多个互斥投资方案优选的灰靶决策模型

关于项目投资决策中的多个互斥投资方案优选的问题,文章借鉴灰色系统理论,简述了灰靶决策的基本思路,提出多指标的优选决策方法,建立多个互斥投资方案优选的灰靶决策模型,提高了优选的精确性和客观性,并给出了算例说明其应用。     

Best-Ball Events in Golf: An Application of the Multinomial Distribution

Probability models are developed for two-man teams in best-ball events in golf. The multinomial distribution is used to develop the theoretical probabilities for possible team scores. Here each individual player is assigned a set of probabilities for making a certain score on each hole of an 18-hole round of golf. The two-man team results are compared with the 1980-1982 Bing Crosby Pro-Ams held in Monterey, California.     

On Proving That and S 2 are Independent

The need to establish the independence of the sample mean and the sample variance in sampling from a normal population arises early in a course in statistics. For the result is an essential ingredient in the derivation of the Student-t distribution for statistical inference. Often this need arises before the tools, notably multivariate methods, for a rigorous proof are available. Occasionally one will find attempts to derive this result using only bivariate assumptions. A recent article in this journal, as well as some current textbooks, offer such a proof. In all cases there are serious questions about the validity of the proofs.     

A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.     

Semiparametric Estimation of a Change-point for Recurrent Events Data

One particular recurrent events data scenario involves patients experiencing events according to a common intensity rate, and then a treatment may be applied. The treatment might be effective for a limited amount of time, so that the intensity rate would be expected to change abruptly when the effect of the treatment wears out. In particular, we allow models for the intensity rate, post-treatment, to be at first decreasing and then change to increasing (and vice versa). Two estimators of the location of this change are proposed.     

Additive Transformation Models for Recurrent Events

In this article, we propose a class of additive transformation models for recurrent event data, which includes the additive rates model as a special case. The new models offer great flexibility in formulating the effects of covariates on the mean function of recurrent events. Estimating equation approaches are developed for the model parameters, and asymptotic properties of the resulting estimators are established. In addition, a model checking procedure is presented to assess the adequacy of the model. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a bladder cancer study is presented.     

A Note on Stagewise Regression

Suppose one estimates the coefficient β₂ in E[Y] = β₀ + β₁ X ₁ + β₂ X ₂ by stagewise regression. That is, first the model E[Y] ≌ β₀ + β₁ X ₁ is fit using simple linear regression followed by a simple linear regression of the residuals from this model on X ₂ to yield the estimator β₂. The ratio of the squared t statistic for the estimate b ₂ from multiple regression to the squared t statistic for β₂ is greater than or equal to 1.0 and is shown to be a convenient function of correlation coefficients among Y, X ₁, and X ₂. Examination of stagewise regression can provide useful insights when introducing concepts of multiple regression.     

A Note on Model-Based Stratification

A slight improvement on the stratification methodology in Godfrey et al. (1984) is proposed and an example is advanced to demonstrate its usefulness.     

A Note on Whittle's Likelihood

The approximate likelihood function introduced by Whittle has been used to estimate the spectral density and certain parameters of a variety of time series models. In this note we attempt to empirically quantify the loss of efficiency of Whittle's method in nonstandard settings. A recently developed representation of some first-order non-Gaussian stationary autoregressive process allows a direct comparison of the true likelihood function with that of Whittle. The conclusion is that Whittle's likelihood can produce unreliable estimates in the non-Gaussian case, even for moderate sample sizes. Moreover, for small samples, and if the autocorrelation of the process is high, Whittle's approximation is not efficient even in the Gaussian case. While these facts are known to some extent, the present study sheds more light on the degree of efficiency loss incurred by using Whittle's likelihood, in both Gaussian and non-Gaussian cases.     

A Note on Change-Over Designs

A change-over model with correlated errors is discussed. In particular the results of Patterson (1950) and Lucas (1951) for balanced change-over designs are extended to more than four treatments and more general variance matrices. A connection with recent work on neighbour models for field trials is made.     

A Useful Property of Some Symmetric Statistics

The distributions of some statistics arising from the comparison of two populations share a common structure. Consequences of this structure are derived and their usefulness indicated. The examples of statistics to which the theory applies include various correlation coefficients.     

A Note on Collinearity Diagnostics and Centering

The usual approach for diagnosing collinearity proceeds by centering and standardizing the regressors. The sample correlation matrix of the predictors is then the basic tool for describing approximate linear combinations that may distort the conclusions of a standard least-square analysis. However, as indicated by several authors, centering may eventually fail to detect the sources of ill-conditioning. In spite of this earlier claim, there does not seem to be in the literature a fully clear explanation of the reasons for this bad potential behavior of the traditional strategy for analyzing collinearity. This note studies this issue in some detail. Results derived are motivated by the analysis of a well-known real dataset. Practical conclusions are illustrated with several examples.     

Dynamic Random Effects Models for Times Between Repeated Events

We consider recurrent event data when the duration or gap times between successive event occurrences are of intrinsic interest. Subject heterogeneity not attributed to observed covariates is usually handled by random effects which result in an exchangeable correlation structure for the gap times of a subject. Recently, efforts have been put into relaxing this restriction to allow non-exchangeable correlation. Here we consider dynamic models where random effects can vary stochastically over the gap times. We extend the traditional Gaussian variance components models and evaluate a previously proposed proportional hazards model through a simulation study and some examples. Besides, semiparametric estimation of the proportional hazards models is considered. Both models are easily used. The Gaussian models are easily interpreted in terms of the variance structure. On the other hand, the proportional hazards models would be more appropriate in the context of survival analysis, particularly in the interpretation of the regression parameters. They can be sensitive to the choice of model for random effects but not to the choice of the baseline hazard function.     

Regression Modeling with Recurrent Events and Time-Dependent Interval-Censored Marker Data

In life history studies involving patients with chronic diseases it is often of interest to study the relationship between a marker process and a more clinically relevant response process. This interest may arise from a desire to gain a better understanding of the underlying pathophysiology, a need to evaluate the utility of the marker as a potential surrogate outcome, or a plan to conduct inferences based on joint models. We consider data from a trial of breast cancer patients with bone metastases. In this setting, the marker process is a point process which records the onset times and cumulative number of bone lesions which reflects the extent of metastatic bone involvement. The response is also a point process, which records the times patients experience skeletal complications resulting from these bone lesions. Interest lies in assessing how the development of new bone lesions affects the incidence of skeletal complications. By considering the marker as an internal time-dependent covariate in the point process model for skeletal complications we develop and apply methods which allow one to express the association via regression. A complicating feature of this study is that new bone lesions are only detected upon periodic radiographic examination, which makes the marker processes subject to interval-censoring. A modified EM algorithm is used to deal with this incomplete data problem.     

含有协变量的复发事件变点模型的参数估计

针对复发事件数据协变量的重要作用,建立含有协变量的复发事件变点模型,考虑协变量作用于强度率函数的情形。对于此模型,使用最大似然方法得到变点及各参数估计,并得到了变点估计的相合性。最后对于同时存在待估参数和待估变点的似然函数,采用最速上升法进行了数据模拟。     

A History of the Development of Craig's Theorem

Craig's theorem on the independence of quadratic forms in normal variates is traced from its first form, for iid standard normal variates, to the form for variates following an arbitrary nonsingular joint normal distribution. This article gives the main thrust of the development and makes recommendations on coverage of the theorem in courses and textbooks. The history of Craig's theorem is not a happy one. The authors of the earlier articles in the literature tended to make errors of a linear-algebraic nature. Authors of more recently published textbooks have given incorrect or misleadingly incomplete coverage of Craig's theorem and its proof.     

A Note on the Kuks-Olman Estimator

In the linear regression model the unknown parameter vector θ is supposed to vary in a known ellipsoid. Under this parameter constraint Kuks and Olman derived an estimator by demanding a minimax property. Since sometimes the Kuks-Olman estimator takes values outside of the ellipsoid a modification is proposed in the paper. It is shown that this modified variant is a least squares estimator in the restricted model.     

A Note on Dirichlet One-Armed Bandits

One of the two independent stochastic processes (or ‘arms’) is selected and observed sequentially at each of n(≤ ∝) stages. Arm 1 yields observations identically distributed with unknown probability measure P with a Dirichlet process prior whereas observations from arm 2 have known probability measure Q. Future observations are discounted and at stage m, the payoff is a _m(≥0) times the observation Z _m at that stage. The objective is to maximize the total expected payoff. Clayton and Berry (1985) consider this problem when a _m equals 1 for m ≤ n and 0 for m > n(< ∝) In this paper, the Clayton and Berry (1985) results are extended to the case of regular discount sequences of horizon n, which may also be infinite. The results are illustrated with numerical examples. In case of geometric discounting, the results apply to a bandit with many independent unknown Dirichlet arms.