A nonlinear structural errors-in-variables model is investigated, where the response variable has a density belonging to an exponential family and the error-prone covariate follows a Gaussian distribution. Assuming the error variance to be known, we consider two consistent estimators in addition to the naive estimator. We compare their relative efficiencies by means of their asymptotic covariance matrices for small error variances. The structural quasi score (SQS) estimator is based on a quasi score function, which is constructed from a conditional mean-variance model. Consistency and asymptotic normality of this estimator is proved. The corrected score (CS) estimator is based on an error-corrected likelihood score function. For small error variances the SQS and CS estimators are approximately equally efficient. The polynomial model and the Poisson regression model are explored in greater detail.

We investigate a stationary random cofficient autoregressive process. Using renewal type arguments tailor-made for such processes we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an autoregressive process with ARCH errors. Hence we obtain the tail behaviour of any such model of arbitrary order.

With the introduction of compulsory long term care (LTC) insurance in Germany in 1995, a large claims portfolio with a significant proportion of censored observations became available. In first part of this paper we present an analysis of part of this portfolio using the Cox proportional hazard model (Cox, 1972) to estimate transition intensities. It is shown that this approach allows the inclusion of censored observations as well as the inclusion of time dependent risk factors such as time spent in LTC. This is in contrast to the more commonly used Poisson regression with graduation approach (see for example Renshaw and Haberman 1995) where censored observations and time dependent risk factors are ignored. In the second part we show how these estimated transition intensities can be used in a multiple state Markov process (see Haberman and Pitacco, 1999) to calculate premiums for LTC insurance plans.

In this paper we analyse data originating from the German Deep Drill Program. We model the amount of 'cataclastic rocks' in a series of measurements taken from deep drill samples ranging from 1000 up to 5000 meters depth. The measurements thereby describe the amount of strongly deformed rock particles and serve as indicator for the occurrence of cataclastic shear zones, which are easily speaking areas of severely 'ground' stones due to movements of different layers in the earth crust. The data represent a 'depth series' as analogue to a 'time series', with mean, dispersion and correlation structure varying in depth. The general smooth structure is thereby disturbed by peaks and outliers so that robust procedures have to be applied for estimation. In terms of statistical modelling technology we have to tackle three different peculiarities of the data simultaneously, that is estimation of the correlation structure, local bandwidth selection and robust smoothing. To do so, existing routines are adapted and combined in new 'two stage' estimation procedures.

In this paper we review certain aspects around the Value-at-Risk, which is nowadays the industry benchmark risk measure. As a small quantile (usually 1%) Value-at-Risk is closely related to extreme value theory. We explain an estimation method based on extreme value theory. Since the variance of the estimated Value-at-Risk may depend on the dependence structure of the data, we investigate the extreme behaviour of some of the most prominent time series models in finance, continuous as well as discrete time models. We also determine optimal portfolios, when risk is measured by the Value-at-Risk. Again we use realistic models, moving away from the traditional Black-Scholes model to the class of Lévy processes. This paper is the contribution to a book by several authors on Extreme Value Theory, which will appear by CRC/Chapman and Hall.

Based on a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm which was developed by Fronk and Giudici (2000) to deal with model selection for Gaussian dags, we propose a new approach for the pure discrete case. Here, the main idea is to introduce latent variables which then allow to fall back on the already treated continuous case. This makes it also straightforward to tackle the mixed case, i.e. to deal simultaneously with continuous and discrete variables. The performance of the approach is investigated by means of a simulation study for different standard situations. In addition, a real data application is provided.

After a short introduction of the model, the missing mechanism and the method of inference some imputation procedures are introduced with special focus on the simulation experiment. Within this experiment, the simple additive model y = f(x) + e is assumed to have missing values in the independent variable according to MCAR. Besides the well-known complete case analysis, mean imputation plus random noise, a single imputation and two ways of nearest neighbor imputation are used. These methods are compared within a simulation experiment based on the average mean square error, variances and biases of \hat{f}(x) at the knots.

Do reported reservation wages correspond to the concept of reservation wages that economists have? Using panel data on British unemployed I calculate reservation wages from a search model and compare these with reported reservation wages. It is shown that men's reported reservation wages are greater than what the model predicts, and that for women there is hardly a relation between the two variables.

The incidence of underweight amongst children under five in Western Africa has been increasing over the last decade (UNICEF, 2002). In Asia, where about two thirds of the world's underweight children live, the rate of underweight declined from about 36 per cent to some 29 per cent between 1990 and 2000. In sub-Saharan Africa, the absolute number of underweight children has increased and is now about 36 per cent. Using new data from Demographic and Health Surveys, I estimate the probability of underweight or a sample of West African children, controlling for selective survival.

Dempster-Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering SETS of basic probability assignments, an appealing constructive approach to general interval probability (general imprecise probabilities) is achieved, which allows for a very flexible modelling of uncertain knowledge.