Bayesian prediction with an asymmetric criterion in a nonparametric model of insurance risk

A median-unbiased estimator of the characteristic exponent of a symmetric stable distribution is constructed.     

Multicollinearity and the value of a priori information

A measure of multicollinearity is defined which is useful in evaluating maintained hypotheses and aiding estimator selection as it suggests when a non-traditional estimator proposed by Bock (1975) is minimax and dominates ordinary least squares. An example is used to illustrate the presented methodology.     

保险风险评估的一个模型

一、引言保险人对自身所经营风险的正确和全面的认识是保障稳健经营的前提。早在本世纪初 ( 190 3 )年 ,ＦｉｌｉｐＬｕｎｄｂｅｒｇ就奠定了古典风险分析理论的基础 ,但直到 1955年才由ＨａｒａｌｄＣｒａｍｅｒ[1]等人所完善。其古典风险模型可用如下的公式描述 :Ｓ(ｔ) =ｕ ｃｔ-ΣＮ (ｔ)ｋ =1Ｘｋ,其中ｕ是保险人为某一种或某一类风险的所准备的初始准备金 ,ｃ是费率 ,Ｎ (ｔ)是ｔ年之前的索赔个数 ,Ｘｋ 表示第ｋ次索赔的索赔额 ,因此Ｓ(ｔ)就表示ｔ年时保险人的盈余额。一个衡量保险公司经营好坏的重要指标就是盈余额Ｓ(ｔ)会不会达…     

Multiple-site updates in maximum a posteriori and marginal posterior modes image estimation

We describe standard single-site Monte Carlo Markov chain methods, the Hastings and Metropolis algorithms, the Gibbs sampler and simulated annealing, for maximum a posteriori and marginal posterior modes image estimation. These methods can experience great difficulty in traversing the whole image space in a finite time when the target distribution is multi-modal. We present a survey of multiple-site update methods, including Swendsen and Wang's algorithm, coupled Markov chains and cascade algorithms designed to tackle the problem of moving between modes of the posterior image distribution. We compare the performance of some of these algorithms for sampling from degraded and non-degraded Ising models     

Statistical methods of risk assessment for continuous variables

Adverse health effects for continuous responses are not as easily defined as adverse health effects for binary responses. Kodell and West (1993) developed methods for defining adverse effects for continuous responses and the associated risk. Procedures were developed for finding point estimates and upper confidence limits for additional risk under the assumption of a normal distribution and quadratic mean response curve with equal variances at each dose level. In this paper, methods are developed for point estimates and upper confidence limits for additional risk at experimental doses when the equal variance assumption is relaxed. An interpolation procedure is discussed for obtaining information at doses other than the experimental doses. A small simulation study is presented to test the performance of the methods discussed.     

Finite time ruin probability and structural density properties in the presence of dependence in insurance risk model

In the present paper, we consider the classical compound Poisson risk model with dependence between claim sizes and claim inter-arrival time. We attempt to analyze the approximation of finite time ruin probability. The finite time ruin probabilities are plotted for fixed threshold value associated to the claim inter-arrival time and also for fixed dependence parameter in Nelsen (2006) copula separately. Additionally, a general form for joint density of the interclaim times and claim sizes is considered. With respect to the classical Gerber-Shiu's (1998) function, first some structural density properties of dependent collective risk model is obtained. Then the ladder height probability density function of claim sizes is computed and the dependency structure investigated for Erlang interclaim time. As the application, some dependent models of the interclaim times and claim sizes are studied.     

Statistical analysis of non-inferiority via non-zero risk difference in stratified matched-pair studies

A stratified study is often designed for adjusting several independent trials in modern medical research. We consider the problem of non-inferiority tests and sample size determinations for a nonzero risk difference in stratified matched-pair studies, and develop the likelihood ratio and Wald-type weighted statistics for testing a null hypothesis of non-zero risk difference for each stratum in stratified matched-pair studies on the basis of (1) the sample-based method and (2) the constrained maximum likelihood estimation (CMLE) method. Sample size formulae for the above proposed statistics are derived, and several choices of weights for Wald-type weighted statistics are considered. We evaluate the performance of the proposed tests according to type I error rates and empirical powers via simulation studies. Empirical results show that (1) the likelihood ratio and the Wald-type CMLE test based on harmonic means of the stratum-specific sample size (SSIZE) weight (the Cochran's test) behave satisfactorily in the sense that their significance levels are much closer to the prespecified nominal level; (2) the likelihood ratio test is better than Nam's [2006. Non-inferiority of new procedure to standard procedure in stratified matched-pair design. Biometrical J. 48, 966–977] score test; (3) the sample sizes obtained by using SSIZE weight are smaller than other weighted statistics in general; (4) the Cochran's test statistic is generally much better than other weighted statistics with CMLE method. A real example from a clinical laboratory study is used to illustrate the proposed methodologies.     

Private households according to socioeconomic classification in national accounting: the model of the Federal Statistical Office

The author notes that "for calculating income distribution and expenditure by groups of households, annual averages are required concerning the number of private households by household groups and...the structure of the household members in a socio-economic classification." Problems of adjusting such household data so that they are compatible with data from other sources such as employment statistics are discussed, and a procedure for adjusting annual micro-census data on households in the Federal Republic of Germany is described. "Results for the year 1982 are presented, showing the main development trends as compared with the year 1972. Finally, the quality of forecasting with the adjustment procedure is studied." (summary in ENG)     

Optimal investment and life insurance strategies in a mixed jump-diffusion framework

Abstract

This article investigates an optimal investment and life insurance strategies in a mixed jump-diffusion framework. The individual life insurance policyholder who has CRRA preferences. The market consists of riskless asset, a zero-coupon bond, a stock and life insurance. The instantaneous interest rate is modeled as the O-U model, while a zero-coupon bond with credit risk follows a BSDE and a risky asset be driven by MJD-fBm model. The problem is solved by the mixed jump diffusion fractional HJB SDE which satisfied the admissible strategy, then the closed form solution and optimal strategies are derived and the simulation of the various parameters are also given.     

Evaluating subject-level incremental values of new markers for risk classification rule

Suppose that we need to classify a population of subjects into several well-defined ordered risk categories for disease prevention or management with their “baseline” risk factors/markers. In this article, we present a systematic approach to identify subjects using their conventional risk factors/markers who would benefit from a new set of risk markers for more accurate classification. Specifically for each subgroup of individuals with the same conventional risk estimate, we present inference procedures for the reclassification and the corresponding correct re-categorization rates with the new markers. We then apply these new tools to analyze the data from the Cardiovascular Health Study sponsored by the US National Heart, Lung, and Blood Institute. We used Framingham risk factors plus the information of baseline anti-hypertensive drug usage to identify adult American women who may benefit from the measurement of a new blood biomarker, CRP, for better risk classification in order to intensify prevention of coronary heart disease for the subsequent 10 years.     

社会保险与商业保险的结合方式及保险资金入市研究

 社会养老保险与个人储蓄养老保险同属社会保障范畴,其共同目标是通过保险基金的增值,为投保人提供稳定可靠的养老保障,以确保安全度过人口老龄化高峰期。多年来,我国社会养老保险与商业人寿保险囿于立法范畴、管理体制、性质、特点、作用、范围、权利与义务关系的相异性,两者互不相融,各自发展,不利于养老保障三大支柱的建立。如今,以保险基金入市为契机,以资本市场为纽带,实现社会养老保险与商业人寿保险的协调与发展,是未来社会保障改革的基本走势。     

统计调查方法改革与统计效益

统计调查方法改革与统计效益龙华,王凡一、改革统计调查方法体系的紧迫性（一）现行统计调查方法体系存在的主要问题中国的统计调查方法体系是按照高度集中的计划经济管理体制和分级管理的要求建立起来的。长期以来,基本上依靠全面统计报表和层层汇总上报采集信息。改革...     

Splines as a Useful and Convenient Statistical Tool

The framework for a unified statistical theory of spline regression assuming fixed knots using the truncated polynomial or “+” function representation is presented. In particular, a partial ordering of some spline models is introduced to clarify their relationship and to indicate the hypotheses that can be tested by using either standard multiple regression procedures or a little-used conditional test developed by Hotelling (1940). The construction of spline models with polynomial pieces of different degrees is illustrated. A numerical example from a chemical experiment is given by using the GLM procedure of the statistical software package SAS (Barr et al. 1976).     

Statistical games against a prophet-proof of a minimax conjecture

“Prophet theory” quantifies the price a statistician has to pay for his lack of information in stochastic sequences. In a recent paper, Schmitz (1991) gave a game-theoretical interpretation of this situation and he formulated in particular a minimax conjecture for the difference case. In this note we prove that conjecture and, moreover, present minimax ran domized stopping times (minimax procedures for the statistician).     

Statistical inference of risk difference in K correlated 2×2 tables with structural zero

K correlated 2×2 tables with structural zero are commonly encountered in infectious disease studies. A hypothesis test for risk difference is considered in K independent 2×2 tables with structural zero in this paper. Score statistic, likelihood ratio statistic and Wald‐type statistic are proposed to test the hypothesis on the basis of stratified data and pooled data. Sample size formulae are derived for controlling a pre‐specified power or a pre‐determined confidence interval width. Our empirical results show that score statistic and likelihood ratio statistic behave better than Wald‐type statistic in terms of type I error rate and coverage probability, sample sizes based on stratified test are smaller than those based on the pooled test in the same design. A real example is used to illustrate the proposed methodologies. Copyright © 2009 John Wiley & Sons, Ltd.     

On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization

This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is “matched” to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.     

New concepts and applications in growth phenomena

This paper reviews earlier research on new concepts for growth curve modelling, expands on this work and explores the practical feedback from industry. The definition of growth is refined and the consequences of the new concepts are considered in greater depth. Reference is made to diffusion as a subset of growth, and the importance of the generalized Norden model is highlighted by comparison with the Bass and logistic models for dominant growth or diffusion elements. The extensive implications of the new principles are explored, including growth differentials, and open and closed temporal and spatial systems. Various examples are given, distinguishing between 'micro' (one product) and 'macro' (tens of products) case studies. These range from a study of the Spanish tractor economy to the production of a helicopter. Cashflows are shown to be a growth process. Finally, the stochastic issues are examined both for a dominant growth element and, by use of an example of the construction of a new model, at the level of stochastic differential equations.