MOMENT ESTIMATION IN THE CLASS OF BISEXUAL BRANCHING PROCESSES WITH POPULATION–SIZE DEPENDENT MATING

This paper concerns the estimation of the offspring mean vector, the covariance matrix and the growth rate in the class of bisexual branching processes with population‐size dependent mating. For the proposed estimators, some unconditional moments and some conditioned to non‐extinction are determined and asymptotic properties are established. Confidence intervals are obtained and, as illustration, a simulation example is given.     

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     

On the Second‐Order Random Walk Model for Irregular Locations

Abstract. The second‐order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considering the RW2 model as the solution of a stochastic differential equation (SDE), a discretely observed integrated Wiener process, it is possible to derive the density preserving the Markov properties by augmenting the state‐space with the velocities. Here, we derive a computationally more efficient RW2 model for irregular locations using a Galerkin approximation to the solution of the SDE without the need of augmenting the state‐space. Numerical comparison with the exact solution demonstrates that the error in the Galerkin approximation is small and negligible in applications.     

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.     

论大学生文明素养

本文通过对一些在校大学生文明素养欠缺的现象进行分析与原因探讨,认为大学责无旁贷,应积极帮助大学生提高自身的文明素养,主动肩负起培养知礼、守礼并具有健全人格大学生的教育责任,并提出应树立"全校一盘棋"的教育理念,系统地通过加强校园硬件和软件设施的综合建设来实现优秀大学生的培养。     

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.     

企业质量成本信息集成化管理与系统设计

为促进质量成本管理在企业中的推广实践，对企业质量成本信息集成化管理系统进行研究。在分析质量成本管理中所涉及的数据信息及其与企业现有系统中其他数据联系的基础上，根据企业实践提出一种切实可行的质量成本管理信息化设计方案。为便于质量成本管理信息系统与企业现有系统的对接，分析说明其集成化管理设计，以期为企业推广实施质量成本管理提供实践指导。     

Polynomial approximation of nonlinear regression functions

In the present paper a nonlinear regression function is approximated by a polynomial estimator according to the expectation of the quadratic L ²-distance as risk is given. For special experimental designs with repeating experimental points this estimator coincides with the estimator by the method of the reproducing kernel.

Considerations about the relation for the sample size and the degree of the approximation polynomial and about the quadratic mean are given.