摘要:

A useful lemma for proving the equality of two matrices is given. The result is then applied to proving the equality of certain quadratic forms arising in least squares models.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501029

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The concepts of the “median significance level” (MSL) and the “significance level of the average” (SLA) are introduced and some relationships among these measures and the recently introduced “expected significance level” (ESL), “average critical value” (ACV), and “median critical value” (MCV) are considered. The median significance level is defined as the median of the distribution of the observed significance level for a given alternative and is shown to be equivalent to the significance level attained by the median of the test statistic for one-sided tests. The “significance level of the average” is analogously defined to be the significance level attained by the average (expectation) of the test statistic and the MSL and SLA are shown to be inverse functions of Geary's MCV and ACV. Some relations between these small sample measures of test efficacy, and Pitmans' and Bahadur's asymptotic measures are described. The MCV is shown to be formally related to Hamaker's “indifference quality” method of classifying acceptance sampling plans. Several simple examples are given illustrating some relationships among the several criteria.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501030

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Consider the problem of testing the hypothesisH0: θ ∈W0against the alternativeH1: θ ∈W1when a certain subsetE0⊂W1is given. This subsetE0is such that the risk of acceptingH0will be significant economically only if θ ∈E0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations with a standard are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501031

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

LetX1, …,XmandY1, …,Ynbe independent random samples from populations having continuous d.f.'s Ψ((x-μ)/σ) and Ψ ((y-v)/τ) respectively. The classicalF-test of a hypothesis concerning λ = τ/σ is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e. and Monte Carlo studies of power functions. An approximate permutation test [13] and a “jackknife” procedure [9] are found to be most satisfactory; while a class of “rank-like” tests [10] are found to be “useful inefficient statistics”

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501032

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Estimation of variance components when the design is a balanced incomplete block, the model is additive, and error, block and treatment components are normal, independent, with zero expectations, is considered using variance as a criterion.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501033

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

In simple linear regression the 100pth percentile of the distribution ofYfor a given value ofXis β0+ β1X+Zpσ, whereZpis the 100pth percentile of the standard normal distribution. The problem considered is to estimate the value ofXfor which this percentile is equal to some specified value,Yp. Both point and interval estimates are considered. A procedure for obtaining exact confidence intervals is derived, and in addition, two approximate and two conservative procedures for obtaining intervals are presented and compared. An example is given to illustrate these procedures and an application to covariance analysis is given.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501034

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The problem considered in this paper is how to combine estimators of the common mean from two samples corresponding to normal populations with different unknown variances. Attention is confined to the case where it is known that the variance of one specific population exceeds that of the other. Three classes of unbiased estimators are presented, one of which is based on a preliminary test of significance regarding the ratio of the population variances. The gain achieved by utilizing the knowledge that the ratio of variances exceeds one is investigated by comparing the efficiencies of these estimators with an estimator presented by Graybill and Deal [1] in which no restriction on the ratio of variances is present.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501035

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical lower bounds on the variance of unbiased estimators, such as the Cramér-Rao bound, lead to the trivial resultV(t) ≧0, wheretis any unbiased estimator. A number of alternative bounds for application in the non-regular case have been derived. In this paper previous results of this type are reviewed and an additional bound is given. The specific applications of interest involve estimation of a location parameter. Applications of the bounds to the exponential, uniform and Pearson Type III distributions are investigated.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501036

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The personalistic theory of probability prescribes that personal probability assessments to be used in decision-making situations should correspond with the assessor's judgments. A payoff function which depends on the assessor's stated probabilities and on the event which actually occurs may be used (1) to keep the assessor honest or (2) to evaluate the assessor. It is shown that with the exception of a logarithmic payoff function, these two uses of payoff functions for assessors are not compatible. This conflict is explained in terms of the differences in the situations facing the assessor and the evaluator (the user of the probabilistic predictions).

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501037

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

In many situations approximation of a set of data by a polygonal curve is more advantageous than approximation by a polynomial. If the join points of the polygonal curve are known, the problem is quite simple. If, however, they are to be chosen in some expeditious fashion, considerable numerical difficulties can arise if the curve-fitting problem is approached directly. In this paper it is shown that dynamic programming offers a simple direct approach to the determination of an optimal fit.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501038

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor