A statistical model for orientation mechanism

A variance components model with response variable depending on both fixed effects of explanatory variables and random components is specified to model longitudinal circular data, in order to study the directional behaviour of small animals, as insects, crustaceans, amphipods, etc. Unknown parameter estimators are obtained using a simulated maximum likelihood approach. Issues concerning log-likelihood variability and the related problems in the optimization algorithm are also addressed. The procedure is applied to the analysis of directional choices under full natural conditions ofTalitrus saltator from Castiglione della Pescaia (Italy) beaches.     

Estimation of variance components in linear mixed measurement error models

In this paper, we consider a linear mixed model with measurement errors in fixed effects. We find the corrected score function estimators for the variance components. An iterative algorithm is proposed for estimating the parameters. The computations on each iteration of this algorithm are those associated with computing estimates of fixed and random effects for given values of the variance components. We also derive the consistency of the estimators under regularity conditions. The simulation study shows that for relatively small sample size the corrected estimators perform very well. Finally, an example of real data is given for illustration.     

A hierarchical approach to the study of the exponential failure model

The exponential failure model is studied from the hierarchical point of view. The parameter of the exponential is considered as a random variable with a gamma function as a prior. Futhermore, the scale parameter of the gamma prior isassumed to be a random variable with known hyperprior. Under these assumptions estimators are derived for the exponential parameter and reliability function. Monte Carlo simulation is utilized to compare the various estimators.     

On the difference between ML and REML estimators in the modelling of multivariate longitudinal data

A random effects model is examined in the multivariate setting where more than one characteristics are measured at each time point. ML and REML estimators are obtained under the restriction that estimates of variance matrices being at least p.s.d. It is shown that REML has greater probability of giving full rank estimates of variance components matrices but as regards the efficiency in the estimation of the location parameter, correct specification of the number of random effects is needed. In general, REML provides larger estimates of variance of model parameters than ML.     

Maximum likelihood estimation of variance components of heteroscedastic random anova model

the estimation of variance components of heteroscedastic random model is discussed in this paper. Maximum Likelihood (ML) is described for one-way heteroscedastic random models. The proportionality condition that cell variance is proportional to the cell sample size, is used to eliminate the efffect of heteroscedasticity. The algebraic expressions of the estimators are obtained for the model. It is seen that the algebraic expressions of the estimators depend mainly on the inverse of the variance-covariance matrix of the observation vector. So, the variance-covariance matrix is obtained and the formulae for the inversions are given. A Monte Carlo study is conducted. Five different variance patterns with different numbers of cells are considered in this study. For each variance pattern, 1000 Monte Carlo samples are drawn. Then the Monte Carlo biases and Monte Carlo MSE’s of the estimators of variance components are calculated. In respect of both bias and MSE, the Maximum Likelihood (ML) estimators of variance components are found to be sufficiently good.     

An Extended Single‐index Model with Missing Response at Random

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators.     

A Jackknife Method for Estimation of Variance Components

This paper concerns a method of estimation of variance components in a random effect linear model. It is mainly a resampling method and relies on the Jackknife principle. The derived estimators are presented as least squares estimators in an appropriate linear model, and one of them appears as a MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimator. Our resampling method is illustrated by an example given by C. R. Rao [7] and some optimal properties of our estimator are derived for this example. In the last part, this method is used to derive an estimation of variance components in a random effect linear model when one of the components is assumed to be known.     

Location and scale parameter estimation from randomly censored data

The problem of location and scale parameter estimation from randomly censored data is analyzed through use of a regression model for the Kaplan-Meier quantlle process. Continuous time regression techniques are employed to construct estimators that are both asymptotically normal and efficient. Estimators with a particularly simple form are obtained for the Koziol-Green model for random censorship. In the event of no censoring the regression model, and resulting estimators, reduce to those proposed by Parzen (1979 a, b).     

The mixed model for survey regression estimation

Estimation of the population mean under the regression model with random components is considered. Conditions under which the random components regression estimator is design consistent are given. It is shown that consistency holds when incorrect values are used for the variance components. The regression estimator constructed with model parameters that differ considerably from the true parameters performed well in a Monte Carlo study. Variance estimators for the regression predictor are suggested. A variance estimator appropriate for estimators constructed with a biased estimator for the between-group variance component performed well in the Monte Carlo study.     

VARIANCE ESTIMATION IN THE ERROR COMPONENTS REGRESSION MODEL

ABSTRACT

In a regression model with a random individual and a random time effect explicit representations of the nonnegative quadratic minimum biased estimators of the corresponding variances are deduced. These estimators always exist and are unique. Moreover, under normality assumption of the dependent variable unbiased estimators of the mean squared errors of the variance estimates are derived. Finally, confidence intervals on the variance components are considered.     

Robust R-Estimation of a Consensus Value from Multi-Center Studies

We consider multi-center experiments (for determining a consensus value) conducted in possibly heterogeneous set-ups leading to unbalanced heteroscedastic one-way random effects models. When normality of both the random components and their homoscedasticity are in doubt, standard statistical methods may not be valid. Two robust R-estimators (for the common location parameter), based on signed-rank statistics, are proposed and their properties studied. When large heteroscedasticity is present or the distribution of random effect is abnormal, the proposed estimators perform better than the classical weighted least squares and selected estimators. This feature is illustrated with an arsenic in oyster tissue problem, along with some other simulation studies.     

Least Squares estimation for the multivariate weibull model of bougaard based on accelerated life test of system and component

Accelerated life testing of products quickly yields information on life. In this article, we present a simple method to incorporate the information collected from accelerated life tests of both components and (series) systems. The multivariate Weibull distribution of Hougaard is applied to model lifetimes of components. Least-squares (LS) estimators of the model parameters and their joint asymptotic distribution are derived. The effects of the dependence parameter and the proportion of the system-data to the asymptotic relative efficiencies of the LS estimators are investigated.     

On empirical Bayes estimation of variance components in random effects model

In this paper, Bayes estimators of variance components are derived for the one-way random effects model, and empirical Bayes (EB) estimators are constructed by the kernel estimation method of a multivariate density and its mixed partial derivatives. It is shown that the EB estimators are asymptotically optimal and convergence rates are established. Finally, an example concerning the main results is given.     

The Superiorities of Empirical Bayes Estimation of Variance Components in Random Effects Model

In this article, the Bayes estimators of variance components are derived and the parametric empirical Bayes estimators (PEBE) for the balanced one-way classification random effects model are constructed. The superiorities of the PEBE over the analysis of variance (ANOVA) estimators are investigated under the mean square error (MSE) criterion, some simulation results for the PEBE are obtained. Finally, a remark for the main results is given.     

Bayesian estimates in a one-way ANOVA random effects model

Bayesian estimators of variance components are developed, based on posterior mean and posterior mode, respectively, in a one-way ANOVA random effects model with independent prior distributions. The formulas for the proposed estimators are simple. The estimators give sensible results for 'badly-behaved' datasets, where the standard unbiased estimates are negative. They are markedly robust as compared to the existing estimators such as the maximum likelihood estimators and the maximum posterior density estimators.     

Maximum likelihood from spatial random effects models via the stochastic approximation expectation maximization algorithm

We introduce a class of spatial random effects models that have Markov random fields (MRF) as latent processes. Calculating the maximum likelihood estimates of unknown parameters in SREs is extremely difficult, because the normalizing factors of MRFs and additional integrations from unobserved random effects are computationally prohibitive. We propose a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood functions of spatial random effects models. The SAEM algorithm integrates recent improvements in stochastic approximation algorithms; it also includes components of the Newton-Raphson algorithm and the expectation-maximization (EM) gradient algorithm. The convergence of the SAEM algorithm is guaranteed under some mild conditions. We apply the SAEM algorithm to three examples that are representative of real-world applications: a state space model, a noisy Ising model, and segmenting magnetic resonance images (MRI) of the human brain. The SAEM algorithm gives satisfactory results in finding the maximum likelihood estimate of spatial random effects models in each of these instances.     

On the Value of derivative evaluations and random walk suppression in Markov Chain Monte Carlo algorithms

Two strategies that can potentially improve Markov Chain Monte Carlo algorithms are to use derivative evaluations of the target density, and to suppress random walk behaviour in the chain. The use of one or both of these strategies has been investigated in a few specific applications, but neither is used routinely. We undertake a broader evaluation of these techniques, with a view to assessing their utility for routine use. In addition to comparing different algorithms, we also compare two different ways in which the algorithms can be applied to a multivariate target distribution. Specifically, the univariate version of an algorithm can be applied repeatedly to one-dimensional conditional distributions, or the multivariate version can be applied directly to the target distribution.     

Parameter estimation for a new distribution for the strength of brittle fibers: a simulation study

Parameter estimates of a new distribution for the strength of brittle fibers and composite materials are considered. An algorithm for generating random numbers from the distribution is suggested. Two parameter estimation methods, one based on a simple least squares procedure and the other based on the maximum likelihood principle, are studied using Monte Carlo simulation. In most cases, the maximum likelihood estimators were found to have somewhat smaller root mean squared error and bias than the least squares estimators. However, the least squares estimates are generally good and provide useful initial values for the numerical iteration used to find the maximum likelihood estimates.     

Estimating the negative binomial dispersion parameter with highly stratified surveys

We investigate several estimators of the negative binomial (NB) dispersion parameter for highly stratified count data for which the statistical model has a separate mean parameter for each stratum. If the number of samples per stratum is small then the model is highly parameterized and the maximum likelihood estimator (MLE) of the NB dispersion parameter can be biased and inefficient. Some of the estimators we investigate include adjustments for the number of mean parameters to reduce bias. We extend other estimators that were developed for the iid case, to reduce bias when there are many mean parameters. We demonstrate using simulations that an adjusted double extended quasi-likelihood estimator we proposed gives much improved estimates compared to the MLE. Adjusted extended quasi-likelihood and adjusted maximum likelihood estimators also give much-improved results. We illustrate the various estimators with stratified random bottom trawl survey data for cod (Gadus morhua) off the south coast of Newfoundland, Canada.     

基于格点搜索的随机效应的GLS估计

面板数据随机效应模型两步回归法参数估计使用的方差分量来自第一步的回归估计,它没有考虑方差分量的精度。为了弥补这一缺陷,故提出最优方差分量法（Optimal Variance Component）,简称OVC。OVC方法增加了＂格点搜索＂技术,能够提供更多的方差分量组合,因此在一定程度上提高了参数估计的精度。蒙特卡罗模拟的结果虽然支持上述论点,但该方法却存在一定的问题,仍有待进一步完善。