论文检索

通过幂变换估计极端条件分位数AI 解读

The estimation of extreme conditional quantiles is an important issue in numerous disciplines. Quantile regression (QR) provides a natural way to capture the covariate effects at different tails of the response distribution. However, without any distributional assumptions, estimation from conventional QR is often unstable at the tails, especially for heavy-tailed distributions due to data sparsity. In this article, we develop a new three-stage estimation procedure that…

从数据深度到局部深度：聚焦中心性AI 解读

Aiming at analyzing multimodal or nonconvexly supported distributions through data depth, we introduce a local extension of depth. Our construction is obtained by conditioning the distribution to appropriate depth-based neighborhoods and has the advantages, among others, of maintaining affine-invariance and applying to all depths in a generic way. Most importantly, unlike their competitors, which (for extreme localization) rather measure probability mass, the resulting local…

任意样本选择偏差下未知对称总体的半参数有效稳健估计AI 解读

We propose semiparametric methods to estimate the center and shape of a symmetric population when a representative sample of the population is unavailable due to selection bias. We allow an arbitrary sample selection mechanism determined by the data collection procedure, and we do not impose any parametric form on the population distribution. Under this general framework, we construct a family of consistent estimators of the center that is robust to population model…

纵向研究中时变变换模型的条件分布与秩追踪概率估计AI 解读

An objective of longitudinal analysis is to estimate the conditional distributions of an outcome variable through a regression model. The approaches based on modeling the conditional means are not appropriate for this task when the conditional distributions are skewed or cannot be approximated by a normal distribution through a known transformation. We study a class of time-varying transformation models and a two-step smoothing method for the estimation of the conditional…

视觉统计推断的验证及其线性模型应用AI 解读

Statistical graphics play a crucial role in exploratory data analysis, model checking, and diagnosis. The lineup protocol enables statistical significance testing of visual findings, bridging the gulf between exploratory and inferential statistics. In this article, inferential methods for statistical graphics are developed further by refining the terminology of visual inference and framing the lineup protocol in a context that allows direct comparison with conventional tests…

阈值化参数空间中正则化方法的渐近等价性AI 解读

High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular methods being convex and concave ones. A long debate has taken place on whether one class dominates the other, an important question both in theory and to practitioners. In this article, we characterize the asymptotic equivalence of regularization methods, with general penalty functions, in a thresholded parameter space under the…

误设模型惩罚似然估计中正则化参数选择的效率AI 解读

It has been shown that Akaike information criterion (AIC)-type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regression, it is known that AIC tends to select overly…

含交互项协方差分析模型中有序均值的估计与推断AI 解读

When interactions are identified in analysis of covariance models it becomes important to identify values of the covariates for which there are significant differences or, more generally, significant contrasts among the group mean responses. Inferential procedures that incorporate a priori order restrictions among the group mean responses would be expected to be superior to those that ignore this information. In this paper we focus on analysis of covariance models with…

存在非随机缺失的牙周数据非参数空间模型AI 解读

Periodontal disease progression is often quantified by clinical attachment level (CAL) defined as the distance down a tooth's root that is detached from the surrounding bone. Measured at 6 locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data set-up. These data are often reduced to a one-number summary, such as the whole mouth average or the number of observations greater than a threshold, to be used as the response in a…

通过 EM 算法实现最大 Lq 似然的混合模型稳健估计AI 解读

We introduce a maximum Lq-likelihood estimation (MLqE) of mixture models using our proposed expectation-maximization (EM) algorithm, namely the EM algorithm with Lq-likelihood (EM-Lq). Properties of the MLqE obtained from the proposed EM-Lq are studied through simulated mixture model data. Compared with the maximum likelihood estimation (MLE), which is obtained from the EM algorithm, the MLqE provides a more robust estimation against outliers for small sample sizes. In…

偏微分方程模型的参数估计AI 解读

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of…

用于局部聚类的非参数贝叶斯模型及其蛋白质组学应用AI 解读

We propose a nonparametric Bayesian local clustering (NoB-LoC) approach for heterogeneous data. NoB-LoC implements inference for nested clusters as posterior inference under a Bayesian model. Using protein expression data as an example, the NoB-LoC model defines a protein (column) cluster as a set of proteins that give rise to the same partition of the samples (rows). In other words, the sample partitions are nested within protein clusters. The common clustering of the…

纵向数据的时变加性模型AI 解读

The additive model is an effective dimension-reduction approach that also provides flexibility in modeling the relation between a response variable and key covariates. The literature is largely developed to scalar response and vector covariates. In this article, more complex data are of interest, where both the response and the covariates are functions. We propose a functional additive model together with a new backfitting algorithm to estimate the unknown regression…

第一价格采购拍卖中进入成本的非参数估计AI 解读

SUMMARY In this paper, I investigate Samuelson's low‐price auction model with entry costs. The model's equilibrium implies that the distribution of bids is truncated at the threshold for participation. I use the model to estimate the cost of participation in Michigan highway procurement auctions. The null hypothesis of zero entry costs is rejected. Using my empirical results, I then construct an estimate of the optimal auction, which employs regular policy tools such as…

高维度对有限样本的影响AI 解读

High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one. With the probabilistic view, we establish the concentration property and robust spark bound for large random design matrix generated from elliptical distributions, with the former related to the sure screening property and the latter…

完整参数空间上的经验似然AI 解读

We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90–120] by partitioning its domain into the collection of its contours and mapping the contours through a continuous sequence of similarity transformations onto the full parameter space. The resulting extended empirical likelihood is a natural generalization of the original empirical likelihood to the full parameter space; it has the same asymptotic properties and identically shaped contours as the original…

固定或增长维度下的协方差矩阵检验AI 解读

Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given…

高维正态分布经典似然比检验的中心极限定理AI 解读

For random samples of size $n$ obtained from $p$-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis, and their limiting distributions under the null hypothesis were proved to be chi-square distributions as $n$ goes to infinity and $p$ remains fixed. In this paper, we consider the…

高斯白噪声模型中的非参数 Bernstein–von Mises 定理AI 解读

Bernstein–von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact $1-\alpha$ frequentist coverage level and whose $L^{2}$-diameter shrinks at the minimax rate of convergence (within logarithmic factors)…

非平稳非对称 GARCH 模型的统计推断AI 解读

This paper considers the statistical inference of the class of asymmetric power-transformed $\operatorname{GARCH}(1,1)$ models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two…

随机分块模型最大似然估计及其变分近似的渐近正态性AI 解读

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the…

基于新量子似然比的量子局部渐近正态性AI 解读

We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.

含测量误差的高维 Itô 过程稀疏波动率矩阵最优估计AI 解读

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Itô process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a…

高维稀疏主成分的最优检测AI 解读

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on…