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## Back Matter - Keine Panik vor Statistik!

### Keine Panik vor Statistik! (2012-01-01) , January 01, 2012

## A competing risks model for correlated data based on the subdistribution hazard

### Lifetime Data Analysis (2011-10-01) 17: 473-495 , October 01, 2011

Family-based follow-up study designs are important in epidemiology as they enable investigations of disease aggregation within families. Such studies are subject to methodological complications since data may include multiple endpoints as well as intra-family correlation. The methods herein are developed for the analysis of age of onset with multiple disease types for family-based follow-up studies. The proposed model expresses the marginalized frailty model in terms of the subdistribution hazards (SDH). As with Pipper and Martinussen’s (Scand J Stat 30:509–521, 2003) model, the proposed multivariate SDH model yields marginal interpretations of the regression coefficients while allowing the correlation structure to be specified by a frailty term. Further, the proposed model allows for a direct investigation of the covariate effects on the cumulative incidence function since the SDH is modeled rather than the cause specific hazard. A simulation study suggests that the proposed model generally offers improved performance in terms of bias and efficiency when a sufficient number of events is observed. The proposed model also offers type I error rates close to nominal. The method is applied to a family-based study of breast cancer when death in absence of breast cancer is considered a competing risk.

## A characterization of admissible linear estimators of fixed and random effects in linear models

### Metrika (2008-09-01) 68: 157-172 , September 01, 2008

In the paper the problem of simultaneous linear estimation of fixed and random effects in the mixed linear model is considered. A necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in balanced nested and crossed classification models to be admissible are given.

## Maximum likelihood estimation for a special exponential family under random double-truncation

### Computational Statistics (2015-12-01) 30: 1199-1229 , December 01, 2015

Doubly-truncated data often appear in lifetime data analysis, where samples are collected under certain time constraints. Nonparametric methods for doubly-truncated data have been studied well in the literature. Alternatively, this paper considers parametric inference when samples are subject to double-truncation. Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999) proposed to fit a parametric family, called the special exponential family, with doubly-truncated data. However, non-trivial technical aspects, such as parameter space, support of the density, and computational algorithms, have not been discussed in the literature. This paper fills this gap by providing the technical aspects, including adequate choices of parameter space as well as support, and reliable computational algorithms. Simulations are conducted to verify the suggested techniques, and real data are used for illustration.

## Rates of almost sure convergence of plug-in estimates for distortion risk measures

### Metrika (2011-09-01) 74: 267-285 , September 01, 2011

In this article, we consider plug-in estimates for distortion risk measures as for instance the Value-at-Risk, the Expected Shortfall or the Wang transform. We allow for fairly general estimates of the underlying unknown distribution function (beyond the classical empirical distribution function) to be plugged in the risk measure. We establish strong consistency of the estimates, we investigate the rate of almost sure convergence, and we study the small sample behavior by means of simulations.

## Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms

### AStA Advances in Statistical Analysis (2011-12-01) 95: 375-413 , December 01, 2011

Continuous time models with sampled data possess several advantages over conventional discrete time series and panel models (cf., e.g. special issue Stat. Neerl. 62(1), 2008). For example, data with unequal time intervals between the waves can be treated efficiently, since the model parameters of the dynamical system model are not affected by the measurement process. The continuous-discrete state space model is a combination of continuous time dynamics (stochastic differential equations, SDE) and discrete time noisy measurements.

Maximum likelihood (ML) estimation of linear panel models is discussed using Kalman filtering and structural equations models (SEM). Pure time series and correlated panel data (e.g. with random time effects) can be treated exactly by SEM methods.

Nonlinear panel models are estimated by approximate filtering methods such as the extended Kalman filter (EKF), the local linearization filter (LLF), the Gauss–Hermite filter (GHF) and the unscented Kalman filter (UKF). Again, correlated panels are treated by stacking the panel units in a vector Itô equation.

Finally, spatial dynamical models are discussed. The state variables are random fields given as solutions of stochastic partial differential equations (SPDE), driven by a space–time white noise. Furthermore, the fields are filtered and estimated with noisy and sampled measurements.

## Numerische Merkmale: Dichteschätzung und Modelldiagnostik

### Einführung in die Statistik (2016-01-01): 123-147 , January 01, 2016

### Zusammenfassung

In Kap. 4 betrachteten diverse reelle Kenngrößen der Verteilung *P*. Nun beschäftigen wir uns wieder mit der Visualisierung von
$$\widehat{P}$$
bzw. der Schätzung der gesamten Verteilung *P*, diesmal unter der weitergehenden Annahme, dass *P* durch eine Dichtefunktion *f* beschrieben wird. Außerdem werden Methoden beschrieben, mit denen man graphisch oder formal prüfen kann, ob ein bestimmtes Modell für *P* plausibel ist.

## On ANOVA-Like Matrix Decompositions

### Modern Nonparametric, Robust and Multivariate Methods (2015-01-01): 425-439 , January 01, 2015

The analysis of variance plays a fundamental role in statistical theory and practice, the standard Euclidean geometric form being particularly well established. The geometry and associated linear algebra underlying such standard analysis of variance methods permit, essentially direct, generalisation to other settings. Specifically, as jointly developed here: (a) to minimum distance estimation problems associated with subsets of pairwise orthogonal subspaces; (b) to matrix, rather than vector, contexts; and (c) to general, not just standard Euclidean, inner products, and their induced distance functions. To make such generalisation, we solve the following problem: given a set of nontrivial subspaces of a linear space, any two of which meet only at its origin, exactly which inner products make these subspaces pairwise *orthogonal*? Applications in a variety of areas are highlighted, including: (i) the analysis of asymmetry, and (ii) asymptotic comparisons in Invariant Coordinate Selection and Independent Component Analysis. A variety of possible further generalisations and applications are noted.