The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

Statistik für bivariate gemischte Poisson–Prozesse am Beispiel der Kraftfahrthaftpflichtversicherung

Zusammenfassung: In diesem Artikel wird der Weg von einem univariaten gemischten Poisson–Prozess, der in vielen Bereichen zum Z?hlen von Ereignissen benutzt wird, zu einem bivariaten gemischten Poisson–Prozess aufgezeigt. Dazu werden einige Eigenschaften des bivariaten Prozesses angegeben. Im zweiten Teil der Arbeit wird gezeigt, wie mit Hilfe dieses Prozesses der übergang von einem herk?mmlichen Bonus–Malus–System in der Kraftfahrthaftpflichtversicherung zu einem Bonus–Malus–System mit Berücksichtigung der Schadenart beschritten werden kann. Dazu wird zuerst eine Modellprüfung der gegebenen Daten vorgenommen und sodann werden für verschiedene mischende Verteilungen die Verteilungsparameter gesch?tzt und Nettopr?mien angegeben sowie die Prognosegenauigkeit getestet.

---

Summary: In this paper we show that the model of the bivariate mixed Poisson process arises in a natural way from the univariate mixed Poisson process, which is used in several areas for counting certain events. Furthermore we state some properties of the bivariate process. In the second part of the paper we illustrate how by means of the bivariate mixed Poisson process a bonus–malus system handling different types of accidents can be derived from the classical bonus–malus system in third–party liability insurance. To this end we first check the model on the given data and then estimate distribution parameters and compute net premiums for different mixing distributions as well as test the prediction probabilities.

* Vortrag am Dresdner Forum zur Versicherungsmathematik: Tarifierung in Erst- und Rückversicherung am 25. Juni 2004. Für die Unterstützung zu dieser Arbeit m?chte der Autor Lothar Partzsch, Klaus D. Schmidt (beide Dresden) und Friedemann Spies (München) recht herzlich danken.     

再议“革命军起、革命党消”

文章在订正相关史实 ,厘清原初意义的基础上 ,试图着重说明“革命军起、革命党消”这一口号之所以在辛亥民初产生重大影响 ,与当时普遍流行的“革命党非政党”的观念及民初政党政治的实践有紧密关联 ,而这一口号的长期为人诟病 ,则与孙中山重组、改组国民党时对辛亥革命的总结及后人有关民国初年政党政治的整体记忆有关     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

Generalized partially linear varying-coefficient models

Generalized varying-coefficient models are useful extensions of generalized linear models. They arise naturally when investigating how regression coefficients change over different groups characterized by certain covariates such as age. In this paper, we extend these models to generalized partially linear varying-coefficient models, in which some coefficients are constants and the others are functions of certain covariates. Procedures for estimating the linear and non-parametric parts are developed and their associated statistical properties are studied. The methods proposed are illustrated using some simulations and real data analysis.     

短杆菌(Brevibacterium sp WX-10)产酶条件研究

研究了碳源、氮源、无机盐、金属离子等培养基组成和初始pH、通风量、温度等发酵条件对短杆菌(Bre vibacteriumspWX 10)产酶的影响,通过正校试验优化得到的产酶培养基组成及发酵条件:蔗糖1%,NaCl2 5%,牛肉膏0 05%,NaNO30 05%,pH7 5,500mL三角瓶装培养基50mL,30℃于220r/min旋转式摇床上培养72h.在该培养条件下WX 10产酶量是原培养条件下的1 85倍.     

A graphical summary of disparities in health care and related summary measures

In order to assess the effectiveness of government programs designed to reduce disparities in the health care minority groups receive relative to the majority white population, a proper statistical measure should be used. This article proposes a measure of and its accompanying graph, which is readily interpretable and is not affected by the number of minority subgroups examined.     

Estimating the distribution function using k-tuple ranked set samples

The basic assumption underlying the concept of ranked set sampling is that actual measurement of units is expensive, whereas ranking is cheap. This may not be true in reality in certain cases where ranking may be moderately expensive. In such situations, based on total cost considerations, k-tuple ranked set sampling is known to be a viable alternative, where one selects k units (instead of one) from each ranked set. In this article, we consider estimation of the distribution function based on k-tuple ranked set samples when the cost of selecting and ranking units is not ignorable. We investigate estimation both in the balanced and unbalanced data case. Properties of the estimation procedure in the presence of ranking error are also investigated. Results of simulation studies as well as an application to a real data set are presented to illustrate some of the theoretical findings.     

Nonparametric estimation of the conditional distribution function in a semiparametric censorship model

In this paper we propose a new nonparametric estimator of the conditional distribution function under a semiparametric censorship model. We establish an asymptotic representation of the estimator as a sum of iid random variables, balanced by some kernel weights. This representation is used for obtaining large sample results such as the rate of uniform convergence of the estimator, or its limit distributional law. We prove that the new estimator outperforms the conditional Kaplan–Meier estimator for censored data, in the sense that it exhibits lower asymptotic variance. Illustration through real data analysis is provided.     

Two point priors and Γ-minimax estimating in families of uniform distributions

It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.