Unbiased risk estimation and scoring rules

Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general divergence type distances. The development relies on a connection with local proper scoring rules.Comment: This is the author's version of a work that was accepted for publication in Comptes rendus Mathematiqu

Functional Bipartite Ranking: a Wavelet-Based Filtering Approach

It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is randomly assigned, the objective is to learn a scoring function s with optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it is shown how to select compact finite dimensional representations of the input curves adaptively, in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback. Beyond theoretical considerations, the performance of the learning methods for functional bipartite ranking proposed in this paper are illustrated by numerical experiments

Stated versus inferred beliefs: A methodological inquiry and experimental test

If asking subjects their beliefs during repeated game play changes the way those subjects play, using those stated beliefs to evaluate and compare theories of strategic behavior is problematic. We experimentally verify that belief elicitation can alter paths of play in a repeated asymmetric matching pennies game. In this setting, belief elicitation improves the goodness of fit of structural models of belief learning, and the prior beliefs implied by such structural models are both stronger and more realistic when beliefs are elicited than when they are not. These effects are, however, confined to the player type who sees a strong asymmetry between payoff possibilities for her two strategies in the game. We also find that “inferred beliefs” (beliefs estimated from past observed actions of opponents) can be better predictors of observed actions than the “stated beliefs” resulting from belief elicitation.beliefs; stated beliefs; belief elicitation; inferred beliefs; estimated beliefs; belief updating; repeated games; experimental methods

Semiparametric Multinomial Logit Models for Analysing Consumer Choice Behaviour

The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing applications. It allows to relate an unordered categorical response variable, for example representing the choice of a brand, to a vector of covariates such as the price of the brand or variables characterising the consumer. In its classical form, all covariates enter in strictly parametric, linear form into the utility function of the MNL model. In this paper, we introduce semiparametric extensions, where smooth effects of continuous covariates are modelled by penalised splines. A mixed model representation of these penalised splines is employed to obtain estimates of the corresponding smoothing parameters, leading to a fully automated estimation procedure. To validate semiparametric models against parametric models, we utilise proper scoring rules and compare parametric and semiparametric approaches for a number of brand choice data sets

Development and Validation of Credit-Scoring Models

Accurate credit-granting decisions are crucial to the efficiency of the decentralized capital allocation mechanisms in modern market economies. Credit bureaus and many .nancial institutions have developed and used credit-scoring models to standardize and automate, to the extent possible, credit decisions. We build credit scoring models for bankcard markets using the Office of the Comptroller of the Currency, Risk Analysis Division (OCC/RAD) consumer credit database (CCDB). This unusu- ally rich data set allows us to evaluate a number of methods in common practice. We introduce, estimate, and validate our models, using both out-of-sample contempora- neous and future validation data sets. Model performance is compared using both separation and accuracy measures. A vendor-developed generic bureau-based score is also included in the model performance comparisons. Our results indicate that current industry practices, when carefully applied, can produce models that robustly rank-order potential borrowers both at the time of development and through the near future. However, these same methodologies are likely to fail when the the objective is to accurately estimate future rates of delinquency or probabilities of default for individual or groups of borrowers.

Hybrid model using logit and nonparametric methods for predicting micro-entity failure

Following the calls from literature on bankruptcy, a parsimonious hybrid bankruptcy model is developed in this paper by combining parametric and non-parametric approaches.To this end, the variables with the highest predictive power to detect bankruptcy are selected using logistic regression (LR). Subsequently, alternative non-parametric methods (Multilayer Perceptron, Rough Set, and Classification-Regression Trees) are applied, in turn, to firms classified as either “bankrupt” or “not bankrupt”. Our findings show that hybrid models, particularly those combining LR and Multilayer Perceptron, offer better accuracy performance and interpretability and converge faster than each method implemented in isolation. Moreover, the authors demonstrate that the introduction of non-financial and macroeconomic variables complement financial ratios for bankruptcy prediction