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Peter Hall 对自助法的贡献AI 解读

Professor Peter Hall's first publication appeared in 1977, one year after he was awarded DPhil from the University of Oxford and MSc from the Australian National University (ANU).His first paper on the bootstrap appeared in 1985[Hall (1985))] on the block bootstrap of spatial point patterns, six years after the seminal paper [Efron (1979)] that introduced the bootstrap method.Hall (1985) was his 103rd publication and proposed resampling "tiles" of spatial data ("coverage…

Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling…

非参数协变量调整回归AI 解读

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied…

第一投影方向的渐近理论AI 解读

For a response variable $Y$, and a $d$ dimensional vector of covariates $\mathbf{X}$, the first projective direction, $\mathbf{\vartheta}$, is defined as the direction that accounts for the most variability in $Y$. The asymptotic distribution of an estimator of a trimmed version of $\mathbf{\vartheta}$ has been characterized only under the assumption of the single index model (SIM). This paper proposes the use of a flexible trimming function in the objective function, which…

随机块模型社区检测的极小极大速率AI 解读

Recently, network analysis has gained more and more attention in statistics, as well as in computer science, probability and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic in network analysis. Many methodologies have been proposed. Some beautiful and significant phase transition results are obtained in various settings. In this paper, we provide a general minimax theory for community detection. It gives…

全基因组关联研究中高维误设混合模型的分析AI 解读

We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent genome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random…

超大规模高斯图模型中的创新型可扩展高效估计AI 解读

Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient estimation (ISEE) for estimating large precision matrix. Motivated by the innovated transformation, we convert the original problem into that of large covariance matrix estimation. The suggested method combines the strengths of recent advances…

局部内蕴平稳性及其统计推断AI 解读

Dense spatial data are commonplace nowadays, and they provide the impetus for addressing nonstationarity in a general way. This paper extends the notion of intrinsic random function by allowing the stationary component of the covariance to vary with spatial location. A nonparametric estimation procedure based on gridded data is introduced for the case where the covariance function is regularly varying at any location. An asymptotic theory is developed for the procedure on a…

用于大型精度矩阵估计的偏相关筛选及其分类应用AI 解读

Given $n$ samples $X_{1},X_{2},\ldots,X_{n}$ from $N(0,\Sigma)$, we are interested in estimating the $p\times p$ precision matrix $\Omega=\Sigma^{-1}$; we assume $\Omega$ is sparse in that each row has relatively few nonzeros. We propose Partial Correlation Screening (PCS) as a new row-by-row approach. To estimate the $i$th row of $\Omega$, $1\leq i\leq p$, PCS uses a Screen step and a Clean step. In the Screen step, PCS recruits a (small) subset of indices using a…

纵向与聚类数据半变系数模型的有效估计AI 解读

In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are…

Harris 常返马尔可夫链下非线性回归的估计AI 解读

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov…

学生化两样本 U 统计量的 Cramér 型中等偏差及应用AI 解读

Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramér-type moderate deviation theorems for Studentized two-sample $U$-statistics in a general framework, including the two-sample $t$-statistic and Studentized Mann–Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is…

稀疏主成分估计中的统计与计算权衡AI 解读

In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed; some of these are fast to compute, while others are known to achieve the minimax optimal rate over…

阈值化 Wirtinger 流实现含噪稀疏相位恢复的最优收敛速率AI 解读

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $\mathbf{x}\in\mathbb{R}^{p}$ from noisy quadratic measurements $y_{j}=(\mathbf{a}_{j}'\mathbf{x})^{2}+\varepsilon_{j}$, $j=1,\ldots,m$, with independent sub-exponential noise $\varepsilon_{j}$. The goals are to understand the effect of the sparsity of $\mathbf{x}$ on the estimation precision and to construct a computationally feasible estimator to achieve the optimal rates adaptively.…

正则化对谱聚类的影响AI 解读

The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et al. [Ann. Statist. 41 (2013) 2097–2122]. Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario…

利用过完备字典求解线性不适定问题AI 解读

In the present paper, we consider the application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using an overcomplete dictionary. One of the most popular methods, Lasso and its variants, is based on maximizing the likelihood, and relies on stringent assumptions on the dictionary, the so-called compatibility conditions,…

函数型 Cox 模型的最优估计AI 解读

Functional covariates are common in many medical, biodemographic and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the…

具有 ARMA 误差的半变系数时间序列模型估计AI 解读

Serial correlation in the residuals of time series models can cause bias in both model estimation and prediction. However, models with such serially correlated residuals are difficult to estimate, especially when the regression function is nonlinear. Existing estimation methods require strong assumption for the relation between the residuals and the regressors, which excludes the commonly used autoregressive models in time series analysis. By extending the Whittle likelihood…

依赖情形下自归一化的 Cramér 型中等偏差AI 解读

We establish a Cramér-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider three types of self-normalization: the equal-block scheme, the big-block-small-block scheme and the interlacing scheme.…

F 型矩阵最大特征值的 Tracy–Widom 分布律AI 解读

Let ${\mathbf{A}}_{p}=\frac{{\mathbf{Y}}{\mathbf{Y}}^{*}}{m}$ and ${\mathbf{B}}_{p}=\frac{{\mathbf{X}}{\mathbf{X}}^{*}}{n}$ be two independent random matrices where ${\mathbf{X}}=(X_{ij})_{p\times n}$ and ${\mathbf{Y}}=(Y_{ij})_{p\times m}$ respectively consist of real (or complex) independent random variables with $\mathbb{E}X_{ij}=\mathbb{E}Y_{ij}=0$, $\mathbb{E}|X_{ij}|^{2}=\mathbb{E}|Y_{ij}|^{2}=1$. Denote by $\lambda_{1}$ the largest root of the determinantal equation $\det(\lambda{\mathbf{A}}_{p}-{\mathbf{B}}_{p})=0$…

一般高维线性逆问题的几何推断AI 解读

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize…

马尔可夫链参数估计的信息几何方法AI 解读

We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.

无限方差线性过程的筛方法推断AI 解读

We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit…

时频分析中针对稀疏备择的全局检验AI 解读

In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore,…