115,388 research outputs found
Simultaneous Inference in General Parametric Models
Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here
A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures
In this paper robust statistical procedures are presented for the analysis of skewed and heavy-tailed outcomes as they typically occur in health care data. The new estimators and test statistics are extensions of classical maximum likelihood techniques for generalized linear models. In contrast to their classical counterparts, the new robust techniques show lower variability and excellent effciency properties in the presence of small deviations form the assumed model, i.e. when the underlying distribution of the data lies in a neighborhood of the model. A simulation study, an analysis on real data, and a sensitivity analysis confirm the good theoretical statistical properties of the new techniques.Deviations from the model; GLM modeling; health econometrics; heavy tails; robust estimation; robust inference
Cluster-Robust Variance Estimation for Dyadic Data
Dyadic data are common in the social sciences, although inference for such
settings involves accounting for a complex clustering structure. Many analyses
in the social sciences fail to account for the fact that multiple dyads share a
member, and that errors are thus likely correlated across these dyads. We
propose a nonparametric sandwich-type robust variance estimator for linear
regression to account for such clustering in dyadic data. We enumerate
conditions for estimator consistency. We also extend our results to repeated
and weighted observations, including directed dyads and longitudinal data, and
provide an implementation for generalized linear models such as logistic
regression. We examine empirical performance with simulations and applications
to international relations and speed dating
Robust Inference for Generalized Linear Mixed Models: An Approach Based on Score Sign Flipping
Despite the versatility of generalized linear mixed models in handling
complex experimental designs, they often suffer from misspecification and
convergence problems. This makes inference on the values of coefficients
problematic. To address these challenges, we propose a robust extension of the
score-based statistical test using sign-flipping transformations. Our approach
efficiently handles within-variance structure and heteroscedasticity, ensuring
accurate regression coefficient testing. The approach is illustrated by
analyzing the reduction of health issues over time for newly adopted children.
The model is characterized by a binomial response with unbalanced frequencies
and several categorical and continuous predictors. The proposed approach
efficiently deals with critical problems related to longitudinal nonlinear
models, surpassing common statistical approaches such as generalized estimating
equations and generalized linear mixed models
The Standardized Influence Matrix and Its Applications to Generalized Linear Models
The standardized influence matrix is a generalization of the standardized influence function and Cook’s approach to local influence. It provides a general and unified approach to judge the suitability of statistical inference based on parametric models. It characterizes the local influence of data deviations from parametric models on various estimators, including generalized linear models. Its use for both robustness measures and diagnostic procedures has been studied. With global robust estimators, diagnostic statistics are proposed and shown to be useful in detecting influential points for linear regression and logistic regression models. Robustness of various estimators is compared via. the standardized influence matrix and a new robust estimator for logistic regression models is presented
Robust bootstrap procedures for the chain-ladder method
Insurers are faced with the challenge of estimating the future reserves
needed to handle historic and outstanding claims that are not fully settled. A
well-known and widely used technique is the chain-ladder method, which is a
deterministic algorithm. To include a stochastic component one may apply
generalized linear models to the run-off triangles based on past claims data.
Analytical expressions for the standard deviation of the resulting reserve
estimates are typically difficult to derive. A popular alternative approach to
obtain inference is to use the bootstrap technique. However, the standard
procedures are very sensitive to the possible presence of outliers. These
atypical observations, deviating from the pattern of the majority of the data,
may both inflate or deflate traditional reserve estimates and corresponding
inference such as their standard errors. Even when paired with a robust
chain-ladder method, classical bootstrap inference may break down. Therefore,
we discuss and implement several robust bootstrap procedures in the claims
reserving framework and we investigate and compare their performance on both
simulated and real data. We also illustrate their use for obtaining the
distribution of one year risk measures
A review of R-packages for random-intercept probit regression in small clusters
Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision
Robust empirical likelihood inference for generalized partial linear models with longitudinal data
AbstractIn this paper, we propose a robust empirical likelihood (REL) inference for the parametric component in a generalized partial linear model (GPLM) with longitudinal data. We make use of bounded scores and leverage-based weights in the auxiliary random vectors to achieve robustness against outliers in both the response and covariates. Simulation studies demonstrate the good performance of our proposed REL method, which is more accurate and efficient than the robust generalized estimating equation (GEE) method (X. He, W.K. Fung, Z.Y. Zhu, Robust estimation in generalized partial linear models for clustered data, Journal of the American Statistical Association 100 (2005) 1176–1184). The proposed robust method is also illustrated by analyzing a real data set
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