The forecasting performance of mortality models

Mortality projections are of special interest in many applications. For example, they are essential in life insurances to determine the annual contributions of their members as well as for population predictions. Due to their importance, there exists a huge variety of mortality forecasting models from which to seek the best approach. In the demographic literature, statements about the quality of the various models are mostly based on empirical ex-post examinations of mortality data for very few populations. On the basis of such a small number of observations, it is impossible to precisely estimate statistical forecasting measures. We use Monte Carlo (MC) methods here to generate time trajectories of mortality tables, which form a more comprehensive basis for estimating the root-mean-square error (RMSE) of different mortality forecasts.     

企业失败判别模型实证研究

一、问题的提出企业失败是一个世界性的问题。根据Ｄｕｎ＆Ｂｒａｄｓｔｒｅｅｔ的记录 ,美国 1991年失败企业有 872 66家。报纸“ＴｏＶｉｍａ”1997年 6月 8日报道 ,1996年部分欧洲国家失败企业的数目如下 :法国有 5990 0家 ,德国有 310 0 0家 ,英国有 4 2 90 0家 ,意大利有1560 0家 ,瑞典有 12 2 0 0家 ,瑞士有 10 2 0 0家。美国和部分欧洲国家失败企业的数量是庞大的。由于企业失败问题的极端重要性 ,一直以来就有很多专家学者希望采用定量分析建立模型等方法抓住失败企业的本质特征。 1968年美国专家Ｅｄ ｗａｒｄ .Ｉ .Ａｌｔｍａｎ首…     

Bibliography of Vital Statistics in Australia: a Third List

This list brings up to date the references in my "Bibliography of Vital Statistics in Australia and New Zealand" Austral. J. Statist. 6 (1964) 33–99 and the "Bibliography of Vital Statistics in Australia: a second list" ibid (1973) 1–26. The cover of the Journals remains the same as listed on page 33 of the original bibliography and continues up to the end of 1980 in most cases. As mentioned in the second list, there are few references to New Zealand sources because of the publication of the bibliography of Dr. J. W. Donovan. Some references are given to works devoted to the health of the aboriginal population but this field is more completely done by Moodie & Pedersen (1971).     

How does the DerSimonian and Laird procedure for random effects meta-analysis compare with its more efficient but harder to compute counterparts?

The procedure suggested by DerSimonian and Laird is the simplest and most commonly used method for fitting the random effects model for meta-analysis. Here it is shown that, unless all studies are of similar size, this is inefficient when estimating the between-study variance, but is remarkably efficient when estimating the treatment effect. If formal inference is restricted to statements about the treatment effect, and the sample size is large, there is little point in implementing more sophisticated methodology. However, it is further demonstrated, for a simple special case, that use of the profile likelihood results in actual coverage probabilities for 95% confidence intervals that are closer to nominal levels for smaller sample sizes. Alternative methods for making inferences for the treatment effect may therefore be preferable if the sample size is small, but the DerSimonian and Laird procedure retains its usefulness for larger samples.     

A general method of inference for two-parameter continuous distributions

Abstract

This article presents a general method of inference of the parameters of a continuous distribution with two unknown parameters. Except in a few distributions such as the normal distribution, the classical approach fails in this context to provide accurate inferences with small samples.Therefore, by taking the generalized approach to inference (cf. Weerahandi, 1995 Weerahandi, S. (1995). Exact Statistical Methods for Data Analysis. New York: Springer Verlag. [Google Scholar]), in this article we present a general method of inference to tackle practically useful two-parameter distributions such as the gamma distribution as well as distributions of theoretical interest such as the two-parameter uniform distribution. The proposed methods are exact in the sense that they are based on exact probability statements and exact expected values. The advantage of taking the generalized approach over the classical approximate inferences is shown via simulation studies.

This article has the potential to motivate much needed further research in non normal regressions, multiparameter problems, and multivariate problems for which basically there are only large sample inferences available. The approach that we take should pave the way for researchers to solve a variety of non normal problems, including ANOVA and MANOVA problems, where even the Bayesian approach fails. In the context of testing of hypotheses, the proposed method provides a superior alternative to the classical generalized likelihood ratio method.     

上市公司报表性和实质性资产重组鉴别与分析

１９９７年以来,随着我国国有企业改革的深化,资产重组已经成为证券市场上一道亮丽的风景线,进行过资产重组的上市公司的数量越来越多。１９９８年沪深两市共有３８９家上市公司进行了资产重组。从资产重组方式来看,我们可以把１９９８年上市公司资产重组行为分为五大类：第一类,上市公司对外购并扩张,指上市公司对外收购、兼并或对外股权投资的资产重组行为。该种重组反映了上市公司的对外扩张战略。第二类,上市公司股权转让,指上市公司本身资产不动,而其股权发身控股性的或非控股性的转让。新的股东入主上市公司,必然会给上市公…     

Methods for projecting private households

"Although there exists a reasonable number of methods for projecting the number of private households, only a few of them are used in practice. The reason for this discrepancy is...analysed. All important methods which had been developed until now will be presented, focusing on their assumptions and the data needed." (SUMMARY IN ENG)     

Clustered Survival Data with Left‐truncation

Left‐truncation occurs frequently in survival studies, and it is well known how to deal with this for univariate survival times. However, there are few results on how to estimate dependence parameters and regression effects in semiparametric models for clustered survival data with delayed entry. Surprisingly, existing methods only deal with special cases. In this paper, we clarify different kinds of left‐truncation and suggest estimators for semiparametric survival models under specific truncation schemes. The large‐sample properties of the estimators are established. Small‐sample properties are investigated via simulation studies, and the suggested estimators are used in a study of prostate cancer based on the Finnish twin cohort where a twin pair is included only if both twins were alive in 1974.     

Tabloids

Abstract

Comic books and libraries do not seem to get along, at least not in North American libraries. Aside from a few dozen specialized, noncirculating research collections, retrospective comic book holdings remain virtually unknown as a library resource.1 Browsing collections of current comic books are equally rare in public, school, and college libraries. In a 1984 article, comic book bibliographer Randall Scott observed, “In most communities, if you want to read or refer to a comic book, you have to buy it.” Librarian Doug Highsmith concurred, writing in 1992 that public libraries carrying the latest issues of popular comics titles are “still the exception rather than the rule.” Both statements remain fundamentally true today.     

A comparison of efficient approximations for a weighted sum of chi-squared random variables

In many applications, the cumulative distribution function (cdf) \(F_{Q_N}\) of a positively weighted sum of N i.i.d. chi-squared random variables \(Q_N\) is required. Although there is no known closed-form solution for \(F_{Q_N}\), there are many good approximations. When computational efficiency is not an issue, Imhof’s method provides a good solution. However, when both the accuracy of the approximation and the speed of its computation are a concern, there is no clear preferred choice. Previous comparisons between approximate methods could be considered insufficient. Furthermore, in streaming data applications where the computation needs to be both sequential and efficient, only a few of the available methods may be suitable. Streaming data problems are becoming ubiquitous and provide the motivation for this paper. We develop a framework to enable a much more extensive comparison between approximate methods for computing the cdf of weighted sums of an arbitrary random variable. Utilising this framework, a new and comprehensive analysis of four efficient approximate methods for computing \(F_{Q_N}\) is performed. This analysis procedure is much more thorough and statistically valid than previous approaches described in the literature. A surprising result of this analysis is that the accuracy of these approximate methods increases with N.     

Optimal search procedure on coin-weighing problem

The following coin-weighing problem is considered: suppose among the given n coins there are two counterfeit coins, which are either heavier or lighter than other $n-2$ good coins, this is not known beforehand. The aim is to find an optimal algorithm which identifies these two counterfeit coins using as few weighings as possible. It is proved that the minimal number of weighings is either equal to the information-theoretic lower bound, or exceeds it by 1. Moreover, the information-theoretic lower bound are achievable for even number of weighings; for odd number of weighings, our optimal interval is very close to the theoretic optimal interval. The ideas and techniques of this paper can be used to solve other search models.     

统计模型应用的学术规范研究

在中国社会科学领域研究中,统计模型泛化过程中的误用、滥用现象日益严重,模型应用中的种种失范行为违背了学术精神。统计模型应遵守的学术规范包括:模型的建立和调整要有理论依据,合理的模型是主观与客观的统一;实证分析中应重视数据质量以免错用滥用统计数据,建模中要避免命题不可证伪,陷入"数字游戏"误区等。通过学术规范彰显的学术精神应体现在对模型方法做出有价值有意义的创新或是根据模型结果论证新的命题。当前,中国应制定有关统计学的学术规范,并完善期刊的审稿制度来解决统计模型的学术失范问题。     

Throughput and delay analysis of an opportunistic tree algorithm

Tree algorithms are a well-known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this article, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are allowed to use the channel only if there is no primary user activity. The tree algorithm designed in this article can be used by the secondary users to share the channel capacity left by the primary users.

We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.

Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.     

Structured probability statements

Structured probability statements are defined in an additive and reduced structured model. Under weak assumptions, an estimating set in a structured probability statement is a confidence region, but the corresponding structured probability may differ from the confidence coefficient. Elementary examples are given to show that this difference is an advantage when some estimating sets are empty or consist of the whole parameter space. A structured distribution (Plante 1979) is an extension of a probability measure closely related to structured probability statements.     

Method for simulating non-linear stochastic differential equations in ℝ1

Very few specific stochastic differential equations have explicitly known solutions. The most common procedure to obtain a simulated path of a solution is based on a discretization of the stochastic differential equations. However, there are some cases where the discrete-time discretization cannot be used. In this article, we propose a new method to simulate the solution of a non-linear stochastic differential equation, which, in principle, is exempt from error of simulation and can be widely applied including in cases where the discrete-time discretization cannot be used.     

Accelerated Burn-In Procedures and System Maintenance Policies

Burn-in is a widely used engineering method which is adopted to eliminate defective items before they are shipped to customers or put into field operation. In order to shorten the burn-in process, burn-in is most often accomplished in an accelerated environment. However, there have been few probabilistic or stochastic models for the burn-in procedures in accelerated environment. In this article, under a new stochastic model for accelerated burn-in procedure, the problems of determining both optimal accelerated burn-in time and optimal replacement policy are considered. Components are burned-in under an accelerated environment, then those surviving the burn-in procedure are put into field operation and they are maintained under a replacement policy. The properties of the optimal accelerated burn-in time and optimal replacement policy are obtained and a numerical example which illustrates the usage of obtained results will be presented.     

Inequalities involving expectations of selected functions in reliability theory to characterize distributions

Recently, authors have studied inequalities involving expectations of selected functions, viz. failure rate, mean residual life, aging intensity function, and log-odds rate which are defined for left truncated random variables in reliability theory to characterize some well-known distributions. However, there has been growing interest in the study of these functions in reversed time (X ? x, instead of X > x) and their applications. In the present work we consider reversed hazard rate, expected inactivity time, and reversed aging intensity function to deal with right truncated random variables and characterize a few statistical distributions.     

The Moran coefficient for non-normal data

This paper summarizes findings that extend statistical distribution properties of the Moran coefficient index measuring spatial autocorrelation to non-normal random variables. Pitman–Koopmans theorem results are extended for the mean and the variance of this index. This summary includes a corollary to this theorem, as well as a new theorem (with its proof) and two conjectures implied by it. The first of these statements is supported by asymptotic heuristics; the second is supported by simulation experiment results. Mixture random variables that include heteroscedasticity or overdispersion also are explored. In addition, a simple asymptotic variance for the Moran coefficient is presented, assessed, and found to be very precise for sample sizes as small as 25–100. The principal conclusion is that independence and sample size are the most relevant properties for Pitman–Koopmans theorem results to be extended to non-normal random variables. The independent and identically distributed property reduces the necessary sample size for this extension, as do the properties of symmetry and normal approximation.     

Jerome H. Friedman and Nicholas I. Fisher

Many data analytic questions can be formulated as (noisy) optimization problems. They explicitly or implicitly involve finding simultaneous combinations of values for a set of (input) variables that imply unusually large (or small) values of another designated (output) variable. Specifically, one seeks a set of subregions of the input variable space within which the value of the output variable is considerably larger (or smaller) than its average value over the entire input domain. In addition it is usually desired that these regions be describable in an interpretable form involving simple statements (rules) concerning the input values. This paper presents a procedure directed towards this goal based on the notion of patient rule induction. This patient strategy is contrasted with the greedy ones used by most rule induction methods, and semi-greedy ones used by some partitioning tree techniques such as CART. Applications involving scientific and commercial data bases are presented.     

A study of simple unbalanced factorial designs that use type ii and type iii sums of squares

Methods for analysing unbalanced factorial designs can be traced back to the work of Frank Yates in the 1930s . Yet, still today the question on how his methods of fitting constants (Type II) and weighted squares of means (Type III) behave when negligible or insignificant interactions exist, is still unanswered. In this paper, by means of a simulation study, Type II and Type III ANOVA results are examined for all unbalanced structures originating from a 2x3 balanced factorial design within homogeneous groups (design types) accounting for structure, number of observations lost and which cells contained the missing observations. The two level factor is further analysed to test the null hypothesis, for both Type II and Type III analyses, that the unbalanced structures within each design type provide comparable F values. These results are summarised and the conclusion shows that this work agrees with statements made by Yates Burdick and Herr and Shaw and Mitchell-Olds, but there are some results which require further investigation.