TY  - INPR
A1  - Liero, Hannelore
T1  - Goodness of Fit Tests of L2-Type
N2  - We give a survey on procedures for testing functions which are based on quadratic deviation measures. The following problems are considered: Testing whether a density function lies in a parametric class of functions, whether continuous random variables are independent; testing cell probabilities and independence in sparse data sets; testing the parametric fit of a regression homoscedasticity in a regression model and testing the hazard rate in survival models with censoring and with and without covariates.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2003, 15 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51494
ER  - 
TY  - INPR
A1  - Liero, Hannelore
T1  - Testing the Hazard Rate, Part I
N2  - We consider a nonparametric survival model with random censoring. To test whether the hazard rate has a parametric form the unknown hazard rate is estimated by a kernel estimator. Based on a limit theorem stating the asymptotic normality of the quadratic distance of this estimator from the smoothed hypothesis an asymptotic ®-test is proposed. Since the test statistic depends on the maximum likelihood estimator for the unknown parameter in the hypothetical model properties of this parameter estimator are investigated. Power considerations complete the approach.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2003, 17 
KW  - kernel estimator of the hazard rate
KW  - goodness of fit
KW  - maximum likelihood estimator
KW  - limit theorem for integrated squared difference
KW  - censoring
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51510
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Liero, Hannelore
T1  - Nonparametric estimation and testing in survival models
N2  - The aim of this paper is to demonstrate that nonparametric smoothing methods for estimating functions can be an useful tool in the analysis of life time data. After stating some basic notations we will present a data example. Applying standard parametric methods to these data we will see that this approach fails - basic features of the underlying functions are not reflected by their estimates. Our proposal is to use nonparametric estimation methods. These methods are explained in section 2. Nonparametric approaches are better in the sense that they are more flexible, and misspecifications of the model are avoided. But, parametric models have the advantage that the parameters can be interpreted. So, finally, we will formulate a test procedure to check whether a parametric or a nonparametric model is appropriate.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51586
ER  - 
TY  - INPR
A1  - Liero, Hannelore
A1  - Liero, Matthias
T1  - Testing the acceleration function in life time models
N2  - The accelerated life time model is considered. First, test procedures for testing the parameter of a parametric acceleration function is investigated; this is done under the assumption of parametric and nonparametric baseline distribution. Further, based on nonparametric estimators for regression functions tests are proposed for checking whether a parametric acceleration function is appropriate to model the influence of the covariates. Resampling procedures are discussed for the realization of these methods. Simulations complete the considerations.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 03 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49405
ER  - 
TY  - INPR
A1  - Liero, Hannelore
T1  - A Note on : testing the Copula Based on Densities
N2  - We consider the problem of testing whether the density of a mul- tivariate random variable can be expressed by a prespecified copula function and the marginal densities. The proposed test procedure is based on the asymptotic normality of the properly standardized integrated squared distance between a multivariate kernel density estimator and an estimator of its expectation under the hypothesis. The test of independence is a special case of this approach.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 02 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49393
ER  -