Pseudo‐likelihood ratio tests for semiparametric multivariate copula model selection

The authors propose pseudo‐likelihood ratio tests for selecting semiparametric multivariate copula models in which the marginal distributions are unspecified, but the copula function is parameterized and can be misspecified. For the comparison of two models, the tests differ depending on whether the two copulas are generalized nonnested or generalized nested. For more than two models, the procedure is built on the reality check test of White (2000). Unlike White (2000), however, the test statistic is automatically standardized for generalized nonnested models (with the benchmark) and ignores generalized nested models asymptotically. The authors illustrate their approach with American insurance claim data.     

On Rates of Convergence for Posterior Distributions Under Misspecification

We extend the approach of Walker (2003 Walker , S. ( 2003 ). On sufficient conditions for Bayesian consistency . Biometrika 90 ( 2 ): 482 – 488 .[Crossref], [Web of Science ®] , [Google Scholar]); (2004 Walker , S. ( 2004 ). New approaches to Bayesian consistency . Ann. Statist. 32 ( 5 ): 2028 – 2043 .[Crossref], [Web of Science ®] , [Google Scholar]) to the case of misspecified models. A sufficient condition for establishing rates of convergence is given based on a key identity involving martingales, which does not require construction of tests. We also show roughly that the result obtained by using tests can also be obtained by our approach, which demonstrates the potential wider applicability of this method.     

Robustness of Approaches to ROC Curve Modeling under Misspecification of the Underlying Probability Model

A variety of statistical regression models have been proposed for the comparison of ROC curves for different markers across covariate groups. Pepe developed parametric models for the ROC curve that induce a semiparametric model for the market distributions to relax the strong assumptions in fully parametric models. We investigate the analysis of the power ROC curve using these ROC-GLM models compared to the parametric exponential model and the estimating equations derived from the usual partial likelihood methods in time-to-event analyses. In exploring the robustness to violations of distributional assumptions, we find that the ROC-GLM provides an extra measure of robustness.     

Comparing Possibly Misspecified Forecasts

Abstract

Recent work has emphasized the importance of evaluating estimates of a statistical functional (such as a conditional mean, quantile, or distribution) using a loss function that is consistent for the functional of interest, of which there is an infinite number. If forecasters all use correctly specified models free from estimation error, and if the information sets of competing forecasters are nested, then the ranking induced by a single consistent loss function is sufficient for the ranking by any consistent loss function. This article shows, via analytical results and realistic simulation-based analyses, that the presence of misspecified models, parameter estimation error, or nonnested information sets, leads generally to sensitivity to the choice of (consistent) loss function. Thus, rather than merely specifying the target functional, which narrows the set of relevant loss functions only to the class of loss functions consistent for that functional, forecast consumers or survey designers should specify the single specific loss function that will be used to evaluate forecasts. An application to survey forecasts of U.S. inflation illustrates the results.     

我国管理学研究中的测量模型误设及仿真分析

在实证研究中,构念和观测变量之间的关系经常被忽视.本文详细区分了反映式测量模型和构成式测量模型,通过分析我国管理学领域的三本学术刊物2002年到2007年以结构方程模型(SEM)为数据分析工具的实证研究论文,发现我国管理学研究中测量模型误设的情况普遍存在.蒙特卡罗仿真分析表明,测量模型的误设将导致相关路径系数的被显著扩大或缩小,而且可能导致I型错误和Ⅱ型错误.由于现有的SEM软件不能处理构成式测量模型,本文提出了模型细化法和模型分解法,能够将构成式测量模型转换成反映式测量模型.     

Between stability and higher-order asymptotics

We discuss the effects of model misspecifications on higher-order asymptotic approximations of the distribution of estimators and test statistics. In particular we show that small deviations from the model can wipe out the nominal improvements of the accuracy obtained at the model by second-order approximations of the distribution of classical statistics. Although there is no guarantee that the first-order robustness properties of robust estimators and tests will carry over to second-order in a neighbourhood of the model, the behaviour of robust procedures in terms of second-order accuracy is generally more stable and reliable than that of their classical counterparts. Finally, we discuss some related work on robust adjustments of the profile likelihood and outline the role of computer algebra in this type of research.     

Testing the homogeneity of proportions for clustered binary data without knowing the correlation structure

A robust generalized score test for comparing groups of cluster binary data is proposed. This novel test is asymptotically valid for practically any underlying correlation configurations including the situation when correlation coefficients vary within or between clusters. This structure generally undermines the validity of the typical large sample properties of the method of maximum likelihood. Simulations and real data analysis are used to demonstrate the merit of this parametric robust method. Results show that our test is superior to two recently proposed test statistics advocated by other researchers.     

An overview of model-robust regression

The proper combination of parametric and nonparametric regression procedures can improve upon the shortcomings of each when used individually. Considered is the situation where the researcher has an idea of which parametric model should explain the behavior of the data, but this model is not adequate throughout the entire range of the data. An extension of partial linear regression and two other methods of model-robust regression are developed and compared in this context. The model-robust procedures each involve the proportional mixing of a parametric fit to the data and a nonparametric fit to either the data or residuals. The emphasis of this work is on fitting in the small-sample situation, where nonparametric regression alone has well-known inadequacies. Performance is based on bias and variance considerations, and theoretical mean squared error formulas are developed for each procedure. An example is given that uses generated data from an underlying model with defined misspecification to provide graphical comparisons of the fits and to show the theoretical benefits of the model-robust procedures. Simulation results are presented which establish the accuracy of the theoretical formulas and illustrate the potential benefits of the model-robust procedures. Simulations are also used to illustrate the advantageous properties of a data-driven selector developed in this work for choosing the smoothing and mixing parameters. It is seen that the model-robust procedures (the final proposed method, in particular) give much improved fits over the individual parametric and nonparametric fits.     

Bounds on the effect of heteroscedasticity on the chow test for structural change

This paper considers the effect of heteroscedastic regression errors on the size of the Chow test for structural stability. We show that bounds can be placed on the true size of this test in the light of such misspecification, and on the true critical value needed to achieve any desired significance level when using the test under various degrees of heteroscedasticity. These bounds are data-independent, and some cases are tabulated. Examples are given to illustrate the practical application of the critical value bounds.     

Second‐order bias‐corrected AIC in multivariate normal linear models under non‐normality

This paper deals with a bias correction of Akaike's information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown non‐normal distribution. It is well known that the bias of AIC is $O(1)$ , and there are a number of the first‐order bias‐corrected AICs which improve the bias to $O(n^{-1})$ , where $n$ is the sample size. A new information criterion is proposed by slightly adjusting the first‐order bias‐corrected AIC. Although the adjustment is achieved by merely using constant coefficients, the bias of the new criterion is reduced to $O(n^{-2})$ . Then, a variance of the new criterion is also improved. Through numerical experiments, we verify that our criterion is superior to others. The Canadian Journal of Statistics 39: 126–146; 2011 © 2011 Statistical Society of Canada