极差、平均差和标准差之间测度关系研究

极差（R）、平均差（AD）和标准差（δ）是描述离散程度所采用的三个测度值,通过证明,三者之间存在着R≥δ≥AD≥0的关系式。通过例证还得知,四分位差（Qd）与它们的关系并不确定。在具体运用三个测度值时,应考虑到各自的优缺点。     

Accurate probabilities for the sign test

Limitations in currently available methods for producing significance probabilities for the sign test are discussed. Two simple modifications to the continuity corrected normal approximation are derived and presented in a simple form. These modifications are shown to markedly reduce the relative error in approximating exact probabilities. The relative simplicity of these modifications and the importance of accurate p values suggest that one or both modifications could be useful improvements.     

General saddlepoint approximations to distributions under an elliptical population

General saddlepoint approximations are derived for the distributions of statistics under an elliptical population. The technique is applied to obtain the tail probabilities of latent roots of a sample covariance matrix. It is shown that the method based on normalizing transformations by Tsuchiya and Konishi (1997) is efficient for the sample correlation coefficient in an elliptical sample.     

STATISTICS: REFLECTIONS ON THE PAST AND VISIONS FOR THE FUTURE

Statistics as data is ancient, but as a discipline of study and research it has a short history. Courses leading to degrees in statistics have been introduced in universities some sixty to seventy years ago. They were not considered to constitute a basic discipline with a subject matter of its own. However, during the last seventy five years, it has developed as a powerful blend of science, technology and art for solving problems in all areas of human endeavor. Now-a-days statistics is used in scientific research, economic development through optimum use of resources, increasing industrial productivity, medical diagnosis, legal practice, disputed authorship, and optimum decision making at individual and institutional levels. What is the future of statistics in the coming millennium dominated by information technology encompassing the whole of communications, interaction with intelligent systems, massive data bases, and complex information processing networks? The current statistical methodology based on probabilistic models applied on small data sets appears to be inadequate to meet the needs of the society in terms of quick processing of data and making the information available for practical purposes. Adhoc methods are being put forward under the title Data Mining by computer scientists and engineers to meet the needs of customers. The paper reviews the current state of the art in statistics and discusses possible future developments considering the availability of large data sets, enormous computing power and efficient optimization techniques using genetic algorithms and neural networks.

     

SEPARATE VERSUS SYSTEM METHODS OF STEIN-RULE ESTIMATION IN SEEMINGLY UNRELATED REGRESSION MODELS

ABSTRACT

Despite the sizeable literature associated with the seemingly unrelated regression models, not much is known about the use of Stein-rule estimators in these models. This gap is remedied in this paper, in which two families of Stein-rule estimators in seemingly unrelated regression equations are presented and their large sample asymptotic properties explored and evaluated. One family of estimators uses a shrinkage factor obtained solely from the equation under study while the other has a shrinkage factor based on all the equations of the model. Using a quadratic loss measure and Monte-Carlo sampling experiments, the finite sample risk performance of these estimators is also evaluated and compared with the traditional feasible generalized least squares estimator.     

Median regression model with left truncated and interval-censored data

We consider the problem of fitting a heteroscedastic median regression model from left-truncated and interval-censored data. It is demonstrated that the adapted Efron’s self-consistency equation of McKeague, Subramanian, and Sun (2001) can be extended to analyze left-truncated and interval-censored data. The asymptotic property of the proposed estimator is established. We evaluate the finite sample performance of the proposed estimators through simulation studies.     

Turing’s anticipation of empirical bayes in connection with the cryptanalysis of the naval enigma *

The Enigma was a cryptographic (enciphering) machine used by the German military during WWII. The German navy changed part of the Enigma keys every other day. One of the important cryptanalytic attacks against the naval usage was called Banburismus, a sequentiai Bayesian procedure (anticipating sequential analysis) which was used from the sorine of 1941 until the middle of 1943. It was invented mainlv bv A. M. Turina and was perhaps the first important sequential Bayesian IE is unnecessab to describe it here. Before Banburismus could be started on a given day it was necessary to identifv which of nine ‘biaram’ (or ‘diaraph’) tables was in use on that day. In Turing’s approach to this identification hk had io istimate the probabilities of certain ‘trigraphs’. rrhese trigraphs were used. as described below. for determinine the initial wheel settings of messages). For estimatidg the probabilities, Turing inventedin important special case o the nonparametric (nonhypermetric) Empirid Bayes method independently of Herbert Robbins. The techniaue is the sumxisine form of Emdrical Baves in which a physical prior is assumed to eist but no apbroxiGate functional fonn is assumed for it.     

C471. Does the law of large numbers really say that?

A simulation study is made on several strategies used in the game of roulette. The Law of Large numbers is vindicated but several interesting results occur in spite of the Law.     

Random sequential packing in Rn

We introduce a Monte Carlo method for packing hypercubes in Rⁿ . Rigorous and conceptually simple, it is currently practical for n≥4. Experimental results indicate that Palasti's conjecture is false for R ² and K³ and still undecided for K⁴     

Numerical techniques for estimating probabilities

In this article we consider the pioblem of finding the maximum likelihood estimate for a certain class of discrete sampling models. Methods are adapted from parts of convex optimization theory, includiug aspects of equivalence theory, duality theorv and iterative procedures Their application is illustrated through example.