Modelling extreme wind speeds in the context of risk analysis for high speed trains

For high speed trains there is a potential risk of derailment when driving very fast and being hit by an extraordinary strong gust at the same time. The risk depends on both the wind speed and the angle between train and gust. Several techniques have been established to minimize this risk to acceptable values. To decide which of these techniques at a given site is most appropriate, precise knowledge of the wind process at extreme levels is necessary. Therefore methods adapted to the special requirements of the application are needed. We discuss directional modelling using an approach proposed by Coles and Walshaw [2]. We focus on estimating extreme quantiles and their confidence intervals. Different types of confidence intervals are compared and we show how these calculations can be used for risk analysis

An exact algorithm for estimating breakpoints in segmented generalized linear models

We consider the problem of estimating the unknown breakpoints in segmented generalized linear models. Exact algorithms for calculating maximum likelihood estimators are derived for different types of models. After discussing the case of a GLM with a single covariate having one breakpoint a new algorithm is presented when further covariates are included in the model. The essential idea of this approach is then used for the case of more than one breakpoint. As further extension an algorithm for the situation of two regressors each having a breakpoint is proposed. These techniques are applied for analysing the data of the Munich rental table. It can be seen that these algorithms are easy to handle without too much computational effort. The algorithms are available as GAUSS-programs

Restricted Likelihood Ratio Testing in Linear Mixed Models with General Error Covariance Structure

We consider the problem of testing for zero variance components in linear mixed models with correlated or heteroscedastic errors. In the case of independent and identically distributed errors, a valid test exists, which is based on the exact finite sample distribution of the restricted likelihood ratio test statistic under the null hypothesis. We propose to make use of a transformation to derive the (approximate) test distribution for the restricted likelihood ratio test statistic in the case of a general error covariance structure. The proposed test proves its value in simulations and is finally applied to an interesting question in the field of well-being economics

Partially Identified Prevalence Estimation under Misclassification using the Kappa Coefficient

We discuss a new strategy for prevalence estimation in the presence of misclassification. Our method is applicable when misclassification probabilities are unknown but independent replicate measurements are available. This yields the kappa coefficient, which indicates the agreement between the two measurements. From this information, a direct correction for misclassification is not feasible due to non-identifiability. However, it is possible to derive estimation intervals relying on the concept of partial identification. These intervals give interesting insights into possible bias due to misclassification. Furthermore, confidence intervals can be constructed. Our method is illustrated in several theoretical scenarios and in an example from oral health, where prevalence estimation of caries in children is the issue

Asymptotic Variance Estimation for the Misclassification SIMEX

Most epidemiological studies suffer from misclassification in the response and/or the covariates. Since ignoring misclassification induces bias on the parameter estimates, correction for such errors is important. For measurement error, the continuous analog to misclassification, a general approach for bias correction is the SIMEX (simulation extrapolation) originally suggested by Cook and Stefanski (1994). This approach has been recently extended to regression models with a possibly misclassified categorical response and/or the covariates by Küchenhoff et al. (2005), and is called the MC-SIMEX approach. To assess the importance of a regressor not only its (corrected) estimate is needed, but also its standard error. For the original SIMEX approach. Carroll et al. (1996) developed a method for estimating the asymptotic variance. Here we derive the asymptotic variance estimators for the MC-SIMEX approach, extending the methodology of Carroll et al. (1996). We also include the case where the misclassification probabilities are estimated by a validation study. An extensive simulation study shows the good performance of our approach. The approach is illustrated using an example in caries research including a logistic regression model, where the response and a binary covariate are possibly misclassified

Consistent Estimation of a Simple Linear Model Under Microaggregation

A problem statistical offices are increasingly faced with is guaranteeing confidentiality when releasing microdata sets. One method to provide safe microdata to is to reduce the information content of a data set by means of masking procedures. A widely discussed masking procedure is microaggregation, a technique where observations are grouped and replaced with their corresponding group means. However, while reducing the disclosure risk of a data file, microaggregation also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a simple linear model. We show that parameter estimates are biased if the dependent variable is used to group the data. It turns out that the bias of the slope parameter estimate is a non-monotonic function of this parameter. By means of this non-monotonic relationship we develop a method for consistently estimating the model parameters

A General Approach for the Analysis of Habitat Selection

Investigating habitat selection of animals aims at the detection of preferred and avoided habitat types as well as at the identification of covariates influencing the choice of certain habitat types. The final goal of such analyses is an improvement of the conservation of animals. Usually, habitat selection by larger animals is assessed by radio-tracking or visual observation studies, where the chosen habitat is determined for a number of animals at a set of time points. Hence the resulting data often have the following structure: A categorical variable indicating the habitat type selected by an animal at a specific time point is repeatedly observed and shall be explained by covariates. These may either describe properties of the habitat types currently available and / or properties of the animal. In this paper, we present a general approach for the analysis of such data in a categorical regression setup. The proposed model generalises and improves upon several of the approaches previously discussed in the literature and in particular allows to account for changing habitat availability due to the movement of animals within the observation area. It incorporates both habitat- and animal-specific covariates, and includes individual-specific random effects in order to account for correlations introduced by the repeated measurements on single animals. The methodology is implemented in a freely available software package. We demonstrate the general applicability and the capabilities of the proposed approach in two case studies: The analysis of a songbird in South-America and a study on brown bears in Central Europe

Statistical Inference in a Simple Linear Model Under Microaggregation

A problem statistical offices are increasingly faced with is guaranteeing confidentiality when releasing microdata sets. One method to provide safe microdata is to reduce the information content of a data set by means of masking procedures. A widely discussed masking procedure is microaggregation, a technique where observations are grouped and replaced with their corresponding group means. However, while reducing the disclosure risk of a data file, microaggregation also affects the results of statistical analyses. We focus on the effect of microaggregation on a simple linear model. In a previous paper we have shown how to correct for the aggregation bias of the naive least-squares estimator that occurs when the dependent variable is used to group the data. The present paper deals with the asymptotic variance of the corrected least-squares estimator and with the asymptotic variance of the naive least-squares estimator when either the dependent variable or the regressor is used to group the data. We derive asymptotic confidence intervals for the slope parameter. Furthermore, we show how to test for the significance of the slope parameter by analyzing the effect of microaggregation on the asymptotic power function of the naive t-test

Asymptotics for generalized linear segmented regression models with an unknown breakpoint

We consider asymptotic theory for the maximum likelihood estimator in the generalized linear model with an unknown breakpoint. A proof for the asymptotic normality is given. The methods are based on the work of Huber (1967). The main problem is the non--differentiability of the likelihood and the score function, which requires non--standard methods. An example from epidemiology is presented, where confidence intervals for the parameters are calculated with the asymptotic results

Testing for a Breakpoint in Two-Phase Linear and Logistic Regression Models

In many practical problems, it is of interest to check whether a functional relationship between an explanatory and a response variable remains unchanged over the whole domain of the explanatory variable or whether the functional form changes at certain unknown points, the so-called breakpoints. Thus, testing for the existence of a breakpoint is often an essential task. In this paper, we consider likelihood-ratio tests for different regression models such as broken line and threshold models. The problem related to the use of likelihood-ratio tests in this context concerns the determination of the null distribution of the likelihood-ratio statistic which has not been solved yet analytically. It is shown by means of Monte-Carlo experiments that the proposals of a limiting distribution discussed in the literature often yield unreliable results. It is therefore recommended to determine appropriate critical values by simulating the null distribution according to the data situation under investigation