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线性模型中的高效经验贝叶斯变量选择与估计AI 解读

We propose an empirical Bayes method for variable selection and coefficient estimation in linear regression models. The method is based on a particular hierarchical Bayes formulation, and the empirical Bayes estimator is shown to be closely related to the LASSO estimator. Such a connection allows us to take advantage of the recently developed quick LASSO algorithm to compute the empirical Bayes estimate, and provides a new way to select the tuning parameter in the LASSO…

人工增广样本、收缩与均方误差降低AI 解读

An inequality is provided that determines when shrinkage reduces the mean squared error (MSE) of an unbiased estimate. Artificially augmented samples are then used to obtain, among others, shrinkage estimates of the population's variance and covariance, which improve the unbiased estimates for all parameter values and for all probability models with marginals having finite second moments, and alternative jackknife estimates that complement the usual jackknife estimates in…

协变量缺失时比例风险回归的加权估计量AI 解读

Missing covariate data are common in epidemiologic studies and disease prevention trials. In this article regression parameter estimation in the Cox proportional hazards model is considered when certain covariates are observed for all study subjects and other covariate data are collected only for a subset. The article presents both simple weighted and kernel-assisted fully augmented weighted estimators that use the partially incomplete data nonparametrically. We use…

圆周上的一族对称分布AI 解读

We propose a new family of symmetric unimodal distributions on the circle that contains the uniform, von Mises, cardioid, and wrapped Cauchy distributions, among others, as special cases. The basic form of the densities of this family is very simple, although its normalization constant involves an associated Legendre function. The family of distributions can also be derived by conditioning and projecting certain bivariate spherically and elliptically symmetric distributions…

聚类数据广义部分线性模型的稳健估计AI 解读

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated…

似然推断中的分部最大化AI 解读

This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the…

两个时间尺度的故事AI 解读

It is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns. However, market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. The present work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving…

线性回归模型的组合AI 解读

Model-combining (i.e., mixing) methods have been proposed in recent years to deal with uncertainty in model selection. Even though advantages of model combining over model selection have been demonstrated in simulations and data examples, it is still unclear to a large extent when model combining should be preferred. In this work, first we propose an instability measure to capture the uncertainty of model selection in estimation, called perturbation instability in estimation…

Michaelis–Menten 酶动力学函数拟合优度的最优设计AI 解读

We construct efficient designs for the Michaelis–Menten enzyme kinetic model capable of checking model assumptions. An extended model called EMAX is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis–Menten model for a specific choice of parameter settings. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis–Menten model…

非参数加性分位数回归模型的估计AI 解读

This article is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n−r/(2r+1) when the additive components are r-times continuously differentiable for some r ≥ 2. This result holds regardless of the dimension of the covariates, and thus the new estimator has no curse of dimensionality. In addition, the…

含协变量误差的半参数生存回归：伪偏似然方法AI 解读

This article presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures; it is not restricted to the independent additive…

线性回归中对离群值稳健的模型选择AI 解读

We propose a new approach to the selection of regression models based on combining a robust penalized criterion and a robust conditional expected prediction loss function that is estimated using a stratified bootstrap. Both components of the procedure use robust criteria (i.e., robust ρ-functions) rather than squared error loss to reduce the effects of large residuals and poor bootstrap samples. A key idea is to separate estimation from model selection by choosing estimators…

贝叶斯密度估计中非参数正态混合的一致性AI 解读

The past decade has seen a remarkable development in the area of Bayesian nonparametric inference from both theoretical and applied perspectives. As for the latter, the celebrated Dirichlet process has been successfully exploited within Bayesian mixture models, leading to many interesting applications. As for the former, some new discrete nonparametric priors have been recently proposed in the literature that have natural use as alternatives to the Dirichlet process in a…

独立粒子滤波AI 解读

Sequential Monte Carlo methods, especially the particle filter (PF) and its various modifications, have been used effectively in dealing with stochastic dynamic systems. The standard PF samples the current state through the underlying state dynamics, then uses the current observation to evaluate the sample's importance weight. However, there is a set of problems in which the current observation provides significant information about the current state but the state dynamics…

计数数据的分位数AI 解读

This article studies the estimation of conditional quantiles of counts. Given the discreteness of the data, some smoothness must be artificially imposed on the problem. We show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques. The performance and implementation of the estimators are illustrated by simulations and an application.

发散矩与参数估计AI 解读

Heavy-tailed distributions are enjoying increased popularity and are becoming more readily applicable as the arsenal of analytical and numerical tools grows. They play key roles in modeling approaches in networking, finance, and hydrology, to name but a few areas. The tail parameterα is of central importance, because it governs both the existence of moments of positive order and the thickness of the tails of the distribution. Some of the best-known tail estimators, such as…

用于蒙特卡洛计算的广义 Wang–Landau 算法AI 解读

Inference for a complex system with a rough energy landscape is a central topic in Monte Carlo computation. Motivated by the successes of the Wang–Landau algorithm in discrete systems, we generalize the algorithm to continuous systems. The generalized algorithm has some features that conventional Monte Carlo algorithms do not have. First, it provides a new method for Monte Carlo integration based on stochastic approximation; second, it is an excellent tool for Monte Carlo…

调查抽样中的非参数模型校准估计AI 解读

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary…

采用归一化逆高斯先验的层级混合建模AI 解读

In recent years the Dirichlet process prior has experienced a great success in the context of Bayesian mixture modeling. The idea of overcoming discreteness of its realizations by exploiting it in hierarchical models, combined with the development of suitable sampling techniques, represent one of the reasons of its popularity. In this article we propose the normalized inverse-Gaussian (N–IG) process as an alternative to the Dirichlet process to be used in Bayesian…

非随机样本下的预测AI 解读

The 1990s was not the best of decades for electoral polls, with striking errors occurring in, among others, the British, French, and Spanish elections, including election night, when errors are more evident. This article proposes a model for predicting final election outcomes based on the consistency that polling stations show between elections. Using both past and incoming polling station vote proportions, the model produces continuously revised predictions. The method is…

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