Quantification of model risk that is caused by model misspecification

In this paper, we suggest a technique to quantify model risk, particularly model misspecification for binary response regression problems found in financial risk management, such as in credit risk modelling. We choose the probability of default model as one instance of many other credit risk models that may be misspecified in a financial institution. By way of illustrating the model misspecification for probability of default, we carry out quantification of two specific statistical predictive response techniques, namely the binary logistic regression and complementary log–log. The maximum likelihood estimation technique is employed for parameter estimation. The statistical inference, precisely the goodness of fit and model performance measurements, are assessed. Using the simulation dataset and Taiwan credit card default dataset, our finding reveals that with the same sample size and very small simulation iterations, the two techniques produce similar goodness-of-fit results but completely different performance measures. However, when the iterations increase, the binary logistic regression technique for balanced dataset reveals prominent goodness of fit and performance measures as opposed to the complementary log–log technique for both simulated and real datasets.     

On the relevance of weaker instruments

ABSTRACT

We study the asymptotic properties of the standard GMM estimator when additional moment restrictions, weaker than the original ones, are available. We provide conditions under which these additional weaker restrictions improve the efficiency of the GMM estimator. To detect “spurious” identification that may come from invalid moments, we rely on the Hansen J-test that assesses the compatibility between existing restrictions and additional ones. Our simulations reveal that the J-test has good power properties and that its power increases with the weakness of the additional restrictions. Our theoretical characterization of the J-test provides some intuition for why that is.     

Robust variance estimators for fixed-effect estimates with hierarchical-likelihood

In longitudinal studies, robust sandwich variance estimators are often used, and are especially useful when model assumptions are in doubt. However, the usual sandwich estimator does not allow for models with crossed random effects. The hierarchical likelihood extends the idea of the sandwich estimator to models not currently covered. By simulation studies, we show that the new sandwich estimator is robust against heteroscedastic errors and against misspecification of overdispersion in the y | v component.     

Covariate adjustment for randomized controlled trials revisited

Covariate adjustment for the estimation of treatment effect for randomized controlled trials (RCT) is a simple approach with a long history, hence, its pros and cons have been well‐investigated and published in the literature. It is worthwhile to revisit this topic since recently there has been significant investigation and development on model assumptions, robustness to model mis‐specification, in particular, regarding the Neyman‐Rubin model and the average treatment effect estimand. This paper discusses key results of the investigation and development and their practical implication on pharmaceutical statistics. Accordingly, we recommend that appropriate covariate adjustment should be more widely used for RCTs for both hypothesis testing and estimation.     

Testing inference in variable dispersion beta regressions

The class of beta regression models proposed by Ferrari and Cribari-Neto [Beta regression for modelling rates and proportions, Journal of Applied Statistics 31 (2004), pp. 799–815] is useful for modelling data that assume values in the standard unit interval (0, 1). The dependent variable relates to a linear predictor that includes regressors and unknown parameters through a link function. The model is also indexed by a precision parameter, which is typically taken to be constant for all observations. Some authors have used, however, variable dispersion beta regression models, i.e., models that include a regression submodel for the precision parameter. In this paper, we show how to perform testing inference on the parameters that index the mean submodel without having to model the data precision. This strategy is useful as it is typically harder to model dispersion effects than mean effects. The proposed inference procedure is accurate even under variable dispersion. We present the results of extensive Monte Carlo simulations where our testing strategy is contrasted to that in which the practitioner models the underlying dispersion and then performs testing inference. An empirical application that uses real (not simulated) data is also presented and discussed.     

On the robustness of maximum composite likelihood estimate

Composite likelihood methods have been receiving growing interest in a number of different application areas, where the likelihood function is too cumbersome to be evaluated. In the present paper, some theoretical properties of the maximum composite likelihood estimate (MCLE) are investigated in more detail. Robustness of consistency of the MCLE is studied in a general setting, and clarified and illustrated through some simple examples. We also carry out a simulation study of the performance of the MCLE in a constructed model suggested by Arnold (2010) that is not multivariate normal, but has multivariate normal marginal distributions.     

Evaluating model misspecification in independent component analysis

Independent component analysis (ICA) is a popular blind source separation technique used in many scientific disciplines. Current ICA approaches have focused on developing efficient algorithms under specific ICA models, such as instantaneous or convolutive mixing conditions, intrinsically assuming temporal independence or autocorrelation of the sources. In practice, the true model is not known and different ICA algorithms can produce very different results. Although it is critical to choose an ICA model, there has not been enough research done on evaluating mixing models and assumptions, and how the associated algorithms may perform under different scenarios. In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases. Our simulation studies show that the performance of ICA algorithms is highly dependent on mixing conditions and temporal independence of the sources. Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters.     

Misspecified T2 tests. i. location and scale

Properties of Hotelling's (1931) T ² are studied under model misspecification in the model for a multivariate experiment. Stochastic bounds on T ² and further properties of the T ² test are studied under misspecified location and scale. The bounds are evaluated numerically in selected cases.