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稀疏协方差矩阵估计的自适应阈值法AI 解读

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal…

用非凸惩罚回归检测异常值AI 解读

This article studies the outlier detection problem from the standpoint of penalized regression. In the regression model, we add one mean shift parameter for each of the n data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual L1 penalty yields a convex criterion, but fails to deliver a robust estimator. The L1 penalty corresponds to soft thresholding. We introduce a thresholding (denoted by Θ) based iterative procedure for…

稳健且高效的单因素多元方差分析检验AI 解读

We propose robust tests as alternatives to the classical Wilks’ Lambda test in one-way MANOVA. The robust tests use highly robust and efficient multisample multivariate S-estimators or MM-estimators instead of the empirical covariances. The properties of several robust test statistics are compared. Under the null hypothesis, the distribution of the test statistics is proportional to a chi-square distribution. As an alternative to the asymptotic distribution, we develop a…

用Lévy噪声驱动的部分观测随机微分方程分析印度西北部疟疾AI 解读

Many biological systems are appropriately described by partially observed Markov process (POMP) models, also known as state space models. Such models also arise throughout the physical and social sciences, in engineering, and in finance. Statistical challenges arise in carrying out inference on nonlinear, nonstationary, vector-valued POMP models. Methodologies that depend on the Markov process model only through numerical solution of sample paths are said to have the…

混样检测数据的非参数回归分析AI 解读

Group testing is a procedure used to reduce the cost and increase the speed of large screening studies in which infection or contamination of individuals is detected by a test carried out on a sample of, for example, blood, urine, or water. Instead of testing the sample of each individual, the method involves pooling samples of groups of several individuals and testing those pooled samples. We construct a nonparametric procedure for estimating the conditional probability of…

观察期依赖事件时的自控病例系列分析AI 解读

The self-controlled case series method may be used to study the association between a time-varying exposure and a health event. It is based only on cases, and it controls for fixed confounders. Exposure and event histories are collected for each case over a predefined observation period. The method requires that observation periods should be independent of event times. This requirement is violated when events increase the mortality rate, since censoring of the observation…

主分层内基于随机化的推断AI 解读

In randomized studies, treatment comparisons conditional on intermediate post-randomization outcomes using standard analytic methods do not have a causal interpretation. An alternate approach entails treatment comparisons within principal strata defined by the potential outcomes for the intermediate outcome that would be observed under each treatment assignment. In this paper, we develop methods for randomization-based inference within principal strata. The proposed methods…

Lasso估计量的Bootstrap方法AI 解读

In this article, we consider bootstrapping the Lasso estimator of the regression parameter in a multiple linear regression model. It is known that the standard bootstrap method fails to be consistent. Here, we propose a modified bootstrap method, and show that it provides valid approximation to the distribution of the Lasso estimator, for all possible values of the unknown regression parameter vector, including the case where some of the components are zero. Further, we…

利用含噪高频观测估计跳跃活跃指数AI 解读

It is widely accepted that the high-frequency data are contaminated by microstructure noise, whose effect on the statistical inference has been of increasing interest in the literature. Much of it, however, has focused on the integrated volatility. In this article, we investigate another important characteristic, namely, the jump activity index (JAI) of a discretely sampled semi-martingale corrupted by microstructure noise. We point out that ignoring the microstructure noise…

嵌套病例对照研究中生物标志物准确性的非参数评价AI 解读

To evaluate the clinical utility of new risk markers, a crucial step is to measure their predictive accuracy with prospective studies. However, it is often infeasible to obtain marker values for all study participants. The nested case-control (NCC) design is a useful cost-effective strategy for such settings. Under the NCC design, markers are only ascertained for cases and a fraction of controls sampled randomly from the risk sets. The outcome dependent sampling generates a…

广义线性模型的投影估计量AI 解读

We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction ε of outlier contamination. For small ε, this bias is approximately twice the…

核密度估计的双侧验证带宽选择AI 解读

Bandwidth selection in kernel density estimation is one of the fundamental model selection problems of mathematical statistics. The study of this problem took major steps forward with the articles of Hall and Marron (1987) and Hall and Johnstone (1992). Since then, the focus seems to have been on various versions of implementing the so-called plug-in method aimed at estimating the minimum mean integrated squared error (MISE). The most successful of these efforts still seems…

利用时空信息估计长期空气污染效应AI 解读

There is substantial observational evidence that long-term exposure to particulate air pollution is associated with premature death in urban populations. Estimates of the magnitude of these effects derive largely from cross-sectional comparisons of adjusted mortality rates among cities with varying pollution levels. Such estimates are potentially confounded by other differences among the populations correlated with air pollution, for example, socioeconomic factors. An…

偏最小二乘回归的自由度AI 解读

The derivation of statistical properties for partial least squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of partial least squares regression. Our contribution is an…

稀疏超高维加性模型的非参数独立筛选AI 解读

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening is called NIS, a specific member of the sure independence screening. Several closely related…

项目计数法的多变量回归分析AI 解读

The item count technique is a survey methodology that is designed to elicit respondents’ truthful answers to sensitive questions such as racial prejudice and drug use. The method is also known as the list experiment or the unmatched count technique and is an alternative to the commonly used randomized response method. In this article, I propose new nonlinear least squares and maximum likelihood estimators for efficient multivariate regression analysis with the item count…

稀疏精度矩阵估计的约束 ℓ1 最小化方法AI 解读

This article proposes a constrained ℓ1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is when the population distribution has either exponential-type tails or polynomial-type tails. We present…

有限总体复杂抽样设计的直接自助法AI 解读

In complex designs, classical bootstrap methods result in a biased variance estimator when the sampling design is not taken into account. Resampled units are usually rescaled or weighted in order to achieve unbiasedness in the linear case. In the present article, we propose novel resampling methods that may be directly applied to variance estimation. These methods consist of selecting subsamples under a completely different sampling scheme from that which generated the…

半参数贝叶斯层级模型估计利率期限结构：公司债应用AI 解读

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its…

测量误差下形状约束非参数密度与回归的检验和估计AI 解读

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the…

自适应的概率型拉丁超立方设计AI 解读

Adaptive sampling is an effective method developed mainly for regular regions. However, experimental regions in irregular shapes are commonly observed in practice. Motivated by a data center thermal management study, a new class of adaptive designs is proposed to accommodate a specific type of irregular region. Because the adaptive procedure introduces biases into conventional estimators, several design-unbiased estimators are given for estimating the population mean.…

将高维数据串联为函数型数据进行分析AI 解读

We propose stringing, a class of methods where one views high-dimensional observations as functional data. Stringing takes advantage of the high dimension by representing such data as discretized and noisy observations that originate from a hidden smooth stochastic process. Assuming that the observations result from scrambling the original ordering of the observations of the process, stringing reorders the components of the high-dimensional vectors, followed by transforming…

VIF回归：面向大规模数据的快速回归算法AI 解读

We propose a fast and accurate algorithm, VIF regression, for doing feature selection in large regression problems. VIF regression is extremely fast; it uses a one-pass search over the predictors and a computationally efficient method of testing each potential predictor for addition to the model. VIF regression provably avoids model overfitting, controlling the marginal false discovery rate. Numerical results show that it is much faster than any other published algorithm for…

EEBoost：基于估计方程的预测与变量选择AI 解读

The modern statistical literature is replete with methods for performing variable selection and prediction in standard regression problems. However, simple models may misspecify or fail to capture important aspects of the data generating process such as missingness, correlation, and over/underdispersion. In this article we describe EEBoost, a strategy for variable selection and prediction which can be applied in high-dimensional settings where inference for low-dimensional…