Volume estimation by monte carlo methods *

In estimating a multiple integral, it is known that Monte Carlo methods are more efficient than analytical techniques when the number of dimensions is beyond seven. In general, the sample-mean method is better than the hit-or-miss Monte Carlo method. However, when the volume of a domain in a high-dimensional space is of interest, the hit-or-miss method is usually preferred. It is because of the difficulty in generalizing the sample-mean method for the computation of the volume of a domain. This paper develops a technique to make such a generalization possible. The technique can be interpreted as a volume-preserving transformation procedure. A volume-preserving transformation is first performed to transform the concerned domain into a hypersphere. The volume of the domain is then evaluated by computing the volume of the hypersphere.     

On Bayesian model and variable selection using MCMC

Several MCMC methods have been proposed for estimating probabilities of models and associated 'model-averaged' posterior distributions in the presence of model uncertainty. We discuss, compare, develop and illustrate several of these methods, focussing on connections between them.     

Lp convergence and complete convergence for weighted sums of AANA random variables

Let {X_n, n ? 1} be a sequence of asymptotically almost negatively associated (AANA, for short) random variables which is stochastically dominated by a random variable X, and {d_ni, 1 ? i ? n, n ? 1} be a sequence of real function, which is defined on a compact set E. Under some suitable conditions, we investigate some convergence properties for weighted sums of AANA random variables, especially the L^p convergence and the complete convergence. As an application, the Marcinkiewicz–Zygmund-type strong law of large numbers for AANA random variables is obtained.     

Goodness‐of‐fit tests for distributions estimated from complex survey data

We propose nonparametric procedures for comparing the empirical distribution function of data from a complex survey with a hypothesized parametric reference distribution. The hypothesized distribution may be fully specified, or it may be a family with the parameters to be estimated from the data. Of the procedures studied, a modification of the Cramér–von Mises test proposed by Lockhart, Spinelli & Stephens [Lockhart, Spinelli and Stephens, The Canadian Journal of Statistics 2007; 35, 125–133] is supported theoretically and performs well in two simulation studies. The methods are applied to examine the distribution of body mass index in the U.S. National Health and Nutrition Examination Survey. The Canadian Journal of Statistics 47: 409–425; 2019 © 2019 Statistical Society of Canada     

Information bounds and MCMC parameter estimation for the pile-up model

This paper is concerned with the pile-up model defined as a nonlinear transformation of a distribution of interest. An observation of the pile-up model is the minimum of a random number of independent variables from the distribution of interest. One specific pile-up model is encountered in time-resolved fluorescence where only the first photon of a random number of photons is observed. In the first part of the paper the Cramér-Rao bound is studied to optimize the experimental conditions by choosing the best tuning parameter which is the average number of variables over which the minimum is taken. The implication is that the tuning parameter currently used in fluorescence does not minimize the acquisition time. However, data obtained at the optimal choice of the tuning parameter require an estimator adapted to the pile-up effect, therefore, an appropriate Gibbs sampler is presented. The covariance matrix of this estimator turns out to be close to the Cramér-Rao bound and hence the acquisition time may be reduced considerably.     

A robust multivariate measurement error model with skew-normal/independent distributions and Bayesian MCMC implementation

Skew-normal/independent distributions are a class of asymmetric thick-tailed distributions that include the skew-normal distribution as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in multivariate measurement errors models. We propose the use of skew-normal/independent distributions to model the unobserved value of the covariates (latent variable) and symmetric normal/independent distributions for the random errors term, providing an appealing robust alternative to the usual symmetric process in multivariate measurement errors models. Among the distributions that belong to this class of distributions, we examine univariate and multivariate versions of the skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.     

Complete convergence for weighted sums of mixingale sequences and statistical applications

In this paper, the complete convergence of weighted sums of L^r-mixingale is established, from which the complete convergence of martingale differences is also derived. As statistical applications, non parametric regression model and simpler linear errors-in-variables model with mixingale errors are discussed.     

Complete convergence for weighted sums of i.i.d. random variables with applications in regression estimation and EV model

In this paper, we obtain complete convergence results for Stout type weighted sums of i.i.d. random variables. A strong law for weighted sums of i.i.d. random variables is also obtained. As the applications of the strong law, the strong consistency and rate of the nonparametric regression estimations and the rates of the strong consistency of LS estimators for the unknown parameters of the simple linear errors in variables (EV) model are given.     

General results of complete convergence and complete moment convergence for weighted sums of some class of random variables

ABSTRACT

In the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013 Shen, A.T. (2013). On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal.2013, Article ID 216236: 1–7. [Google Scholar]).     

Maximum likelihood estimation for outcome‐dependent samples

In outcome‐dependent sampling, the continuous or binary outcome variable in a regression model is available in advance to guide selection of a sample on which explanatory variables are then measured. Selection probabilities may either be a smooth function of the outcome variable or be based on a stratification of the outcome. In many cases, only data from the final sample is accessible to the analyst. A maximum likelihood approach for this data configuration is developed here for the first time. The likelihood for fully general outcome‐dependent designs is stated, then the special case of Poisson sampling is examined in more detail. The maximum likelihood estimator differs from the well‐known maximum sample likelihood estimator, and an information bound result shows that the former is asymptotically more efficient. A simulation study suggests that the efficiency difference is generally small. Maximum sample likelihood estimation is therefore recommended in practice when only sample data is available. Some new smooth sample designs show considerable promise.     

On complete and complete moment convergence for weighted sums of ANA random variables and applications

In this article, the complete convergence and complete moment convergence for weighted sums of asymptotically negatively associated (ANA, for short) random variables are studied. Several sufficient conditions of the complete convergence and complete moment convergence for weighted sums of ANA random variables are presented. As an application, the complete consistency for the weighted estimator in a nonparametric regression model based on ANA random errors is established by using the complete convergence that we established. We also give a simulation to verify the validity of the theoretical result.     

A sequential method for the evaluation of the VaR model based on the run between exceedances

Summary: A technique for sequential assessment of the appropriateness of the VaR model is developed, by drawing on a tool from statistical process control, namely the control chart. We show that an EWMA control chart is the most appropriate instrument for detecting changes in the process of the magnitude of interest in risk management. The robustness of our procedure with respect to violations of some assumptions is examined and it is concluded that our model evaluation technique remains suitable in such cases.     

Simulated maximum likelihood estimation in joint models for multiple longitudinal markers and recurrent events of multiple types,in the presence of a terminal event

In medical studies we are often confronted with complex longitudinal data. During the follow-up period, which can be ended prematurely by a terminal event (e.g. death), a subject can experience recurrent events of multiple types. In addition, we collect repeated measurements from multiple markers. An adverse health status, represented by ‘bad’ marker values and an abnormal number of recurrent events, is often associated with the risk of experiencing the terminal event. In this situation, the missingness of the data is not at random and, to avoid bias, it is necessary to model all data simultaneously using a joint model. The correlations between the repeated observations of a marker or an event type within an individual are captured by normally distributed random effects. Because the joint likelihood contains an analytically intractable integral, Bayesian approaches or quadrature approximation techniques are necessary to evaluate the likelihood. However, when the number of recurrent event types and markers is large, the dimensionality of the integral is high and these methods are too computationally expensive. As an alternative, we propose a simulated maximum-likelihood approach based on quasi-Monte Carlo integration to evaluate the likelihood of joint models with multiple recurrent event types and markers.     

基于MCMC模拟和伪似然估计法的交叉分类信度模型费率厘定简

针对传统交叉分类信度模型计算复杂且在结构参数先验信息不足的情况下不能得到参数无偏后验估计的问题,利用MCMC模拟和GLMM方法,对交叉分类信度模型进行实证分析证明模型的有效性。结果表明：基于MCMC方法能够动态模拟参数的后验分布,并可提高模型估计的精度;基于GLMM能大大简化计算过程且操作方便,可利用图形和其它诊断工具选择模型,并对模型实用性做出评价。     

Complete convergence for weighted sums of END random variables and its application to nonparametric regression models

In this article, the complete convergence for weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence are provided. In addition, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of END random variables is obtained. The results obtained in the article generalise and improve the corresponding one of Wang et al. [(2014b), ‘On Complete Convergence for an Extended Negatively Dependent Sequence’, Communications in Statistics-Theory and Methods, 43, 2923–2937]. As an application, the complete consistency for the estimator of nonparametric regression model is established.     

Complete moment convergence of weighted sums for arrays of negatively dependent random variables and its applications

For testing goodness-of-fit in a k cell multinomial distribution having very small frequencies, the usual chi-square approximation to the upper tail of the likelihood ratio statistic, G² is not satisfactory. A new adjustment to G² is determined on the basis of analytical investigation in terms of asymptotic bias and variance of the adjusted G² A Monte Carlo simulation is performed for several one-way tables to assess the adjustment of G² in order to obtain a closer approximation to the nomial level of significance.