By starting from a natural class of robust estimators for generalized linear models based on the notion of quasi-likelihood, we define robust deviances that can be used for stepwise model selection as in the classical framework.We derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination. The binomial and Poisson models are treated in detail. Two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures.

This paper compares alternative methods of controlling for the spatial dependence of house prices in a mass appraisal context. Explicit modeling of the error structure is characterized as a relatively fluid approach to defining housing submarkets. This approach allows the relevant submarket to vary from house to house and for transactions involving other dwellings in each submarket to have varying impacts depending on distance. We conclude that—for our Auckland, New Zealand, data—the gains in accuracy from including submarket variables in an ordinary least squares specification are greater than any benefits from using geostatistical or lattice methods. This conclusion is of practical importance, as a hedonic model with submarket dummy variables is substantially easier to implement than spatial statistical methods

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Litter characteristics at birth were recorded in 4 genetic types of sows with differing maternal abilities. Eighty-two litters from F(1) Duroc x Large White sows, 651 litters from Large White sows, 63 litters from Meishan sows, and 173 litters from Laconie sows were considered. Statistical models included random effects of sow, litter, or both; fixed effects of sow genetic type, parity, birth assistance, and piglet sex, as well as gestation length, farrowing duration, piglet birth weight, and litter size as linear covariates. The quadratic components of the last 2 factors were also considered. For statistical analyses, GLM were first considered, assuming a binomial distribution of stillbirth. Hierarchical models were also fitted to the data to take into account correlations among piglets from the same litter. Model selection was performed based on deviance and deviance information criterion. Finally, standard and robust generalized estimating equations (GEE) procedures were applied to quantify the importance of each effect on a piglet's probability of stillbirth. The 5 most important factors involved were, in decreasing order (contribution of each effect to variance reduction): difference between piglet birth weight and the litter mean (2.36%), individual birth weight (2.25%), piglet sex (1.01%), farrowing duration (0.99%), and sow genetic type (0.94%). Probability of stillbirth was greater for lighter piglets, for male piglets, and for piglets from small or very large litters. Probability of stillbirth increased with sow parity number and with farrowing duration. Piglets born from Meishan sows had a lower risk of stillbirth (P < 0.0001) and were little affected by the sources of variation mentioned above compared with the 3 other sow genetic types. Standard and robust GEE approaches gave similar results despite some disequilibrium in the data set structure highlighted with the robust GEE approach.

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Much of the trading activity in Equity markets is directed to brokerage houses. In exchange they provide so-called "soft dollars" which basically are amounts spent in "research" for identifying profitable trading opportunities. Soft dollars represent about USD 1 out of every USD 10 paid in commissions. Obviously they are costly, and it is interesting for an institutional investor to determine whether soft dollar inputs are worth being used (and indirectly paid for) or not, from a statistical point of view. To address this question, we develop association measures between what broker-dealers predict and what markets realize. Our data are ordinal predictions by two broker-dealers and realized values on several markets, on the same ordinal scale. We develop a structural equation model with latent variables in an ordinal setting which allows us to test broker-dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. The method is then used to analyze our dataset.

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust M-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference.

In this paper robust statistical procedures are presented for the analysis of skewed and heavy-tailed outcomes as they typically occur * Corresponding author. JEL classification: C10, I10.