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混合模型复杂度的稳健估计AI 解读

In many applications, it is important to find the mixture with fewest number of components, known as the mixture complexity, that provides a satisfactory fit to the data. This article focuses on developing an estimator of mixture complexity that is consistent when the form of component densities are unknown but are postulated to be members of some parametric family and is simultaneously robust against model misspecification. We treat the estimation of mixture complexity as a…

随机缺失下析因设计的非参数分析AI 解读

We propose a nonparametric approach to the analysis of factorial designs where each subject is observed at two time points and both observations are subject to missingness. The procedures are fully nonparametric in that they do not require continuity, and do not impose models to describe the relation of the response distribution in different factor-level combinations. The approach for estimating and testing treatment and time effects is based on a method, which we introduce,…

通过几何下界推断物种数量AI 解读

Estimating the number of species in a population from a sample of individuals is investigated in a nonparametric Poisson mixture model. A sequence of lower bounds to the odds that a species is unseen in the sample are proposed from a geometric perspective. A lower bound and its representing mixing distribution can be computed by linear programming with guaranteed convergence. These lower bounds can be estimated by the maximum likelihood method and used to construct lower…

半参数测量误差模型的局部有效估计量AI 解读

We derive constructive locally efficient estimators in semiparametric measurement error models. The setting is one in which the likelihood function depends on variables measured with and without error, where the variables measured without error can be modeled nonparametrically. The algorithm is based on backfitting. We show that if one adopts a parametric model for the latent variable measured with error and if this model is correct, then the estimator is semiparametric…

拟合空间点过程模型的复合似然方法AI 解读

We propose a new likelihood-based approach in fitting spatial point process models. A composite likelihood is first formed by adding some pairwise composite likelihood functions that are defined in terms of the second-order intensity function of the underlying process, and then used for estimating the unknown parameters. The estimation procedure is computationally simple and yields consistent and asymptotically normal estimators under some mild conditions. We demonstrate…

马尔可夫链蒙特卡洛的固定宽度输出分析AI 解读

Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard…

用于时间序列预测的广义指数预测器AI 解读

We consider the problem of prediction for stationary and nonstationary univariate time series using a modification suggested by the usual exponentially weighted moving average method. The modification leads to a class of general exponential predictors that can improve on the usual finite approximations to an infinite autoregressive process. We provide the theoretical justifications and suggest a class of predictors that covers modified and finite autoregressive fits as…

有限 Pólya 树混合模型的推断AI 解读

Mixtures of Polya tree models provide a flexible alternative when a parametric model may only hold approximately. I provide computational strategies for obtaining full semiparametric inference for mixtures of finite Polya tree models given a standard parameterization, including models that would be troublesome to fit using Dirichlet process mixtures. Recommendations are put forth on choosing the level of a finite Polya tree, and model comparison is discussed. Several…

一类带标记双随机 Poisson 过程的蒙特卡洛滤波AI 解读

Marked doubly stochastic Poisson processes are a particular type of marked point processes that are characterized by the number of events in any time interval as being conditionally Poisson distributed, given another positive stochastic process called intensity. Here we consider a subclass of these processes in which the intensity is assumed to be a deterministic function of another nonexplosive marked point process. In particular, we will investigate an intensity jump…

构造合并分层方差估计量的算法AI 解读

A jackknife or balanced repeated replication variance estimator in a large survey typically requires a large number of replicates and replicate weights. Reducing the number of replicates may have important advantages for computations and for limiting the risk of data disclosure from public use data files. This article proposes algorithms adapted from scheduling theory to combine variance strata and, thus, reduce the number of replicates. The algorithms are simple and…

基于 Rosenblatt 构造的多元分布族AI 解读

Recently, Jones pointed out a useful device for enriching families of univariate distributions. Typically, one may construct a random variable with distribution F by considering F−1(U),where U is a uniform (0,1) random variable. Jones suggested replacing the uniform random variable by a beta-distributed random variable. In this article an analogous enriching process is applied to the Rosenblatt construction of multivariate distributions. Several parametric families are…

用 Fourier 方法估计回归的中心子空间与中心均值子空间AI 解读

In regression with a high-dimensional predictor vector, it is important to estimate the central and central mean subspaces that preserve sufficient information about the response and the mean response. Using the Fourier transform, we have derived the candidate matrices whose column spaces recover the central and central mean subspaces exhaustively. Under the normality assumption of the predictors, explicit estimates of the central and central mean subspaces are derived.…

利用倾向得分进行因果推断的分布方法AI 解读

Drawing inferences about the effects of treatments and actions is a common challenge in economics, epidemiology, and other fields. We adopt Rubin's potential outcomes framework for causal inference and propose two methods serving complementary purposes. One can be used to estimate average causal effects, assuming no confounding given measured covariates. The other can be used to assess how the estimates might change under various departures from no confounding. Both methods…

利用工具变量进行因果推断的回归与加权方法AI 解读

Please see the supplementary material for a correction and a new result.Recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables (IVs) for causal inference. A basic idea is that IVs serve as an experimental handle, the turning of which may change each individual's treatment status and, through and only through this effect, also change observed outcome. The average difference in observed outcome relative to that…

多种生物条件下微阵列时间序列数据的隐马尔可夫模型AI 解读

Among the first microarray experiments were those measuring expression over time, and time course experiments remain common. Most methods to analyze time course data attempt to group genes sharing similar temporal profiles within a single biological condition. However, with time course data in multiple conditions, a main goal is to identify differential expression patterns over time. An intuitive approach to this problem would be to apply at each time point any of the many…

自适应 Lasso 及其 Oracle 性质AI 解读

The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for…

层次 Dirichlet 过程AI 解读

We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior…

Cox 风险回归模型的聚焦信息准则与模型平均AI 解读

This article is concerned with variable selection methods for the Cox proportional hazards regression model. Including excessive covariates causes extra variability and inflated confidence intervals for regression parameters; thus regimes for discarding the less informative ones are needed. Our framework has p covariates designated as “protected,” while variables from a further set of q covariates are examined for possible inclusion or exclusion. We develop a focused…

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