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半参数回归模型估计中的 Robbins–Monro 程序AI 解读

This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins–Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins–Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the…

Kullback–Leibler 聚合与误设广义线性模型AI 解读

In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is shown that this problem can be solved by constrained and/or penalized likelihood…

确定性设计矩阵下高维线性模型的估计AI 解读

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems with deterministic design points is very different from those in the case of random covariates, due to the identifiability of the high-dimensional regression parameter vector. We show that a reasonable approach is to focus on the…

高维时间序列因子建模：因子个数的推断AI 解读

This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are estimated in terms of an eigenanalysis for a nonnegative definite matrix, and is therefore applicable when the dimension of time series is on the order of a few thousands. Asymptotic properties of the proposed method are investigated…

Yule–Walker估计量的同时置信带与阶数选择AI 解读

Let {Xk, k ∈ ℤ} be an autoregressive process of order q. Various estimators for the order q and the parameters Θq = (θ1, …, θq)T are known; the order is usually determined with Akaike’s criterion or related modifications, whereas Yule–Walker, Burger or maximum likelihood estimators are used for the parameters Θq. In this paper, we establish simultaneous confidence bands for the Yule–Walker estimators θ̂i; more precisely, it is shown that the limiting distribution of…

相关性的检测AI 解读

We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of…

由支持函数估计凸集的最优收敛率AI 解读

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.

平稳时间序列的协方差矩阵估计AI 解读

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376] idea and relate eigenvalues of covariance matrices to the spectral densities or…

高维因子模型的统计分析AI 解读

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification…

信息密集型高维回归中的预测变量充分降维估计AI 解读

We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.

函数型数据偏最小二乘的方法与理论AI 解读

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often…

存在潜在变量与选择变量时的高维有向无环图学习AI 解读

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations…

均值函数可变的高斯随机场及相关过程的若干渐近结果AI 解读

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple applications such as hypothesis testing for spatial models and financial applications.

半参数 Bernstein–von Mises 定理AI 解读

In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is shown that, under certain straightforward and interpretable conditions, the assertion of Le Cam’s acclaimed, but strictly parametric, Bernstein–von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277–329] holds in the…

高斯图模型中极大似然估计的几何分析AI 解读

We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one,…

乘法删失下核密度估计量的大样本研究AI 解读

The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989) 751–761] is an incomplete data problem whereby two independent samples from the lifetime distribution G, $\mathcal{X}_{m}=(X_{1},\ldots,X_{m})$ and $\mathcal{Z}_{n}=(Z_{1},\ldots,Z_{n})$, are observed subject to a form of coarsening. Specifically, sample $\mathcal{X}_{m}$ is fully observed while $\mathcal{Y}_{n}=(Y_{1},\ldots,Y_{n})$ is observed instead of $\mathcal{Z}_{n}$, where Yi = UiZi and (U1,…

同质分组检测数据的非参数回归AI 解读

We introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence. In particular, when the level of pooling is moderate, then despite the cost savings, the method enjoys the same convergence rate as in the case of no pooling. In the setting of “over-pooling” the convergence rate differs from that of an optimal estimator by no more than a logarithmic factor. Our…

UPS 实现高维变量选择的最优相图AI 解读

Consider a linear model Y = Xβ + z, z ∼ N(0, In). Here, X = Xn,p, where both p and n are large, but p > n. We model the rows of X as i.i.d. samples from N(0, 1/n Ω), where Ω is a p × p correlation matrix, which is unknown to us but is presumably sparse. The vector β is also unknown but has relatively few nonzero coordinates, and we are interested in identifying these nonzeros. We propose the Univariate Penalization Screeing (UPS) for variable selection. This is a screen and…

网格现时状态数据的似然推断：边界现象与自适应程序AI 解读

In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with multiple subjects sharing the same observation time. This is of interest since observation time ties occur frequently with current status data. The grid resolution is specified as cn−γ with c > 0 being a scaling constant and γ > 0 regulating the…

基于条件随机化检验的序贯监测AI 解读

Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a population model. We describe a computational method to implement sequential monitoring in a randomization-based context. In particular, we discuss a new technique for the computation of approximate conditional tests following restricted…

一类马尔可夫随机场模型的拟合优度检验AI 解读

This paper develops goodness of fit statistics that can be used to formally assess Markov random field models for spatial data, when the model distributions are discrete or continuous and potentially parametric. Test statistics are formed from generalized spatial residuals which are collected over groups of nonneighboring spatial observations, called concliques. Under a hypothesized Markov model structure, spatial residuals within each conclique are shown to be independent…

多重量子假设检验的渐近误差界AI 解读

We consider the problem of detecting the true quantum state among r possible ones, based of measurements performed on n copies of a finite-dimensional quantum system. A special case is the problem of discriminating between r probability measures on a finite sample space, using n i.i.d. observations. In this classical setting, it is known that the averaged error probability decreases exponentially with exponent given by the worst case binary Chernoff bound between any…

Wishart 分布混合的极小极大估计AI 解读

The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition…

基于最小平均方差估计集成的充分降维AI 解读

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box–Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible…