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层级模型：当时的计算视角AI 解读

Hierarchical models (HMs) provide a flexible framework for modeling data. The ongoing development of techniques like the EM algorithm and Markov chain Monte Carlo has enabled statisticians to make use of increasingly more complicated HMs over the last few decades. In this article, we consider Bayesian and frequentist versions of a general, two-stage HM, and describe several examples from the literature that illustrate its versatility. Some key aspects of the computational…

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变量选择问题AI 解读

The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. This vignette reviews some of the key developments that have led to the wide variety of approaches for this…

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更简便的仿射不变多元分布无关符号检验AI 解读

A simpler multivariate sign test is proposed that uses the transformation-retransformation approach of Chakraborty, Chaudhuri, and Oja together with a directional transformation due to Tyler. This produces a multivariate sign test that is practical to apply to data of any dimension, makes minimal assumptions about the underlying distribution, and has a small-sample distribution-free property over a broad class of population models. It is shown to perform very well in…

利用多样本广义L统计量稳健分析交叉设计AI 解读

In a crossover study, some or all subjects receive more than one treatment sequentially. Using a clinical example as motivation, we develop multisample generalized L-statistics (GL-statistics) to estimate and test for treatment effects in crossovers when the distribution of the response data deviates from normality. The basic idea is to adapt simple L-statistics, such as the trimmed mean and median, to data with dependencies. GL-statistics may be applied to crossovers with…

确定性模拟模型的推断：贝叶斯融合方法AI 解读

Deterministic simulation models are used in many areas of science, engineering, and policy making. Typically, these are complex models that attempt to capture underlying mechanisms in considerable detail, and they have many user-specified inputs. The inputs are often specified by some form of trial-and-error approach in which plausible values are postulated, the corresponding outputs inspected, and the inputs modified until plausible outputs are obtained. Here we address the…

非平稳时间序列的 Whittle 伪极大似然估计AI 解读

Whittle pseudo-maximum likelihood estimates of parameters for stationary time series have been found to be consistent and asymptotically normal in the presence of long-range dependence. Generalizing the definition of the memory parameter d we extend these results to include possibly nonstationary (.5 ≤ d < 1) or antipersistent (-.5 < d < 0) observations. Using adequate data tapers, we can apply this estimation technique to any degree of nonstationarity d ≥ .5 without a…

基于积分似然的指数次序统计量模型推断AI 解读

Methods of statistical inference are developed for the exponential order statistic (EOS) model, where only a subset of order statistics from a collection of N iid exponential random detection times is observable. When the rate parameter for detections is unknown, the maximum likelihood estimator (MLE) of the unknown integer parameter N can be infinite with substantial probability. Inference for N is developed using a pseudolikelihood function obtained by integrating out the…

准确协变量无法获得时的 Cox 回归：非参数校正方法AI 解读

Many survival studies involve covariates that are not accurately ascertainable; CD4 lymphocyte count in HIV/AIDS research is a typical example for which the gold standard of the measurement is not available. This article proposes a consistent estimation procedure for Cox regression under the additive measurement error model. Distinct from existing methods, the proposed estimation for regression coefficients does not require any additional assumptions. We establish the…

删失停止时刻下递增随机过程均值的估计AI 解读

Data often come in the form of a longitudinal series, say N(·), whose observation has been “stopped” either by a terminal event U (e.g., death) or censoring event C (e.g., lost to follow-up). When N(·) is not deterministic, it is generally not possible to use standard survival analysis tools (e.g., the Kaplan-Meier estimator) to consistently estimate functionals of the distribution of N(U) because of “induced” informative censoring. Various seemingly unrelated estimators…

基于输出等值面的分层抽样方案AI 解读

If the probability distribution of the input variables to a system described by a computer code is known, the distribution function of the output variable can be obtained by computer simulations. With a complicated program, each simulation can take very long time. It thus is necessary to choose the combinations of the input parameters carefully to get as much information as possible with a small number of computer runs. Different methods (true random sampling, stratified…

通过限制极大似然降低时间序列回归中自回归估计的偏差AI 解读

This article considers maximum likelihood (ML) and restricted maximum likelihood (REML) estimation of time series regression models with autoregressive AR(p) noise. Approximate biases of the ML and REML estimators of the AR parameters, based on their approximate representations, are derived. In addition, a bias result for the ML estimator (MLE) of the error variance is established. Numerical results are presented to illustrate the biases of the MLE and REML estimator for the…

复合原假设模型中 p 值的渐近分布AI 解读

We investigate the compatibility of a null model H 0 with the data by calculating a p value; that is, the probability, under H 0, that a given test statistic T exceeds its observed value. When the null model consists of a single distribution, the p value is readily obtained, and it has a uniform distribution under H 0. On the other hand, when the null model depends on an unknown nuisance parameter θ one must somehow get rid of θ, (e.g., by estimating it) to calculate a p…

复合原假设模型的p值AI 解读

The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters, p values are not uniquely defined. The proposals for computing a p value in such a situation include…

利用阈值以上样本非参数贝叶斯估计污染水平AI 解读

Data on contamination concentrations for chromium from one of the EPA's toxic waste sites consist of independent and identically distributed (iid) measurements along with additional observations from the residual distribution. The residual sample is obtained by sampling from hot spots, where contamination concentrations are assumed to be above a given threshold value. The data are modeled using a nonparametric Bayes estimator of the distribution function. The Dirichlet…

慢性阻塞性肺疾病死亡率的贝叶斯分析与制图AI 解读

This article summarizes our research on estimation of age-specific and age-adjusted mortality rates for chronic obstructive pulmonary disease (COPD) for white males. Our objectives are more precise and informative displays (than previously available) of geographic variation of the age-specific mortality rates for COPD, and investigation of the relationships between the geographic variation in mortality rates and the corresponding variation in selected covariates. For a given…

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