Jörg Pawlitschko

Estimating the survival function under a generalized Koziol-Green model with partially informative censoring

Abstract.In survival analysis, a simple model of informative censoring is the so-called Koziol-Green (KG) model, where the survival function of the censoring times is supposed to be a power of the survival function of the lifetimes. It is well known that this model does not fit well to real data sets. Therefore, in this paper, we propose a generalization of this KG model, where only a part of the censored observations is supposed to be informatively censored. Under the new model, we propose a semiparametric estimator of the survival function of the lifetimes and investigate its asymptotic properties. Finally, we give an example for the practical application of the new estimator.

Outlier Identification Rules for Generalized Linear Models

Observations which seem to deviate strongly from the main part of the data may occur in every statistical analysis. These observations, usually labelled as outliers, may cause completely misleading results when using standard methods and may also contain information about special events or dependencies. We discuss outliers in situations where a generalized linear model is assumed as null model for the regular data and introduce rules for their identification. For the special cases of a loglinear Poisson model and a logistic regression model some one-step identifiers based on robust and non-robust estimators are proposed and compared.

Identification of outliers in exponential samples with stepwise procedures

In this paper we consider the problem of identifying outliers in exponential samples with stepwise procedures, namely inward and outward testing procedures. We treat outliers in the spirit of Davies and Gather (1993) as points which for given > 0 lie in a certain -outlier region and focus especially on the worst-case behaviour of the identi cation rules. Best results yield stepwise procedures which use test statistics based on a standardized version of the sample median.

On efron's and gill's version of the kaplan-meier integral

For randomly censored data, a widely used estimator of an integral of the type ∫φ dF is the Kaplan-Meier (KM) integral. In this paper, we show that for increasing φ ≥ 0 the KM integral based on Efrons version of the KM estimator has smaller bias than the KM integral based on Gills version. Some computations in the Koziol-Green model give an impression of the magnitude of the bias and variance of the two estimators. Further, we investigate the almost sure convergence of Efrons version of the KM integral in the spirit of Stute and Wang (1993).

Robust Estimation of the Location Parameter from a Two-Parameter Exponential Distribution

This paper deals with the problem of estimating the location parameter of a two parameter exponential distribution in case of contaminated data. Since in this case the sample minimum is an extremely unreliable estimator, robust alternatives are necessary. We investigate two types of estimators closer. The first type is based on a simple relation for the median. The second type has originally been suggested for Type-II-censored samples, but it also has good robustness properties. We discuss the breakdown properties of the two types of estimators and compare their performance for various patterns of data contamination in an extensive simulation study.