矩阵双加权广义逆的Zlobec型公式

本文提出了双加权广义逆的概念，将常用的四种加权广义逆统一为一种形式，并依据加权广义逆矩阵的Zlobec型公式得到了双加权广义逆矩阵的Zlobec型公式．     

EFFICIENT ESTIMATION IN REGRESSION FRAILTY OR TRANSFORMATION MODELS BASED ON AN ALGORITHM

This paper considers a regression frailty or transformation model in which the structural parameter is the vector of regression coefficients and the nuisance parameter is a vector of arbitrarily high dimension. It proposes jointly (implicitly) defined parameter estimators which have been proved to be consistent and asymptotically efficient, and develops an algorithmic procedure that provides these estimators. The behaviour of the algorithm is illustrated by analysing simulated and real data.     

浅谈数学在现代商业中的应用

本文建立反平方数学模型描述顾客对特定商场的选择度与商场对顾客的吸引度，通过对两个商场的影响区域分析，刻划两个商场竞争平衡状态与竞争进行状态，从而探析商场盈亏原因和竞争策略。     

Models for surveillance data under reporting delay: applications to US veteran first-time suicide attempters

Surveillance data provide a vital source of information for assessing the spread of a health problem or disease of interest and for planning for future health-care needs. However, the use of surveillance data requires proper adjustments of the reported caseload due to underreporting caused by reporting delays within a limited observation period. Although methods are available to address this classic statistical problem, they are largely focused on inference for the reporting delay distribution, with inference about caseload of disease incidence based on estimates for the delay distribution. This approach limits the complexity of models for disease incidence to provide reliable estimates and projections of incidence. Also, many of the available methods lack robustness since they require parametric distribution assumptions. We propose a new approach to overcome such limitations by allowing for separate models for the incidence and the reporting delay in a distribution-free fashion, but with joint inference for both modeling components, based on functional response models. In addition, we discuss inference about projections of future disease incidence to help identify significant shifts in temporal trends modeled based on the observed data. This latter issue on detecting ‘change points’ is not sufficiently addressed in the literature, despite the fact that such warning signs of potential outbreak are critically important for prevention purposes. We illustrate the approach with both simulated and real data, with the latter involving data for suicide attempts from the Veteran Healthcare Administration.     

Non-informative priors for the inverse Weibull distribution

In this paper, we develop the non-informative priors for the inverse Weibull model when the parameters of interest are the scale and the shape parameters. We develop the first-order and the second-order matching priors for both parameters. For the scale parameter, we reveal that the second-order matching prior is not a highest posterior density (HPD) matching prior, does not match the alternative coverage probabilities up to the second order and is not a cumulative distribution function (CDF) matching prior. Also for the shape parameter, we reveal that the second-order matching prior is an HPD matching prior and a CDF matching prior and also matches the alternative coverage probabilities up to the second order. For both parameters, we reveal that the one-at-a-time reference prior is the second-order matching prior, but Jeffreys’ prior is not the first-order and the second-order matching prior. A simulation study is performed to compare the target coverage probabilities and a real example is given.     

Some matrix results related to a partitioned singular linear model

Consider the linear model (y, Xβ V), where the model matrix X may not have a full column rank and V might be singular. In this paper we introduce a formula for the difference between the BLUES of Xβ under the full model and the model where one observation has been deleted. We also consider the partitioned linear regression model where the model matrix is (X₁: X₂) the corresponding vector of unknown parameters being (β′₁ : β′₂)′. We show that the BLUE of X₁ β₁ under a specific reduced model equals the corresponding BLUE under the original full model and consider some interesting consequences of this result.     

Prediction from a normal model using a generalized inverse Gaussian prior

In this paper, we derive prediction distribution of future response(s) from the normal distribution assuming a generalized inverse Gaussian (GIG) prior density for the variance. The GIG includes as special cases the inverse Gaussian, the inverted chi-squared and gamma distributions. The results lead to Bessel-type prediction distributions which is in contrast with the Student-t distributions usually obtained using the inverted chi-squared prior density for the variance. Further, the general structure of GIG provides us with new flexible prediction distributions which include as special cases most of the earlier results obtained under normal-inverted chi-squared or vague priors.     

逆系统方法在人口预测中的应用

本文尝试运用逆系统方法设计一个人口预测系统的逆系统。系统仿真结果表明该方法在人口与社会经济系统的研究中,是一种有着广阔应用前景的分析技术;仿真结果还揭示了我国未来人口总和生育率的可行性区间。     

Frailty Models for Arbitrarily Censored and Truncated Data

In this paper, we propose a frailty model for statistical inference in the case where we are faced with arbitrarily censored and truncated data. Our results extend those of Alioum and Commenges (1996), who developed a method of fitting a proportional hazards model to data of this kind. We discuss the identifiability of the regression coefficients involved in the model which are the parameters of interest, as well as the identifiability of the baseline cumulative hazard function of the model which plays the role of the infinite dimensional nuisance parameter. We illustrate our method with the use of simulated data as well as with a set of real data on transfusion-related AIDS.     

The Efficacy of Different Methods for Informing the Public About the Range Dependency of Magnetic Fields from High Voltage Power Lines

The AC electric and magnetic fields associated with high voltage power lines have become a concern as a possible health risk. In most cases the strength of these fields decreases as the inverse square of the distance from the line. In earlier work, we found that laypeople do not understand how rapidly field strength decreases with distance. Most believe that any high voltage power line they can see is exposing them to strong fields. This paper confirms the earlier finding and explores a number of strategies which might be used in risk communications to correct this misperception. We found it relatively easy to provide subjects with a better understanding of the range-dependency of magnetic field strength. Moreover, the quality of this acquisition was apparently independent of the manner in which they were instructed. Such successful instruction is markedly different from the well-established difficulty of teaching people about many qualitative domains, such as physics or ideas in probability. Clearly, while some erroneous beliefs are highly resistant to change, others can be altered quite readily. We suspect that an important distinction between knowledge about the range-dependency of power-frequency magnetic fields and less tractable topics involves the presence or absence of prior folk-theories or "mental models" of the domain.