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离散持续时间模型的贝叶斯半参数估计：Dirichlet 过程先验应用AI 解读

Abstract This paper proposes a Bayesian estimator for a discrete time duration model which incorporates a non‐parametric specification of the unobserved heterogeneity distribution, through the use of a Dirichlet process prior. This estimator offers distinct advantages over the Nonparametric Maximum Likelihood estimator of this model. First, it allows for exact finite sample inference. Second, it is easily estimated and mixed with flexible specifications of the baseline…

聚类生存数据脆弱性模型中的协变量测量误差AI 解读

We propose a new class of frailty measurement error models for clustered survival data when covariates are measured with error. We show that the induced hazard function conditional on the observed covariates also follows a frailty model but of a more complicated form. We study the asymptotic bias in regression coefficients and variance components when measurement error is ignored, and the impact of censoring on this asymptotic bias. We show that the naive estimator of the…

校准与经验贝叶斯变量选择AI 解读

For the problem of variable selection for the normal linear model, selection criteria such as aic, Cp , bic and ric have fixed dimensionality penalties. Such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical Bayes formulation. Based on this calibration, we propose empirical Bayes selection criteria that use hyperparameter estimates instead of fixed choices. For obtaining these…

离散情形下最大似然估计量条件分布的似然比近似AI 解读

The likelihood ratio approximation, also called Barndorff‐Nielsen's approximation and often denoted by p*, provides a highly accurate approximation to the conditional density of a maximum likelihood estimator Θ given an ancillary statistic. In this paper, the properties of p* are considered for the case in which the underlying random variables have a lattice distribution and Θ has a discrete, but not necessarily lattice, distribution. If Θ has a lattice distribution, then p*…

局部平稳过程的似然近似AI 解读

A new approximation to the Gaussian likelihood of a multivariate locally stationary process is introduced. It is based on an approximation of the inverse of the covariance matrix of such processes. The new quasi likelihood is a generalization of the classical Whittle likelihood for stationary processes. Several approximation results are proved for the likelihood function. For parametric models, asymptotic normality and efficiency of the resulting estimator are derived for…

BIC 马尔可夫阶数估计量的一致性AI 解读

The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with finite alphabet $A$) from observation of a sample path $x_1, x_2,\dots, x_n$, as that value $k = \hat{k}$ that minimizes the sum of the negative logarithm of the $k$th order maximum likelihood and the penalty term $\frac{|A|^k(|A|-1)}{2}\log n$. We show that $\hat{k}$ equals the correct order of the chain, eventually almost surely as $n \rightarrow \infty$, thereby strengthening earlier…

异方差下线性自回归动态的检验AI 解读

A puzzling characteristic of asset returns for various frequencies is the often observed positive autocorrelation at lag one. To some extent this can be explained by standard asset pricing models when assuming time-varying risk premia. However, one often finds better results when directly fitting an autoregressive model, for which there is little economic foundation. One may ask whether the underlying process does in fact contain an autoregressive component. It is therefore…

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…

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…

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…

利用阈值以上样本的污染水平非参数贝叶斯估计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…

通过限制极大似然减少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…

最大似然估计的序贯置信域AI 解读

The goal of this paper is to develop a general framework for constructing sequential fixed size confidence regions based on maximum likelihood estimates. Asymptotic properties of the sequential procedure for setting up the confidence regions are analyzed under very broad assumptions on the underlying parametric model. It is shown that the proposed sequential procedure is asymptotically optimal in the sense that it approximates the optimal fixed-sample size procedure. It is…

正脉冲序列的参数反卷积AI 解读

This paper describes a parametric deconvolution method (PDPS) appropriate for a particular class of signals which we call spike-convolution models. These models arise when a sparse spike train —Dirac deltas according to our mathematical treatment —is convolved with a fixed point-spread function, and additive noise or measurement error is superimposed.We view deconvolution as an estimation problem, regarding the locations and heights of the underlying spikes, as well as the…

弱 GARCH 表示的估计AI 解读

The classical definitions of GARCH-type processes rely on strong assumptions on the first two conditional moments. The common practice in empirical studies, however, has been to test for GARCH by detecting serial correlations in the squared regression errors. This can be problematic because such autocorrelation structures are compatible with severe misspecifications of the standard GARCH. Numerous examples are provided in the paper. In consequence, standard (quasi-) maximum…

Recently, the concepts of population and individual bioequivalence have been proposed for assessing the bioequivalence of two drug formulations. Moment-based and probability-based measures of bioequivalence have led to criteria for deciding whether two formulations should be regarded as bioequivalent or not. The US Food and Drug Administration (1997) guidance recommended the use of bootstrap percentile intervals for this purpose. In this paper, we discuss theoretical…

等间隔高斯相关观测的精确高斯最大似然与模拟AI 解读

For regularly-spaced observations with the Gaussian autocorrelation function, the finite and infinite autoregressive and moving-average representations can be obtained theoretically. This allows exact Gaussian maximum likelihood to be performed very accurately, and gives a simple exact simulation method.

杂论：二项回归误分类率的极大似然估计AI 解读

Binomial regression is commonly used to construct a binary classification rule from a set of observable covariates. The accuracy of the rule is summarised by empirical type 1 and type 2 misclassification rates as the threshold of the rule varies. However, the empirical misclassification rates are not the maximum likelihood estimators of the true rates if the binomial regression model is assumed true. We give a simple algorithm for the maximum likelihood estimators of the…

利用循环对称性刻画无明显标志点的对象AI 解读

Grenander & Miller (1994) describe a model for representing amorphous two-dimensional objects with no obvious landmark. Each object is represented by n vertices around its perimeter, and is described by deforming an n-sided regular polygon using edge transformations. A multivariate normal distribution with a block circulant covariance matrix is used to model these edge transformations. The purpose of this paper is to describe in detail the statistical properties of this…

利用期望估计方程处理协变量测量误差AI 解读

Summary Estimating equations which are not necessarily likelihood-based score equations are becoming increasingly popular for estimating regression model parameters. This paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects, but surrogate or mismeasured covariates are available instead. The method is motivated by the covariate measurement error problem in marginal or partly conditional…

似然比统计量的几何理解AI 解读

It is well known that twice a log-likelihood ratio statistic follows asymptotically a chi-square distribution. The result is usually understood and proved via Taylor's expansions of likelihood functions and by assuming asymptotic normality of maximum likelihood estimators (MLEs). We obtain more general results by using a different approach: The Wilks type of results hold as long as likelihood contour sets are fan-shaped. The classical Wilks theorem corresponds to the…

变系数模型的高效估计与推断AI 解读

This article deals with statistical inferences based on the varying-coefficient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also…

空间数据插值：克里金法的若干理论AI 解读

1 Linear Prediction.- 1.1 Introduction.- 1.2 Best linear prediction.- Exercises.- 1.3 Hilbert spaces and prediction.- Exercises.- 1.4 An example of a poor BLP.- Exercises.- 1.5 Best linear unbiased prediction.- Exercises.- 1.6 Some recurring themes.- The Matern model.- BLPs and BLUPs.- Inference for differentiable random fields.- Nested models are not tenable.- 1.7 Summary of practical suggestions.- 2 Properties of Random Fields.- 2.1 Preliminaries.- Stationarity.-…