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平稳高斯场的自适应估计AI 解读

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as approximation sets for the distribution of X, we introduce a novel model selection…

具有高阶精度的调整经验似然AI 解读

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective…

方向边界锥包估计量的渐近分布AI 解读

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs×outputs in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs × outputs space. So far, only the statistical properties of the…

利用 ℓ1 正则化逻辑回归选择高维 Ising 模型AI 解读

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on ℓ1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our…

对《状态空间模型中的有效似然估计》相关问题评论的回复AI 解读

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root…

关于程德福《状态空间模型中的有效似然估计》一文的若干问题AI 解读

On some problems in the article "Efficient Likelihood Estimation in State Space Models" by Cheng-Der Fuh [Ann. Statist. 34 (2006) 2026--2068] [arXiv:math/0611376]

利用自适应重要性抽样估计分位数AI 解读

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles thereby extending the work of Feldman and Tucker [Ann. Math. Statist. 37 (1996) 451–457]. We illustrate the algorithm with an…

两比例之差的最小单侧置信区间构造AI 解读

For any class of one-sided 1−α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then…

纵向数据的协变量调整函数主成分分析AI 解读

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate Z and time scale t while in the second approach only the mean function depends on the covariate Z. Both new…

为随机函数分布定义概率密度AI 解读

The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis. This leads to a transparent and meaningful surrogate for density defined in terms of the average value of…

密度估计中的置信带AI 解读

Given a sample from some unknown continuous density f : ℝ→ℝ, we construct adaptive confidence bands that are honest for all densities in a “generic” subset of the union of t-Hölder balls, 0

超高维数据中基于质心的分类器的最优性质AI 解读

We show that scale-adjusted versions of the centroid-based classifier enjoys optimal properties when used to discriminate between two very high-dimensional populations where the principal differences are in location. The scale adjustment removes the tendency of scale differences to confound differences in means. Certain other distance-based methods, for example, those founded on nearest-neighbor distance, do not have optimal performance in the sense that we propose. Our…

利用扫描统计量最优且快速地检测空间聚集AI 解读

We consider the detection of multivariate spatial clusters in the Bernoulli model with N locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios. Multivariate scan statistics pose a statistical problem due to the multiple testing over many scan windows, as well as a computational problem because statistics have to be evaluated on many…

Dirichlet 过程随机效应模型的估计AI 解读

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of…

高频金融数据的大维度波动率矩阵估计AI 解读

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems involving a large number of assets, the estimation objects we face are volatility matrices of large size. The existing volatility estimators work well for a small number of assets but perform poorly when the number of assets is very large. In…

高斯随机场尺度与方差参数的一致分离估计AI 解读

We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Matérn autocovariance in dimension d>4. When d<4 this is impossible due to the mutual absolute continuity of Matérn Gaussian random fields with different scale and variance (see Zhang [J. Amer. Statist. Assoc. 99 (2004) 250–261]). Informally, when d>4, we show that one can estimate the coefficient on the…

讨论：条件多元分位数的建模选择AI 解读

First I would like to congratulate the authors for developing a new concept of directional quantile contours.The work will contribute well to the pursuit of multivariate quantiles.The multiple output regression provides a new way of estimating the conditional multivariate quantile functions, which will certainly facilitate a large number of applications.I enjoy the paper for its mathematical rigor and computational savvy.My discussion will focus on the modeling aspect of…

高维数据的渐近推断AI 解读

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve situations in which (i) the number of parameters increase with the sample size (that is, allowed to be random) and (ii) there is a possibility of missing data. Under a variety of tail conditions on the components of the data, we provide…

基于时间变换的随机波动率模型推断AI 解读

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrization defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic…

高维高斯线性模型的拟合优度检验AI 解读

Let (Y, (Xi)1≤i≤p) be a real zero mean Gaussian vector and V be a subset of {1, …, p}. Suppose we are given n i.i.d. replications of this vector. We propose a new test for testing that Y is independent of (Xi)i∈{1, …, p}∖V conditionally to (Xi)i∈V against the general alternative that it is not. This procedure does not depend on any prior information on the covariance of X or the variance of Y and applies in a high-dimensional setting. It straightforwardly extends to test the…

矩阵与数组型统计对象的维度折叠AI 解读

We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of predictor arises when measurements are obtained for each combination of two or more underlying variables—for example, the voltage measured at different channels and times in electroencephalography data. For these applications, it is desirable to preserve the array structure of the reduced predictor (e.g., time versus channel), but this cannot be…

马尔可夫链蒙特卡洛中的批均值与谱方差估计AI 解读

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort…

极小极大凹惩罚下的近无偏变量选择AI 解读

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent variable selection. Subset selection is unbiased but computationally costly. The MC+ has two elements: a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP provides the convexity of the penalized…

A new multivariate concept of quantile, based on a directional version of Koenker and Bassett’s traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version, those quantiles can be computed efficiently via linear programming techniques. Consistency, Bahadur representation and asymptotic normality results are established. Most importantly, the contours generated by those quantiles are shown to…