# Inferência Estatística

## A modified signed likelihood ratio test in elliptical structural models

In this paper we deal with the issue of performing accurate testing inference on a scalar parameter of interest in structural errors-in-variables models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as special case. We derive a modified signed likelihood ratio statistic that follows a standard normal distribution with a high degree of accuracy. Our Monte Carlo results show that the modified test is much less size distorted than its unmodified counterpart. An application is presented.

## Sensitivity Analysis for Incomplete Continuous Data

In studies with missing data, statisticians typically identify the model via necessarily untestable assumptions and then perform sensitivity analyses to assess their effect on the conclusions. Both the parameterization and the identification of the model play an important role in translating the assumptions to non-statisticians and, consequently, in obtaining relevant information from experts or historical data. Specifically for continuous data, much of the earlier work has been developed under the assumption of normality and/or with hard-to-interpret sensitivity parameters. We derive a simple approach for estimating means, standard deviations and correlations that avoids parametric distributional assumptions for the outcomes. Adopting a pattern-mixture model parameterization, we use non-identifiable means, standard deviations, correlations or functions thereof as sensitivity parameters, which are more easily elicited.

## The use of quasi U-statistics for undergraduate performance assessment

We propose new methodologies to assess Undergraduate performance dissimilarities. Emphasis is given to the sector of High School education from which the College student comes - private or public. Due to the complex structure of Undergraduate courses, the overall performance of a student is not based upon its GPA (Grade Point Average). The sample consists of all undergraduate students entering Unicamp at years 2000-2005 as follows. For each student a vector is formed by his/her grades in each course taken: multiple scores are considered whenever fail/pass grades happen. These vectors are then used in pairwise comparisons of common courses grades between all individuals that entered college in the same year taking into account the entrance rank. These forms a generalized U-statistic based on the classical signed rank kernel. We apply the decomposability of these quasi U-statistics (Pinheiro et al., 2009, 2010) to define average distance measures within and between groups. A test statistic for a homogeneity test among groups can be developed and asymptotic normality under mild conditions can be proved for the test statistic under the null hypothesis.