BAYESIAN ESTIMATION OF RUIN PROBABILITIES WITH A HETEROGENEOUS AND HEAVY-TAILED INSURANCE CLAIM-SIZE DISTRIBUTION

This paper describes a Bayesian approach to make inference for risk reserve processes with an unknown claim‐size distribution. A flexible model based on mixtures of Erlang distributions is proposed to approximate the special features frequently observed in insurance claim sizes, such as long tails and heterogeneity. A Bayesian density estimation approach for the claim sizes is implemented using reversible jump Markov chain Monte Carlo methods. An advantage of the considered mixture model is that it belongs to the class of phase‐type distributions, and thus explicit evaluations of the ruin probabilities are possible. Furthermore, from a statistical point of view, the parametric structure of the mixtures of the Erlang distribution offers some advantages compared with the whole over‐parametrized family of phase‐type distributions. Given the observed claim arrivals and claim sizes, we show how to estimate the ruin probabilities, as a function of the initial capital, and predictive intervals that give a measure of the uncertainty in the estimations.     

On Comparison of Stopping Times in Sequential Procedures for Exponential Families of Stochastic Processes

For curved ( k + 1), k -exponential families of stochastic processes a natural and often studied sequential procedure is to stop observation when a linear combination of the coordinates of the canonical process crosses a prescribed level. For such procedures the model is, approximately or exactly, a non-curved exponential family. Subfamilies of these stopping rules defined by having the same Fisher (expected) information are considered. Within a subfamily the Bartlett correction for a point hypothesis is also constant. Methods for comparing the durations of the sampling periods for the stopping rules in such a subfamily are discussed. It turns out that some stopping times tend to be smaller than others. For exponential families of diffusions and of counting processes the probability that one such stopping time is smaller than another can be given explicity. More generally, an Edgeworth expansion of this probability is given     

The Cusum of Squares Test for Scale Changes in Infinite Order Moving Average Processes

In this paper we consider the problem of testing for a scale change in the infinite order moving average process X _j = _{i =0} a _{i j i} , where _j are i.i.d. r.v.s with E ₁ < for some > 0. In performing the test, a cusum of squares test statistic analogous to Inclan & Tiao's (1994) statistic is considered. It is well-known from the literature that outliers affect test procedures leading to false conclusions. In order to remedy this, a cusum of squares test based on trimmed observations is considered. It is demonstrated that this test is robust against outliers, is valid for infinite variance processes as well. Simulation results are given for illustration.     

Reduction of n-th moment measures and the special case of the third moment measure of stationary and isotropic planar point processes

Formulae for the reduction of n-th moment measures of stationary point processes and an unbiased estimator for the reduced n-th moment measure are given. In particular, the special case of the third moment measure of planar point processes is considered and the application of the quantities studied is illustrated by an example.     

The Input Evaluation of Generalized Bernoulli Processes for Salary Lines Construction by Means of Continuous Time Generalized Non-Homogeneous Semi-Markov Processes

Salary line forecasting assumes a relevant role in manpower and in pension funds Previously, the authors presented a generalized Bernoulli process, useful for forecasting the evolution of salary lines, taking into account the salary costs, the number of workers at each rank and the probability transitions between the ranks. The problem with applying this model is constructing the probability of transition between the grades. In this article, we will present a model that allows obtaining these probabilities by means of the solution of the evolution equation of a generalization of continuous time non-homogeneous semi-Markov processes.     

Nonstationary Data Analysis by Time Deformation

ABSTRACT

In this article we discuss methodology for analyzing nonstationary time series whose periodic nature changes approximately linearly with time. We make use of the M-stationary process to describe such data sets, and in particular we use the discrete Euler(p) model to obtain forecasts and estimate the spectral characteristics. We discuss the use of the M-spectrum for displaying linear time-varying periodic content in a time series realization in much the same way that the spectrum shows periodic content within a realization of a stationary series. We also introduce the instantaneous frequency and spectrum of an M-stationary process for purposes of describing how frequency changes with time. To illustrate our techniques we use one simulated data set and two bat echolocation signals that show time varying frequency behavior. Our results indicate that for data whose periodic content is changing approximately linearly in time, the Euler model serves as a very good model for spectral analysis, filtering, and forecasting. Additionally, the instantaneous spectrum is shown to provide better representation of the time-varying frequency content in the data than window-based techniques such as the Gabor and wavelet transforms. Finally, it is noted that the results of this article can be extended to processes whose frequencies change like at^α, a > 0, ?∞ < α < ? ∞.     

Agricultural Strategy Development in West Africa: The False Promise of Participation?

Participatory approaches are an increasingly prominent technique for designing agricultural strategies in sub‐Saharan Africa. However, they are frequently criticised for either not involving enough stakeholders or limiting the scope of their participation. This article concludes from a study of the situation in West Africa that a lack of broad‐based participation in these strategies is not a major problem; rather, the real challenge lies in transforming the outcomes of participatory processes into policies that can be feasibly implemented. It highlights why an emphasis on participation can sometimes result in disappointment amongst stakeholders and discusses a range of measures to help overcome this dilemma.     

Testing Semiparametric Hypotheses in Locally Stationary Processes

In this paper, we investigate the problem of testing semiparametric hypotheses in locally stationary processes. The proposed method is based on an empirical version of the L₂‐distance between the true time varying spectral density and its best approximation under the null hypothesis. As this approach only requires estimation of integrals of the time varying spectral density and its square, we do not have to choose a smoothing bandwidth for the local estimation of the spectral density – in contrast to most other procedures discussed in the literature. Asymptotic normality of the test statistic is derived both under the null hypothesis and the alternative. We also propose a bootstrap procedure to obtain critical values in the case of small sample sizes. Additionally, we investigate the finite sample properties of the new method and compare it with the currently available procedures by means of a simulation study. Finally, we illustrate the performance of the new test in two data examples, one regarding log returns of the S&P 500 and the other a well‐known series of weekly egg prices.     

语音及音系格局对英汉象声词生成模式的制约

象声词是对自然界声音的摹拟 ,是语言中的一种普遍现象 ,各种语言中都有丰富的象声词。但是 ,当它们摹拟同一种声音时 ,摹拟出来的结果却有很大的差异。本文试图通过比较英汉象声词的生成模式 ,即感知→摹拟→生成来说明从语音感知、摹拟到生成的整个过程中 ,带有鲜明民族特点的各种语言的语音及音系格局对象声词生成的制约     

Asymptotic results for empirical and partial-sum processes: A review

Two processes of importance in statistics and probability are the empirical and partial-sum processes. Based on d-dimensional data X₁, … X_a the empirical measure is defined for any A ⊂ R^d by the sample proportion of observations in A. When normalized, F_n yields the empirical process W_n: = n^1/2 (F_n - F), where F denotes the “true” probability measure. To define partial-sum processes, one needs data that are assigned to specified locations (in contrast to the above, where specified unit masses are assigned to random locations). A suitable context for many applications is that of data attached to points of a lattice, say {X_j:j ϵ J^d} where J = {1, 2,…}, for which the partial sums are defined for any A ⊂ R^d by Thus S(A) is the sum of the data contained in A. When normalized, S yields the partial-sum process. This paper provides an overview of asymptotic results for empirical and partial-sum processes, including strong laws and central limit theorems, together with some indications of their inferential implications.