, equivalently, for the number of…

谱聚类与高维随机块模型AI 解读

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasible method to discover these communities. The stochastic blockmodel [Social Networks…

不同混合条件下平稳数据密度估计的最优模型选择AI 解读

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are β or τ-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.

广义可加部分线性模型的估计与变量选择AI 解读

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of…