Generalized Modeling Approaches to Risk Adjustment of Skewed Outcomes Data

There are two broad classes of models used to address the econometric problems caused by skewness in data commonly encountered in health care applications: (1) transformation to deal with skewness (e.g., OLS on ln(y)); and (2) alternative weighting approaches based on exponential conditional models (ECM) and generalized linear model (GLM) approaches. In this paper, we encompass these two classes of models using the three parameter generalized gamma (GGM) distribution, which includes several of the standard alternatives as special cases OLS with a normal error, OLS for the log normal, the standard gamma and exponential with a log link, and the Weibull. Using simulation methods, we find the tests of identifying distributions to be robust. The GGM also provides a potentially more robust alternative estimator to the standard alternatives. An example using inpatient expenditures is also analyzed.

A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions

In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffding's maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper we propose a scalefree adaptive statistic for testing exponentiality with optimal power against a specific alternative. We obtain its exact distribution and compare it with other scale-free statistics for testing exponentiality, such as the Stephens' modification of the Shapiro-Wilk statistic, the Gini statistic and the Qn statistic defined in Fortiana and Grané (2002)

New L2-type exponentiality tests

We introduce new consistent and scale-free goodness-of-fit tests for the exponential distribution based on the Puri-Rubin characterization. For the construction of test statistics we employ weighted L2 distance between V-empirical Laplace transforms of random variables that appear in the characterization. We derive the asymptotic behaviour under the null hypothesis as well as under fixed alternatives. We compare our tests, in terms of the Bahadur efficiency, to the likelihood ratio test, as well as some recent characterization based goodness-of-fit tests for the exponential distribution. We also compare the power of our tests to the power of some recent and classical exponentiality tests. According to both criteria, our tests are shown to be strong and outperform most of their competitors.Peer Reviewe