Robust Estimation of a Spatiotemporal Model with Structural Change

A spatiotemporal model is postulated and estimated using a procedure that infuses the forward search algorithm and maximum likelihood estimation into the backfitting framework. The forward search algorithm filters the effect of temporary structural change in the estimation of covariate and spatial parameters. Simulation studies illustrate capability of the method in producing robust estimates of the parameters even in the presence of structural change. The method provides good model fit even for small sample sizes in short time series data and good predictions for a wide range of lengths of contamination periods and levels of severity of contamination.     

Robust estimation of a multilevel model with structural change

We postulate a spatiotemporal multilevel model and estimate using forward search algorithm and MLE imbedded into the backfitting algorithm. Forward search algorithm ensures robustness of the estimates by filtering the effect of temporary structural changes in the estimation of the group-level covariates, the individual-level covariates and spatial parameters. Backfitting algorithm provides computational efficiency of estimation procedure assuming an additive model. Simulation studies show that estimates are robust even in the presence of structural changes induced for example by epidemic outbreak. The model also produced robust estimates even for small sample and short time series common in epidemiological settings.     

Two steps generalized maximum entropy estimation procedure for fitting linear regression when both covariates are subject to error

This paper presents a procedure utilizing the generalized maximum entropy (GME) estimation method in two steps to quantify the uncertainty of the simple linear structural measurement error model parameters exactly. The first step estimates the unknowns from the horizontal line, and then the estimates were used in a second step to estimate the unknowns from the vertical line. The proposed estimation procedure has the ability to minimize the number of unknown parameters in formulating the GME system within each step, and hence reduce variability of the estimates. Analytical and illustrative Monte Carlo simulation comparison experiments with the maximum likelihood estimators and a one-step GME estimation procedure were presented. Simulation experiments demonstrated that the two steps estimation procedure produced parameter estimates that are more accurate and more efficient than the classical estimation methods. An application of the proposed method is illustrated using a data set gathered from the Centre for Integrated Government Services in Delma Island – UAE to predict the association between perceived quality and the customer satisfaction.     

Maximum Likelihood Inference for Multivariate Frailty Models Using an Automated Monte Carlo EM Algorithm

We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples drawn from the posterior distribution of the frailties using rejection sampling. The maximization step reduces to a standard partial likelihood maximization. We also propose a simple rule based on the relative change in the parameter estimates to decide on sample size in each iteration and a stopping time for the algorithm. An important new concept is acquiring absolute convergence of the algorithm through sample size determination and an efficient sampling technique. The method is illustrated using a rat carcinogenesis dataset and data on vase lifetimes of cut roses. The estimation results are compared with approximate inference based on penalized partial likelihood using these two examples. Unlike the penalized partial likelihood estimation, the proposed full maximum likelihood estimation method accounts for all the uncertainty while estimating standard errors for the parameters.     

Bootstrap procedures in a spatial-temporal model

Two bootstrap procedures are introduced into the hybrid of the backfitting algorithm and the Cochrane–Orcutt procedure in the estimation of a spatial-temporal model. The use of time blocks of consecutive observations in resampling steps proved to be optimal in terms of stability and efficiency of estimates. Between iterations, there were minimal changes in the empirical distributions of the parameter estimates associated with the covariate and temporal effects indicating convergence of the algorithm. Crop yield data are used to illustrate the proposed methods.

The simulation study indicated that prediction error from the fitted model (estimated from either Method 1 or Method 2) is very low. Also, the prediction error is relatively robust to the number of spatial units and the number of time points.     

Reducing bias in parameter estimates from stepwise regression in proportional hazards regression with right-censored data

When variable selection with stepwise regression and model fitting are conducted on the same data set, competition for inclusion in the model induces a selection bias in coefficient estimators away from zero. In proportional hazards regression with right-censored data, selection bias inflates the absolute value of parameter estimate of selected parameters, while the omission of other variables may shrink coefficients toward zero. This paper explores the extent of the bias in parameter estimates from stepwise proportional hazards regression and proposes a bootstrap method, similar to those proposed by Miller (Subset Selection in Regression, 2nd edn. Chapman & Hall/CRC, 2002) for linear regression, to correct for selection bias. We also use bootstrap methods to estimate the standard error of the adjusted estimators. Simulation results show that substantial biases could be present in uncorrected stepwise estimators and, for binary covariates, could exceed 250% of the true parameter value. The simulations also show that the conditional mean of the proposed bootstrap bias-corrected parameter estimator, given that a variable is selected, is moved closer to the unconditional mean of the standard partial likelihood estimator in the chosen model, and to the population value of the parameter. We also explore the effect of the adjustment on estimates of log relative risk, given the values of the covariates in a selected model. The proposed method is illustrated with data sets in primary biliary cirrhosis and in multiple myeloma from the Eastern Cooperative Oncology Group.     

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.     

Editorial collaborators

A simulation study of the binomial-logit model with correlated random effects is carried out based on the generalized linear mixed model (GLMM) methodology. Simulated data with various numbers of regression parameters and different values of the variance component are considered. The performance of approximate maximum likelihood (ML) and residual maximum likelihood (REML) estimators is evaluated. For a range of true parameter values, we report the average biases of estimators, the standard error of the average bias and the standard error of estimates over the simulations. In general, in terms of bias, the two methods do not show significant differences in estimating regression parameters. The REML estimation method is slightly better in reducing the bias of variance component estimates.     

Joint estimation of the mean and dispersion parameters in the analysis of proportions: A comparison of efficiency and bias

This paper deals with joint estimation of the mean and dispersion parameters in the analysis of proportions. We consider a parametric model, namely the extended beta-binomial model, and several semiparametric procedures. We study large-sample efficiency and small-sample bias and efficiency properties of the estimates of the mean and intraclass correlation parameters. Estimation and efficiency calculations are présentés for the regression model. However, for simplicity, numerical large-sample efficiency and small-sample bias and efficiency calculations are performed for the two-parameter model only. Numerical efficiency results are présentés in terms of graphs. Estimated asymptotic efficiencies of various estimates are also compared for two data sets. Our findings suggest that for the estimation of the mean (regression) parameters the quasilikelihood procedure performs best. However, for the joint estimation, the Gaussian likelihood estimates perform best.     

Inference for response-limited time-series models

This paper Introduces a robust time series estimation procedure based on a new nonlinear time-series model called the response-limited ARMA model. Under this procedure, In contrast to location or regression, the uncorrected pseudo-observations, which produce the parameter estimates when submitted to a standard analysis, also yield satisfactory standard errors for inference purposes.     

Keep it simple: estimation strategies for ordered response models with fixed effects

By running Monte Carlo simulations, we compare different estimation strategies of ordered response models in the presence of non-random unobserved heterogeneity. We find that very simple binary recoding schemes deliver parameter estimates with very low bias and high efficiency. Furthermore, if the researcher is interested in the relative size of parameters the simple linear fixed effects model is the method of choice.     

Estimation Procedure for a Multiple Time Series Model

Given a multiple time series sharing common autoregressive patterns, we estimate an additive model. The autoregressive component and the individual random effects are estimated by integrating maximum likelihood estimation and best linear unbiased predictions in a backfitting algorithm. The simulation study illustrated that the estimation procedure provides an alternative to the Arellano–Bond generalized method of moments (GMM) estimator of the panel model when T > N and the Arellano–Bond generally diverges. The estimator has high predictive ability. In cases where T ≤ N, the backfitting estimator is at least comparable to Arellano–Bond estimator.     

Effects of level shifts and temporary changes on the estimation of GARCH models

The aim of this article is to analyse the effect of the level shift and temporary change outliers on the estimation of a model with conditional heteroscedasticity, a concept rarely dealt with up to now, the literature focusing more on additive outliers. To do this, we have conducted various Monte Carlo experiments in which the bias produced by these outliers is analysed.     

空间回归模型估计中的最小二乘法

空间回归模型由于引入了空间地理信息而使得其参数估计变得复杂,因为主要采用最大似然法,致使一般人认为在空间回归模型参数估计中不存在最小二乘法。通过分析空间回归模型的参数估计技术,研究发现,最小二乘法和最大似然法分别用于估计空间回归模型的不同的参数,只有将两者结合起来才能快速有效地完成全部的参数估计。数理论证结果表明,空间回归模型参数最小二乘估计量是最佳线性无偏估计量。空间回归模型的回归参数可以在估计量为正态性的条件下而实施显著性检验,而空间效应参数则不可以用此方法进行检验。     

Simulation-based consistent inference for biased working model of non-sparse high-dimensional linear regression

Variable selection in regression analysis is of importance because it can simplify model and enhance predictability. After variable selection, however, the resulting working model may be biased when it does not contain all of significant variables. As a result, the commonly used parameter estimation is either inconsistent or needs estimating high-dimensional nuisance parameter with very strong assumptions for consistency, and the corresponding confidence region is invalid when the bias is relatively large. We in this paper introduce a simulation-based procedure to reformulate a new model so as to reduce the bias of the working model, with no need to estimate high-dimensional nuisance parameter. The resulting estimators of the parameters in the working model are asymptotic normally distributed whether the bias is small or large. Furthermore, together with the empirical likelihood, we build simulation-based confidence regions for the parameters in the working model. The newly proposed estimators and confidence regions outperform existing ones in the sense of consistency.     

Sample-based Maximum Likelihood Estimation of the Autologistic Model

New recursive algorithms for fast computation of the normalizing constant for the autologistic model on the lattice make feasible a sample-based maximum likelihood estimation (MLE) of the autologistic parameters. We demonstrate by sampling from 12 simulated 420×420 binary lattices with square lattice plots of size 4×4, …, 7×7 and sample sizes between 20 and 600. Sample-based results are compared with ‘benchmark’ MCMC estimates derived from all binary observations on a lattice. Sample-based estimates are, on average, biased systematically by 3%–7%, a bias that can be reduced by more than half by a set of calibrating equations. MLE estimates of sampling variances are large and usually conservative. The variance of the parameter of spatial association is about 2–10 times higher than the variance of the parameter of abundance. Sample distributions of estimates were mostly non-normal. We conclude that sample-based MLE estimation of the autologistic parameters with an appropriate sample size and post-estimation calibration will furnish fully acceptable estimates. Equations for predicting the expected sampling variance are given.     

Estimating the Burr XII Parameters in Constant-Stress Partially Accelerated Life Tests Under Multiple Censored Data

In this article, we present the performance of the maximum likelihood estimates of the Burr XII parameters for constant-stress partially accelerated life tests under multiple censored data. Two maximum likelihood estimation methods are considered. One method is based on observed-data likelihood function and the maximum likelihood estimates are obtained by using the quasi-Newton algorithm. The other method is based on complete-data likelihood function and the maximum likelihood estimates are derived by using the expectation-maximization (EM) algorithm. The variance–covariance matrices are derived to construct the confidence intervals of the parameters. The performance of these two algorithms is compared with each other by a simulation study. The simulation results show that the maximum likelihood estimation via the EM algorithm outperforms the quasi-Newton algorithm in terms of the absolute relative bias, the bias, the root mean square error and the coverage rate. Finally, a numerical example is given to illustrate the performance of the proposed methods.     

A general maximum likelihood analysis of overdispersion in generalized linear models

This paper presents an EM algorithm for maximum likelihood estimation in generalized linear models with overdispersion. The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully non-parametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters may be sensitive to the specification of a parametric form for the mixing distribution. A listing of a GLIM4 algorithm for fitting the overdispersed binomial logit model is given in an appendix.A simple method is given for obtaining correct standard errors for parameter estimates when using the EM algorithm.Several examples are discussed.     

Effects of correlation in modeling clustered binary data

A simulation study is conducted to determine the effects of varying correlation structures on two estimation procedures used to model clustered binary data; a parametric model, the beta-binomial, and a non-parametric model, the exchangeable binary. The simulations detected bias in estimation of the mean response parameter and the correlation parameter when assuming a parametric model. In addition it was found that variance parameters can be severely underestimated if the correlation structure is considered strictly a nuisance parameter.     

A recursive approach to parameter estimation in regression and time series models

In this paper we discuss the recursive (or on line) estimation in (i) regression and (ii) autoregressive integrated moving average (ARIMA) time series models. The adopted approach uses Kalman filtering techniques to calculate estimates recursively. This approach is used for the estimation of constant as well as time varying parameters. In the first section of the paper we consider the linear regression model. We discuss recursive estimation both for constant and time varying parameters. For constant parameters, Kalman filtering specializes to recursive least squares. In general, we allow the parameters to vary according to an autoregressive integrated moving average process and update the parameter estimates recursively. Since the stochastic model for the parameter changes will "be rarely known, simplifying assumptions have to be made. In particular we assume a random walk model for the time varying parameters and show how to determine whether the parameters are changing over time. This is illustrated with an example.