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似然比类统计量的鞍点近似及其置换检验应用AI 解读

We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative…

利用局部极大值多重检验检测一维峰值AI 解读

A topological multiple testing scheme for one-dimensional domains is proposed where, rather than testing every spatial or temporal location for the presence of a signal, tests are performed only at the local maxima of the smoothed observed sequence. Assuming unimodal true peaks with finite support and Gaussian stationary ergodic noise, it is shown that the algorithm with Bonferroni or Benjamini-Hochberg correction provides asymptotic strong control of the family wise error…

自适应与交互式马尔可夫链蒙特卡洛算法的收敛AI 解读

Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions. Motivated by some recently introduced algorithms (such as the adaptive Metropolis algorithm and the interacting tempering algorithm), we develop a general methodological and theoretical framework to establish both the convergence of the…

病例对照抽样下序贯经验ROC、PPV与NPV曲线的渐近性质AI 解读

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough…

分数阶时间序列模型的高斯伪极大似然估计AI 解读

We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible regions. In these circumstances, a proof of consistency (which is a prerequisite for proving asymptotic normality) can be difficult owing to nonuniform convergence of the objective function over a large admissible parameter space. In particular,…

依赖下 Westfall–Young 多重检验置换程序的渐近最优性AI 解读

Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for correlated test statistics, resulting in a loss of power to detect true positives. We show that the Westfall–Young permutation method has asymptotically optimal power for a broad class of testing problems with a block-dependence and sparsity structure among the tests, when the number of tests tends to infinity.

近似因子模型中的高维协方差矩阵估计AI 解读

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By…

用于线性与非线性充分降维的主支持向量机AI 解读

We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support vector machine to find the optimal hyperplanes that separate them. These optimal hyperplanes are then aligned by the principal components of their normal vectors. It is proved that the aligned normal vectors provide an unbiased,…

非多项式维度下 Cox 比例风险模型的正则化AI 解读

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Cox's proportional hazards model. A class of folded-concave penalties are employed and both LASSO and…

高维扩散过程积分协方差矩阵的估计AI 解读

We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV, but…

高于一阶的移动平均模型中的单位根AI 解读

The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root and near unit root cases of a first-order moving average model. Previous studies of the MA(1) unit root problem rely on the special autocovariance structure of the MA(1) process, in which case, the eigenvalues and eigenvectors of the covariance matrix of the data vector have known analytical forms. In this paper, we take a different approach to first consider the…

半参数模型中捆绑参数的筛 M 定理及其删失线性模型有效估计应用AI 解读

In many semiparametric models that are parameterized by two types of parameters - a Euclidean parameter of interest and an infinite-dimensional nuisance parameter, the two parameters are bundled together, i.e., the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument. For example, in a linear regression model for censored survival data, the unspecified error distribution function involves the regression coefficients.…

非参数条件矩限制模型的后验一致性AI 解读

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g0. We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior…

大规模计算机实验的高精度模拟器AI 解读

Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and…

冯·诺依曼熵惩罚与低秩矩阵估计AI 解读

We study a problem of estimation of a Hermitian nonnegatively definite matrix ρ of unit trace (e.g., a density matrix of a quantum system) based on n i.i.d. measurements (X1, Y1), …, (Xn, Yn), where Yj = tr(ρXj) + ξj, j = 1, …, n, {Xj} being random i.i.d. Hermitian matrices and {ξj} being i.i.d. random variables with ${\mathbb{E}}(\xi_{j}|X_{j})=0$. The estimator $$\hat{\rho}^{\varepsilon }:=\mathop{\arg\min}_{S\in{\mathcal{S}}}\Biggl[n^{-1}\sum_{j=1}^{n}\bigl(Y_{j}-\operatorname{tr}(SX_{j})\bigr)^{2}+\varepsilon \operatorname{tr}(S\log S)\Biggr] $$…

L^r 距离下后验分布的收缩速率（1≤r≤∞）AI 解读

The frequentist behavior of nonparametric Bayes estimates, more specifically, rates of contraction of the posterior distributions to shrinking Lr-norm neighborhoods, 1 ≤ r ≤ ∞, of the unknown parameter, are studied. A theorem for nonparametric density estimation is proved under general approximation-theoretic assumptions on the prior. The result is applied to a variety of common examples, including Gaussian process, wavelet series, normal mixture and histogram priors. The…

稳健函数型主成分：投影寻踪方法AI 解读

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are…

扩散过程的近似最大似然估计AI 解读

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Aït-Sahalia [J. Finance 54 (1999) 1361–1395; Econometrica 70 (2002) 223–262] proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on Aït-Sahalia’s [Econometrica…

When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized…

地统计学中的惩罚最大似然估计与变量选择AI 解读

We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and, for ease of computation, PMLE is approximated by one-step sparse estimation (OSE). To further improve computational efficiency, particularly with large sample sizes, we propose penalized maximum covariance-tapered likelihood estimation…

稳健线性最小二乘回归AI 解读

We consider the problem of robustly predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For the ridge estimator and the ordinary least squares estimator, and their variants, we provide new risk bounds of order d/n without logarithmic factor unlike some standard results, where n is the size of the training data. We also provide a new…

系统发育树空间中的主成分分析AI 解读

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary trees on a fixed set of taxa is not a vector space. This paper describes a novel geometrical approach to PCA in tree-space that constructs the first principal path in an analogous way to standard linear Euclidean PCA. Given a data set of…

经验贝叶斯方法与贝叶斯敏感性分析的计算途径AI 解读

We consider situations in Bayesian analysis where we have a family of priors νh on the parameter θ, where h varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity analysis and is stated as follows. Suppose we fix a function f of θ. How do we efficiently estimate the posterior expectation of f(θ) simultaneously for all h in $\mathcal{H}$? The second problem is how do we identify subsets of $\mathcal{H}$ which give…

采用高斯先验的贝叶斯逆问题AI 解读

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage.…