A testing approach to estimation

Results from the theory of uniformly most powerful invariant tests are used to develop a new parameter estimation procedure. The procedure is used to derive parameter estimators for several important distributions. Results of simulation studies comparing the performances of the new estimators and maximum likelihood estimators are presented.     

For what use are tests of hypotheses and tests of significance

Tests of sharp null hypotheses, although frequently computed, are.rarely appropriate as the major end product of statistical analyses, except possibly in some, areas of the natural sciences. But procedures closely akin to tests, although often less formal, are needed in almost every investigation in which exploratory data analysis is used to help to decide upon the statistical model appropriate for the final analysis. The term “diagnostic check”has been suggested by Box and Jenkins for these procedures. Traditional statistical tests often suggest useful diagnostic checks -and this, in my view, is what tests are mainly good for-but visual examination and interpretation of data plots are often equally important. Biere is also much to be gained by the development of new diagnostic checks, and testing theory may be useful as one guide to this development.     

A minimum variance adaptive technique for parameter estimation and hypothesis testing

This report presents numerical results of an approach for parameter estimation and hypothesis testing that does not rely on specific assumptions about the underlying distribution of errors in the measured data. This approach combines robust estimation procedures, the bootstrap method for estimation of parameter uncertainties, permutation techniques for hypothesis testing, and adaptive approaches to estimation in order to obtain the minimum variance estimator or test statistic (within a predefined class) for the data under consideration. The technique produces efficient estimators of central tendency and powerful test statistics, even for small sample sizes. (Portions of this work have been presented in preliminary form (Turkheimer et al., 1996)).     

On lachin'S formulae for sample sizes of survival tests

Lachin [1981] and Lachin and Foulkes [1986] consider two groups of identically independently exponentially distributed random variables and four models of data sampling. The test problem they treat is to decide whether the two distributions are identical (null-hypothesis H⁰) or not (alternative hypothesis H¹). Basing the test on maximum-likelihood estimators and their asymptotic normal densities they obtain formulae for the group sizes necessary to yield asymptotic tests with guaranteed power under a prescribed level for specified hypotheses. It is intuitively reasonable to expect the sizes decrease the more the hypotheses differ. It the distance betwen H⁰ and H¹ is measured by the difference of the exponential parameters this assumption time or the deviation of the exponential parameter ratio from unity is the measure larger distances between the hypotheses do not necessarily lead to smaller sample sizes.     

Nonparametric repeated significance tests for some analysis of covariance models

For a general class of nonparametric analysis of covariance problems (with stochastic covariates), some repeated significance testing procedures are developed. These procedures rest on the construction of suitable rank order statistics based on the partial sequence of sample sizes and allow for a monitoring of experimentation with the objective of a possible early termination of experimentation. The basic theory is based on the weak convergence of certain stochastic processes relating to the rank order statistics. Various properties of the proposed tests are discussed.     

Some inference results on pr(x < y) in the bivariate exponential model

This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.     

Numerical integration of the divisia price index and an application of the equation of measurement to prices

First the linear and the exponential paths are chosen as examples to show how the Divisia price and quantity index can be integrated numerically. Then the equation of measurement by Eichhorn and Gleissner is adapted to price measurement and used to formulate certain properties of indices. A special class of properties, the reversal tests describing certain symmetries, is considered especially, It turns out that the corresponding antitheses form a group of eight elements.     

对非英语专业学生口语词汇量的调查分析

本文通过对我校部分98级本科生进行的两次大学英语口语测试,对学生口头表达中所使用的英语词汇进行了统计.词汇统计的结果表明,在两次口语测试中,学生在口头表达中主要以英语常用词为主,占所使用词汇的80%以上.同时也表明随着学生的词汇量的不断增加,在自由表达时使用常用词以外词汇的数量也有所增加,但数量很少.因此,在教学中值得研究的问题就是在学生词汇量不断提高的同时,怎样丰富学生口头表达的词汇.本文对这一问题的看法是,一方面,加强学生学习方法的指导,提高学生学习的自主性;另一方面,在教学中加强语言基础知识的教学的同时,突出语言的实践性,使语言知识逐步运用到语言使用中来.     

Rank statistics expressible as integrals under P–P-plots and receiver operating characteristic curves

Given a probability measure on the unit square, the measure of the region under an empirical P – P -plot defines a two-sample rank statistic. Instances include trimmed and censored versions of the Mann–Whitney–Wilcoxon statistic and a class of statistics with applications in the analysis of receiver operating characteristic (ROC) curves. A large sample distribution for such a statistic is obtained, which is valid under sampling from general populations. Explicit results are presented for comparing arbitrary quantile segments of two populations. The results are not restricted to continuous data and incorporate adjustments for tied values in the discrete case. A multivariate version of the large sample distribution extends the class of tractable statistics in ROC analysis and facilitates the use of methods based on partial areas when the data are discrete.     

Testing for serial correlation in the presence of dynamic heteroscedasticity

Standard serial correlation tests are derived assuming that the disturbances are homoscedastic, but this study shows that asympotic critical values are not accurate when this assumption is violated. Asymptotic critical values for the ARCH(2)-corrected LM, BP and BL tests are valid only when the underlying ARCH process is strictly stationary, whereas Wooldridge's robust LM test has good properties overall. These tests exhibit similar bahaviour even when the underlying process is GARCH (1,1). When the regressors include lagged dependent variables, the rejection frequencies under both the null and alternative hypotheses depend on the coefficientsof the lagged dependent variables and the other model parameters. They appear to be robust across various disturbance distributions under the null hypothesis.