A note on the geometry of kullback-leibler information numbers

Csiszar (1975) has shown thdt kullhack-Leibler information numbers possess some geometrical properties much like those in Euclidean geometry. Thls paper extends these results by characterizing the shortest line between two ditributions as well as the midpoit of the line.     

离散型模糊概率在方案选择中的应用

针对决策者在进行方案选择时各种自然状态发生概率的不确定性,提出并讨论了离散型模糊状态概率下的方案选择问题。将方案各状态发生概率的三项估计值表示为三角模糊数,从而获得离散型模糊概率分布,利用限制模糊算法确定离散型模糊概率分布的数字特征值,在确定决策者决策准则的前提下,利用方案评价指标的数字特征值选择方案,同时分析了该法处理的优点。     

Lystematic sampling of two-dimensional surfaces and related problems

The paper is largely concerned with twenty-one possible methods of sampling a plane area, with points as sampling units, for the purpose of estimating a portion of this area having certain defined characteristics. These methods result from a combination, two at a time, of random, stratified and systematic sampling in two perpendicular directions, with or without alignment of the sampled points. Eleven of these methods involve systematic sampling in one or both directions. The estimate of the proportion of the area of interest is simply the proportion of points in the total area, falling within the area having the defined characteristics. For each method the variance function is derived. Fourteen different types of space covariance functions are involved in these variance functions.     

Ignorance Is Not Probability

The distinction between ignorance about a parameter and knowing only a probability distribution for that parameter is of fundamental importance in risk assessment. Brief dialogs between a hypothetical decisionmaker and a risk assessor illustrate this point, showing that the distinction has real consequences. These dialogs are followed by a short exposition that places risk analysis in a decision‐theoretic framework, describes the important elements of that framework, and uses these to shed light on Terje Aven's criticism of nonprobabilistic purely “objective” methods. Suggestions are offered concerning a more effective approach to evaluating those methods.     

我国核心通货膨胀的实证比较研究

 本文对比研究了5种度量方法下的核心通货膨胀序列，发现不对称截尾法、中位数法得出的序列受食品类权重过大的影响，不适合作为我国的核心通货膨胀指标；对不对称截尾法、剔除法、共同趋势法和结构向量自回归法产生的序列的进一步研究中，发现它们都与CPI序列一样是一阶平稳的，虽然它们与CPI的相关系数很大，除了30%比率截尾平均法外，与CPI不存在协整关系；因果检验表明，除共同趋势法的序列是CPI的原因外，其余序列的因果关系不是很明确，但是都能在一定程度上预测CPI。     

Some Statistical Methods in Assessing Linear Relational Agreement: An Empirical Comparative Study

Although multiple indices were introduced in the area of agreement measurements, the only documented index for linear relational agreement, which is for interval scale data, is the Pearson product-moment correlation coefficient. Despite its meaningfulness, the Pearson product-moment correlation coefficient does not convey the practical information such as what proportion of observations is within a certain boundary of the target value. To address this need, based on the inverse regression, we proposed the adjusted mean squared deviation (AMSD), adjusted coverage probability (ACP), and adjusted total deviation index (ATDI) for the measurement of the relational agreement. They can serve as reasonable and practically meaningful measurements for relational agreement. Real life data are considered to illustrate the performance of the methods.     

Non Parametric Regression Quantile Estimation for Dependent Functional Data under Random Censorship: Asymptotic Normality

In this paper we study a smooth estimator of the regression quantile function in the censorship model when the covariates take values in some abstract function space. The main goal of this paper is to establish the asymptotic normality of the kernel estimator of the regression quantile, under α-mixing condition and, on the concentration properties on small balls probability measure of the functional regressors. Some applications and particular cases are studied. This study can be applied in time series analysis to the prediction and building confidence bands. Some simulations are drawn to lend further support to our theoretical results and to compare the quality of behavior of the estimator for finite samples with different rates of censoring and sizes.     

A flexible procedure for formulating probability distributions on the unit interval with applications

Abstract

In this paper, we present a flexible mechanism for constructing probability distributions on a bounded intervals which is based on the composition of the baseline cumulative probability function and the quantile transformation from another cumulative probability distribution. In particular, we are interested in the (0, 1) intervals. The composite quantile family of probability distributions contains many models that have been proposed in the recent literature and new probability distributions are introduced on the unit interval. The proposed methodology is illustrated with two examples to analyze a poverty dataset in Peru from the Bayesian paradigm and Likelihood points of view.     

A generalized score confidence interval for a binomial proportion

Constructing a confidence interval for a binomial proportion is one of the most basic problems in statistics. The score interval as well as the Wilson interval with some modified forms have been broadly investigated and suggested by many statisticians. In this paper, a generalized score interval CI_G(a) is proposed by replacing the coefficient 1/4 in the score interval with parameter a. Based on analyzing and comparing various confidence intervals, we recommend the generalized score interval CI_G(0.3) for the nominal confidence levels 0.90, 0.95 and 0.99, which improves the spike phenomenon of the score interval and behaves better and computes more easily than most of other approximate intervals such as the Agresti-Coull interval and the Jeffreys interval to estimate a binomial proportion.     

Comparing waiting times in a multi-stage model: A log-rank approach

A proper log-rank test for comparing two waiting (i.e. sojourn, gap) times under right censored data has been absent in the survival literature. The classical log-rank test provides a biased comparison even under independent right censoring since the censoring induced on the time since state entry depends on the entry time unless the hazards are semi-Markov. We develop test statistics for comparing K waiting time distributions from a multi-stage model in which censoring and waiting times may be dependent upon the transition history in the multi-stage model. To account for such dependent censoring, the proposed test statistics utilize an inverse probability of censoring weighted (IPCW) approach previously employed to define estimators for the cumulative hazard and survival function for waiting times in multi-stage models. We develop the test statistics as analogues to K-sample log-rank statistics for failure time data, and weak convergence to a Gaussian limit is demonstrated. A simulation study demonstrates the appropriateness of the test statistics in designs that violate typical independence assumptions for multi-stage models, under which naive test statistics for failure time data perform poorly, and illustrates the superiority of the test under proportional hazards alternatives to a Mann–Whitney type test. We apply the test statistics to an existing data set of burn patients.