Influence Diagnostics and Estimation Algorithms for Powell's SCLS

This article studies influence diagnostics and estimation algorithms for Powell's symmetrically censored least squares estimator. The proposed measures of influence are based on one-step approximations to the analogous deletion diagnostics used in least squares regression and can be conveniently constructed using a Newton-type algorithm. Additionally, it is found that this algorithm can be used to substantially reduce the computational burden of the estimator. The results of the article are illustrated with an application.     

Estimation in regression models with stationary,dependent errors

Often the unknown covariance structure of a stationary, dependent, Gaussian error sequence can be simply parametrised. The error sequence can either be directly observed or observed only through a random sequence containing a deterministic regression model. The method of scoring is used here, in conjunction with recursive estimation techniques, to effect the maximum likelihood estimation of the covariance parameters. Sequences of recursive residuals, useful in model diagnostics and data analysis, are obtained in the estimation procedure.     

A useful approach to identify the multicollinearity in the presence of outliers

The presence of outliers in the data sets affects the structure of multicollinearity which arises from a high degree of correlation between explanatory variables in a linear regression analysis. This affect could be seen as an increase or decrease in the diagnostics used to determine multicollinearity. Thus, the cases of outliers reduce the reliability of diagnostics such as variance inflation factors, condition numbers and variance decomposition proportions. In this study, we propose to use a robust estimation of the correlation matrix obtained by the minimum covariance determinant method to determine the diagnostics of multicollinearity in the presence of outliers. As a result, the present paper demonstrates that the diagnostics of multicollinearity obtained by the robust estimation of the correlation matrix are more reliable in the presence of outliers.     

Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model

Summary.  'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual.     

Kernel autocorrelogram for time-deformed processes

The purpose of the paper is to propose an autocorrelogram estimation procedure for irregularly spaced data which are modelled as subordinated continuous time-series processes. Such processes, also called time-deformed stochastic processes, have been proposed in a variety of contexts. Before entertaining the possibility of modelling such time series, one is interested in examining simple diagnostics and data summaries. With continuous-time processes this is a challenging task which can be accomplished via kernel estimation. The paper develops the conceptual framework, the estimation procedure and its asymptotic properties. An illustrative empirical example is also provided.     

Non-parametric bootstrap recycling

The double bootstrap provides diagnostics for bootstrap calculations and, if need be, appropriate adjustments. The amount of computation involved is usually considerable, and recycling provides a less computer intensive alternative. Recycling consists of using repeatedly the same samples drawn from a recycling distribution G for estimation under each first-level bootstrap distribution, rather than independently repeating the simulation and estimation steps for each of these.Recycling is successful in parametric applications of the bootstrap, as demonstrated by M.A. Newton and C.J. Geyer (J. Amer. Statist. Assoc. 89: 905–912, 1994). We show that it is bound to fail in non-parametric bootstrap applications, and suggest a modification that makes the method work. The modification consists of smoothing the first-level bootstrap distributions, with the desired consequence that this removes the zero probabilities in the multinomial distributions that define them. We also discuss efficient choices of recycling distributions, both in terms of estimator efficiency and simulation efficiency.     

Identifying Guttman Structures in Incomplete Rasch Datasets

In applications of IRT, it often happens that many examinees omit a substantial proportion of item responses. This can occur for various reasons, though it may well be due to no more than the simple fact of design incompleteness. In such circumstances, literature not infrequently refers to various types of estimation problem, often in terms of generic “convergence problems” in the software used to estimate model parameters. With reference to the Partial Credit Model and the instance of data missing at random, this article demonstrates that as their number increases, so does that of anomalous datasets, intended as those not corresponding to a finite estimate of (the vector parameter that identifies) the model. Moreover, the necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood estimation of the Partial Credit Model (and hence, in particular, the Rasch model) in the case of incomplete data are given – with reference to the model in its more general form, the number of response categories varying according to item. A taxonomy of possible cases of anomaly is then presented, together with an algorithm useful in diagnostics.     

Weighted Wilcoxon Estimators in Nonlinear Regression

In this paper, we consider the estimation of parameters of a general near regression model. An estimator that minimises the weighted Wilcoxon dispersion function is considered and its asymptotic properties established under mild regularity conditions similar to those used in least squares and least absolute deviations estimation. As in linear models, the procedure provides estimators that are robust and highly efficient. The estimates depend on the choice of a weight function and diagnostics which differentiate between nonlinear fits are provided along with appropriate benchmarks. The behavior of these estimates is discussed on a real data set. A simulation study verifies the robustness, efficiency and validity of these estimates over several error distributions including the normal and a family of contaminated normal distributions.     

Local influence regression diagnostics for gamma data

The local influence diagnostics proposed in general terms irl Cook (1986), Thomas and Cook (1989) and Billor and Loynes (1993). arc adapted for gamma data. A data set prcviously analysed using different methods is then reexamined, and conclusions based on wing the new approach are made.     

Small-area estimation based on survey data from a left-censored Fay-Herriot model

This paper develops methodology for survey estimation and small-area prediction using Fay-Herriot (1979) models in which the responses are left-censored. Parameter and small-area estimators are derived both by censored-data likelihoods and by an estimating-equation approach which adjusts a Fay-Herriot analysis restricted to the uncensored observations. Formulas for variances of estimators and mean-squared errors of small-area predictions are provided and supported by a simulation study. The methodology is applied to provide diagnostics for the left-censored Fay-Herriot model which are illustrated in the context of the Census Bureau's ongoing Small-Area Income and Poverty Estimation (SAIPE) project.     

Non-Gaussian Conditional Linear AR(1) Models

This paper gives a general formulation of a non-Gaussian conditional linear AR(1) model subsuming most of the non-Gaussian AR(1) models that have appeared in the literature. It derives some general results giving properties for the stationary process mean, variance and correlation structure, and conditions for stationarity. These results highlight similarities with and differences from the Gaussian AR(1) model, and unify many separate results appearing in the literature. Examples illustrate the wide range of properties that can appear under the conditional linear autoregressive assumption. These results are used in analysing three real datasets, illustrating general methods of estimation, model diagnostics and model selection. In particular, the theoretical results can be used to develop diagnostics for deciding if a time series can be modelled by some linear autoregressive model, and for selecting among several candidate models.     

A robust logistic discrimination model

Logistic discrimination is a well documented method for classifying observations to two or more groups. However, estimation of the discriminant rule can be seriously affected by outliers. To overcome this, Cox and Ferry produced a robust logistic discrimination technique. Although their method worked in practice, parameter estimation was sometimes prone to convergence problems. This paper proposes a simplified robust logistic model which does not have any such problems and which takes a generalized linear model form. Misclassification rates calculated in a simulation exercise are used to compare the new method with ordinary logistic discrimination. Model diagnostics are also presented. The newly proposed model is then used on data collected from pregnant women at two district general hospitals. A robust logistic discriminant is calculated which can be used to predict accurately which method of feeding a woman will eventually use: breast feeding or bottle feeding.     

Prediction in multilevel generalized linear models

Summary.  We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix . For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic random-intercept models under a range of conditions.     

Heteroscedastic log-exponentiated Weibull regression model

We introduce a new class of heteroscedastic log-exponentiated Weibull (LEW) regression models. The class of regression models can be applied to censored data and be used more effectively in survival analysis. Maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model is investigated. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the heteroscedastic LEW regression model. The normal curvatures for studying local influence are derived under various perturbation schemes. An empirical application to a real data set is provided to illustrate the usefulness of the new class of heteroscedastic regression models.     

倒向随机微分方程中非参数估计的核函数选择

比较了多种类型的核函数下倒向随机微分方程（BSDE）中生成元z的非参数估计方法,利用不同的核函数估计BSDE中的生成元z的非参数估计,在均方误差意义下比较了8种不同的核函数下得到的BSDE的生成元z的非参数估计的精度,统计分析结果显示Gaussian核函数下的估计效果最好。     

Local influence of nonlinear mixed effects model based on M-estimation

Abstract

In this work we mainly study the local influence in nonlinear mixed effects model with M-estimation. A robust method to obtain maximum likelihood estimates for parameters is presented, and the local influence of nonlinear mixed models based on robust estimation (M-estimation) by use of the curvature method is systematically discussed. The counting formulas of curvature for case weights perturbation, response variable perturbation and random error covariance perturbation are derived. Simulation studies are carried to access performance of the methods we proposed. We illustrate the diagnostics by an example presented in Davidian and Giltinan, which was analyzed under the non-robust situation.     

Diagnostics for dependence within time series extremes

Summary. The analysis of extreme values within a stationary time series entails various assumptions concerning its long- and short-range dependence. We present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events. These tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and identically distributed variables. Our diagnostic aids are illustrated through theoretical examples, simulation studies and by application to rainfall and exchange rate data. On the basis of these diagnostics we can explain characteristics that are found in the observed extreme events of these series and also gain insight into the properties of events that are more extreme than those observed.     

A general lower bound of minimax risk for absolute-error loss

A general lower bound of minimax risk for absolute-error loss is given in terms of the Hellinger modulus of the estimation problem. The main results are applicable to various parametric, semi-parametric and nonparametric problems. Two examples of parametric estimation problems and two examples of density estimation problems are given. In all of these examples, the general lower bound achieves the convergence rates of minimax risk.     

Outlier detection and robust estimation in linear regression models with fixed group effects

This work studies outlier detection and robust estimation with data that are naturally distributed into groups and which follow approximately a linear regression model with fixed group effects. For this, several methods are considered. First, the robust fitting method of Peña and Yohai [A fast procedure for outlier diagnostics in large regression problems. J Am Stat Assoc. 1999;94:434–445], called principal sensitivity components (PSC) method, is adapted to the grouped data structure and the mentioned model. The robust methods RDL₁ of Hubert and Rousseeuw [Robust regression with both continuous and binary regressors. J Stat Plan Inference. 1997;57:153–163] and M-S of Maronna and Yohai [Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference 2000;89:197–214] are also considered. These three methods are compared in terms of their effectiveness in outlier detection and their robustness through simulations, considering several contamination scenarios and growing contamination levels. Results indicate that the adapted PSC procedure is able to detect a high percentage of true outliers and a small number of false outliers. It is appropriate when the contamination is in the error term or in the covariates, detecting also possibly masked high leverage points. Moreover, in simulations the final robust regression estimator preserved good efficiency under Normality while keeping good robustness properties.