摘要:

If two simultaneous equations economic models, each purporting to explain the same endogenous variable in terms of the same exogenous variable differ only in this respect, that one is in the form of an ‘interdependent’ representation and the other is an ‘explicit causal chain,’ then the question whether one is a more accurate representation of economic reality than the other cannot even in principle be settled by appeal to observations. The failure of proponents of ‘explicit causal chains’ to appreciate the significance of the foregoing theorem has led to the proposal of a remarkable interpretation of unfavorable outcomes of statistical tests of econometric hypotheses (which is mentioned in Section 3.2).

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480852

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

The tendency for particular retail establishments to cluster has been noted by several theorists on the subject of intraurban retail spatial structure. Hotelling, for example, in his classical essay on spatial competition, concludes that as “more and more sellers of the same commodity arise, the tendency is not to become distributed in the socially optimum manner but to cluster unduly.”1Rolph and Proudfoot provide empirical evidence of this tendency,2and Nelson supplies a rationale for it by his “principle of cumulative attraction.”3

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480853

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical inference and prediction—e.g., one observation from a two-parameter normal model is not (in our special sense) sufficient to permit inference about the variance but two observations are. In essence, the procedure stipulates that prior indifference distributions be improper but become proper after an appropriate minimal sample. With some limitation on the family of priors considered, this procedure permits unique specification of indifference for the more commonly encountered statistical models. Furthermore, these specifications are affected neither by change of the scale of measurement of the observations, nor by the sampling rule.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480854

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

A family of two-sample non-parametric tests is described, in which only the tails of the distributions are used. Some are presented as tests of dispersion and some as tests of location. Critical values for certain of the tests are given for large samples. The power of the tests is discussed, and fresh results are given for a test of dispersion against rectangular alternatives.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480855

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

This paper presents a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems. Our proposal is to select two numberspandr(0 <p, r< 1) and then score, with integer weights, the data in the toppthand bottomrthfractions of the combined sample. The percentile modified tests for scale are quite effective. Whenp=r= 1/8 (i.e., we score only the extreme quarter of the combined sample) the A.R.E. of the test to theFtest is .85.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480856

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

One-sided tolerance limits are developed for the three-parameter generalized gamma distribution of Stacy, one parameter at a time being assumed unknown. This distribution includes the exponential, gamma, and Weibull distributions as special cases. Confidence limits for the unknown parameter are also given in each case. Limits are developed based on the statistic and also on ther-th order statistic. The limits based on a single order statistic take into account the distributional form of the variable and are not the familiar nonparametric tolerance limits of Wilks which do not depend on the functional form of the variable. Some comparisons of the limits are considered in special cases and also some of the limits are shown to satisfy the “most stable” criterion of Goodman and Madansky.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480857

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480858

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

In educational and psychological applications as well as in other applications, it may be necessary to make certain comparisons of two regression lines when the variances are unequal. Such problems arise, for example, in studies comparing two alternative curriculums or two different teaching methods. By generalizing an idea which Scheffé used to obtain a test for the Behrens-Fisher problem, this paper develops some tests for comparing two regression lines when the two sets of error terms are normally distributed but with two different variances. Scheffé's test itself is a randomized test, but in this paper we present both randomized and non-randomized tests. Both simple and multiple regression are considered, but the simple regression tests are computationally easier than the multiple regression tests. The basic test statistic which is used is the ordinaryt-statistic. Essentially two types of problems are dealt with: (A) determining whether the two regression lines are identical when they are known to be parallel; and (B) determining whether the two regression lines are parallel. Confidence bounds as well as tests of hypotheses are available. For Problem A, a minimax estimator of the distance between the two lines is obtained. In addition to the Scheffé-type tests, we also consider some tests based on an approach of Welch and Hájek. A numerical example is presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480859

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Letf(μ1, μ2) = constant be a function which is monotone and has no finite termini in the (μ1, μ2) plane. Letx1andx2be either independent normal with unknown means μ1, μ2and unknown variances σ21, σ22or correlated normal with unknown mean vector (μ1, μ2) and unknown variance matrix σ. Suppose, in the first instance, that estimates,s21ands22, of σ21and σ22withv1andv2degrees of freedom are available and, in the second instance, an estimate,S, of σ withvdegrees of freedom is available. Letvis2i/σ2i,i= 1, 2, be distributed as independent chi-squares and letvShave the Wishart distribution. Under the above assumptions we study the characteristics of two procedures for obtaining interval estimates off(μ1, μ2). One procedure bases interval estimation off(μ1, μ2) on separate 1 - α confidence intervals on μ1and μ2. The other procedure bases estimation on an elliptical confidence region for (μ1, μ2). For the first procedure it is shown that the interval estimate off(μ1, μ2) is at least at the 1 - α confidence level, providingv1=v2. (which is automatically satisfied in the correlated case); ifv1v2(case of independence) we give arguments which strongly suggest, but do not prove, that the same result holds. Further, for this case, ifx1andx2are sample means from samples of size (v1+ 1) and (v2+ 1) respectively, a well known randomization argument due to Scheffe can be used to reduce the problem to the equal degree of freedom case, with no loss of precision in estimation of mean values. For the second procedure no definite conclusions are drawn.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480860

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

A special form of a partitioned matrix, similar to Greenberg and Sarhan's, is used to invert it. This method is here shown to be useful in the analysis of some non-orthogonal connected designs.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480861

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor