Generalized Kernel Estimators for the Weibull-Tail Coefficient

We introduce new families of estimators for the Weibull-tail coefficient, obtained from a weighted sum of a power transformation of excesses over a high random threshold. Asymptotic normality of the estimators is proven for an intermediate sequence of upper order statistics, and under classical regularity conditions for L-statistics and a second-order condition on the tail behavior of the underlying distribution. The small sample performance of two specific examples of kernel functions is evaluated in a simulation study.     

Invertibility of non-linear time series models

Sufficient conditions for invertibility of non-linear time series models are available in the literature only for a few special cases. In this paper a practical and general method for checking invertibility is presented. Briefly stated, it consists of feeding independent and identically distributed innovations into the non-linear model and then observing whether the model blows up or not. Using this idea invertibility conditions are derived for several recently proposed non-linear moving average models. Finally, the method is applied to a number of bilinear models fitted to economic time series.     

Lagged Regression Residuals and Serial-Correlation Tests

A new family of statistics is proposed to test for the presence of serial correlation in linear regression models. The tests are based on partial sums of lagged cross-products of regression residuals that define a class of interesting Gaussian processes. These processes are characterized in terms of regressor functions, the serial-correlation structure, the distribution of the noise process, and the order of the lag of the cross-products of residuals. It is shown that these four factors affect the lagged residual processes independently. Large-sample distributional results are presented for test statistics under the null hypothesis of no serial correlation or for alternatives from a range of interesting hypotheses. Some indication of the circumstances to which the asymptotic results apply in finite-sample situations and of those to which they should be applied with some caution are obtained through a simulation study. Tables of selected quantiles of the proposed tests are also given. The tests are illustrated with two examples taken from the empirical literature. It is also proposed that plots of lagged residual processes be used as diagnostic tools to gain insight into the correlation structure of residuals derived from regression fits.     

Variance Estimators of the Gini Coefficient—Probability Sampling

An estimator of the Gini coefficient (the well-known income inequality measure) of a finite population is defined for an arbitrary probability sampling design, taking the sampling design into consideration. Alternative estimators of the variance of the estimated Gini coefficient are introduced. The sampling performance of the Gini coefficient estimator and its variance estimators is studied by means of a Monte Carlo study, using stratified sampling from a miniature population of Swedish households with authentic income data.     

Auf den Rangplatz kommt es an – Wirkung der Rangfolge von Produkten auf das Entscheidungsverhalten

Customers often search for and choose from ordered sets. E. g., online shops present their product assortments as lists; very often the products are listed according to criteria as defined by the customers. Based on theoretical explanations it can be assumed that the rank of a product in a list effects its demand. An empirical study run in the market for used cars shows the importance of that effect. The study also reveals the most preferred rank and provides further insights for an optimal ordering of products. Furthermore, the understanding of individual decision about rank ordered products can be deepened.     

A Study of a Total Social Services Care Population and its Inter-Agency Shared Care Populations

There are very few large population studies and little informationabout the characteristics of social services populations andthe inter-agency populations that social services departmentsshare with other agencies. This study fills this gap. It examinesa total social services adult care population, excluding residentialcare homes (N = 19,461) in the context of its general co-terminoushealth authority population (N = 646,239). Approximately two-thirds(61 per cent) of the social services population were women,compared to the health authority population of 51 per cent.Sixty-two per cent were over sixty-five years compared to 23per cent of the health authority. Age groupings and genderedpatterns of service use are then identified for different caregroups. The study then examines care populations shared betweensocial services and other agencies, identifying the amount ofshared care and the characteristics of specific shared caresubgroups. Forty-two per cent of the social services populationwere shared with the community health trust and 19 per centwith the mental health trust. The proportion of the social servicespopulation in contact with Criminal Justice and accident andemergency was nearly twice that in the overall health authoritypopulation. The limitations of these data are examined and thepotential of this method to inform inter-agency planning andshared care is discussed.     

Assessing uncertain ventures using experts' judgments in the form of subjective probabilities

The paper deals with a procedure known as ASPRO which has been successfull applied at Shell Oil Company. Section II addresses general problems encountered in using subjective assessment procedures. Section III introduces ASPRO's decomposition process which is designed to alleviate some of the problems. The decomposition process produces a questionnaire, the answers to which are the inputs to the ASPRO assessment procedure. Examples of the questionnaire for assessing political risks to oil investment ventures and analyzing new product sectors are given. Section IV explains how the respondents assess the component parts, and Section V outlines the mechanical procedures which are used to combine the assessments. Examples of how ASPRO's output can be used to communicate the respondents' quantified judgments are given in Section VI. Conclusions are in Section VII.