Modified maximum likelihood and modified moment estimators for the three-parameter weibull distribution

This article is concerned with modifications of both maximum likelihood and moment estimators for parameters of the three-parameter Wei bull distribution. Modifications presented here are basically the same as those previously proposed by the authors (1980, 1981, 1982) in connection with the lognormal and the gamma distributions. Computer programs were prepared for the practical application of these estimators and an illustrative example is included. Results of a simulation study provide insight into the sampling behavior of the new estimators and include comparisons with the traditional moment and maximum likelihood estimators. For some combinations of parameter values, some of the modified estimators considered here enjoy advantages over both moment and maximum likelihood estimators with respect to bias, variance, and/or ease of calculation.     

The performance of alternative estimators for the probit model with first-order serial correlation 1

The purpose of the paper is to evaluate the relative performance of two generalized conditional moment (GCM) estimators in terms of their mean squared errors, for the Probit model with first-order serial correlation. The first estimator is a linearized one-step estimator described by Poirier and Ruud (1988). The second one is defined in the present paper. Monte Car10 experiments suggest that the GCM estimators outperform the ordinary Probit estimator. The two GCM estimators do almost equally well, except that the second one may be easier to calculate, especially in large samples.     

Central limit theorem for the empirical process of a linear sequence with long memory

We discuss the functional central limit theorem (FCLT) for the empirical process of a moving-average stationary sequence with long memory. The cases of one-sided and double-sided moving averages are discussed. In the case of one-sided (causal) moving average, the FCLT is obtained under weak conditions of smoothness of the distribution and the existence of (2+δ)-moment of i.i.d. innovations, by using the martingale difference decomposition due to Ho and Hsing (1996, Ann. Statist. 24, 992–1014). In the case of double-sided moving average, the proof of the FCLT is based on an asymptotic expansion of the bivariate probability density.     

Interval estimators for reliability: the bivariate normal case

This paper proposes procedures to provide confidence intervals (CIs) for reliability in stress–strength models, considering the particular case of a bivariate normal set-up. The suggested CIs are obtained by employing either asymptotic variances of maximum-likelihood estimators or a bootstrap procedure. The coverage and the accuracy of these intervals are empirically checked through a simulation study and compared with those of another proposal in the literature. An application to real data is provided.     

The small sample performance of estimators of the standard errors of structural equation models

In this paper, we compare five asymptotically, under a correctly specified likelihood, equivalent estimators of the standard errors for parameters in structural equation models. The estimators are evaluated under different conditions regarding (i) sample size, varying between N=50 and 3200, (ii) distributional assumption of the latent variables and the disturbance terms, namely normal, and heavy tailed (t), and (iii) the complexity of the model. For the assessment of the five estimators we use overall performance, relative bias, MSE and coverage of confidence intervals. The analysis reveals substantial differences in the performance of the five asymptotically equal estimators. Most diversity was found for t distributed, i.e. heavy tailed, data.     

The relative performances of improved ridge estimators and an empirical bayes estimator: some monte carlo results

The relative 'performances of improved ridge estimators and an empirical Bayes estimator are studied by means of Monte Carlo simulations. The empirical Bayes method is seen to perform consistently better in terms of smaller MSE and more accurate empirical coverage than any of the estimators considered here. A bootstrap method is proposed to obtain more reliable estimates of the MSE of ridge esimators. Some theorems on the bootstrap for the ridge estimators are also given and they are used to provide an analytical understanding of the proposed bootstrap procedure. Empirical coverages of the ridge estimators based on the proposed procedure are generally closer to the nominal coverage when compared to their earlier counterparts. In general, except for a few cases, these coverages are still less accurate than the empirical coverages of the empirical Bayes estimator.     

Non-parametric estimation of the long-range dependence exponent for Gaussian processes

We consider a class of long-range-dependent Gaussian processes defined in a semiparametric framework. We propose a new estimator of the long-range dependence parameter, based on the integration of the periodogram in two windows. We show that it is asymptotically Gaussian and calculate the rate of convergence. We optimise parameters defining the window function for the minimum mean-square-error criterion. In a Monte-Carlo study, we compare the proposed estimator with previously studied estimators.     

Sampling properties of estimators of the log-logistic distribution with application to Canadian precipitation data

We consider the probability-weighted moment and the maximum-likelihood estimators of two parameters in the log-logistic distribution. Quantile estimators are obtained using both methods. The distributional properties of these estimators are studied in large samples, via asymptotic theory, and in small and moderate samples, via Monte Carlo simulation. The distribution is shown to be appropriate for a wide variety of meteorological data.     

Bayesian semiparametric inference for the accelerated failure-time model

Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixture-of-Dirichlet-processes prior on the unknown error distribution. A Markov-chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data.     

The relevance of large sample properties of estimators for the errors-in-variables model:a monte carlo study

By means of a Monte Carlo study it is investigated whether moments of the asymptotic distributions of two estimators for the errors-in-variables model are appropriate for employment in small-sample applications.     

A quadratic approximation for Jackknife estimators of the variance of sample mean functions

Jackknife estimators of the variance of estimators which are functions of the sample mean are considered. A quadratic approximation of them is proposed and compared with a linear approximation by Monte Carlo experiments carried out by statistical software Minitab.     

A comparative evaluation of the estimators of the three-parameter generalized pareto distribution

The parameters and quantiles of the three-parameter generalized Pareto distribution (GPD3) were estimated using six methods for Monte Carlo generated samples. The parameter estimators were the moment estimator and its two variants, probability-weighted moment estimator, maximum likelihood estimator, and entropy estimator. Parameters were investigated using a factorial experiment. The performance of these estimators was statistically compared, with the objective of identifying the most robust estimator from amongst them.     

Analysis of the Gibbs sampler for a model related to James-Stein estimators

We analyse a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these results to baseball data from Efron and Morris (1975). For a different range of prior distributions, we prove that the Gibbs sampler will fail to converge, and use this information to prove that in this case the associated posterior distribution is non-normalizable.     

Trimmed mean and bounded influence estimators for the parameters of the ar(1) process

Trimmed mean type estimators are proposcd for estimating the parameters of an AR(1) process. Thcsc definitions are then extended to bounded influence trimmed mcans in analogy to those in the regression case. The behaviour of the estimators are studied numerically under two

outlicr generating models.     

A comparison of parametric conditional error-rate estimators for the two-group linear discriminant function

Using mean absolute deviation, we compare the efficay of two new parametric conditional error rate estimators with six others, four of which are well known.The performance of both new estimators is found to be superior to the six competing estimators examined in this paper, especially when the ratio of the training sample size to the feature dimensionality is small.     

Hierarchical random effect models for coastal erosion of cliffs in the Holderness coast

Prediction of possible cliff erosion at some future date is fundamental to coastal planning and shoreline management, for example to avoid development in vulnerable areas. Historically, to predict cliff recession rates deterministic methods were used. More recently, recession predictions have been expressed in probabilistic terms. However, to date, only simplistic models have been developed. We consider the cliff erosion along the Holderness Coast. Since 1951 a monitoring program has been started in 118 stations along the coast, providing an invaluable, but often missing, source of information. We build hierarchical random effect models, taking account of the known dynamics of the process and including the missing information.     

中国教育收益率统计估计与分析 ——基于参数和半参数估计方法的比较

 本文分别运用参数和半参数估计方法,就如何更准确有效测度中国教育收益率作深入探讨。利用CHNS数据对我国1989年至2006年的教育收益率进行估计,并采用Hausman检验法对两种估计方法结果进行检验。结果表明,从估计效率看,前者比后者的效率更高;但从估计效果看,后者才是一致性估计。而且我们发现虽然教育收益率整体呈逐渐增加趋势,但与实物资本收益率相比仍偏低。中国的教育和劳动力市场亟需加大投资和改革力度。