The extreme residuals in logistic regression models

Goodness of fit tests for logistic regression models using extreme residuals are considered. Moment properties of the Pearson residuals are developed and used to define modified residuals, for the cases when the model fit is made by maximum likelihood, minimum chi-square and weighted least squares. Approximations to the critical values of the extreme statistics based on the ordinary and modified Pearson residuals are developed and assessed for the case when the logistic regression model has a single explanatory variable

Modified standardized Pearson residual for the identification of outliers in logistic regression model

Detection of outlier based on standardized Pearson residuals has gained widespread use in logistic regression model in the presence of a single outlier. An innovation attempts in the same direction but dealing for a group of outliers have been made using generalized standardized Pearson residual which requires a graphical or a robust estimator to find suspected outliers to form a group deletion. In this study, an alternative measure namely modified standardized Pearson residual is derived from the robust logistic diagnostic. The weakness of standardized Pearson residuals and the usefulness of generalized standardized Pearson residual and modified standardized Pearson residual are examined through several real examples and Monte Carlo simulation study. The results of this study signify that the generalized standardized Pearson residual and the modified standardized Pearson residual perform equally good in identifying a group of outliers

Residuals and goodness-of-fit tests for stationary marked Gibbs point processes

The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. (2005) as an empirical counterpart of the {\it Campbell equilibrium} equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs point processes and deals with asymptotic properties of residuals for such processes. In particular, the consistency and the asymptotic normality are obtained for a wide class of residuals including the classical ones (raw residuals, inverse residuals, Pearson residuals). Based on these asymptotic results, we define goodness-of-fit tests with Type-I error theoretically controlled. One of these tests constitutes an extension of the quadrat counting test widely used to test the null hypothesis of a homogeneous Poisson point process

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