摘要:

As is true of any statistical application, testing econometric statistical hypotheses involves constructing critical regions with prescribed probabilities of Type I error and determining probabilities of Type II error under alternative hypotheses. Such constructions and determinations presuppose knowledge of exact statistical distribution functions of econometric estimators and test statistics either directly, or indirectly, as in the case where a statistical distribution function that approximates the exact distribution with known margin of error is used. If this requisite information is not available, econometric statistical inference remains guesswork. Partly because of the complicated nature of systems of simultaneous econometric structural equations and the large numbers of structural constants required to characterize distribution functions of econometric statistics, however, only a few exact marginal distributions of econometric estimators and test statistics have been extracted so far. This article is intended as a contribution to the growing literature of econometric distribution theory and to assist the efforts of econometric statisticians in providing a rational basis for econometric statistical inference.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482231

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

When losses are piecewise linear, optimal decision-making hinges on estimating a specified fractile of a probability distribution. In this article we investigate, through examples, the operating characteristics of an estimation procedure which utilizes simple linear combinations of one or two values in the order statistic generated by an observation vector. Such estimates appear to be remarkably efficient compared to the estimates generated by simple parametric procedures; moreover, this efficiency does not appear to be damaged excessively by the presence of moderate amounts of autocorrelation in the sample values. It also appears to be possible to exploit informal knowledge about the shape of the distribution to improve the efficiency of this procedure.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482232

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Let ᵵ be a statistic sufficient for a parameter θ and let L[θ;t) be the likelihood function of θ for given t. Suppose we recognize a function φ(t) such that L(θ;t) φ(t) regarded as a function of t for a given θ, is a density function. We show here that this is the sampling density of ᵵ if the family of recognized densities is complete. Examples are given to illustrate that in many situations this recognition method provides a neat way of finding sampling distributions.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482233

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In several models of the analysis of variance, inferences can be made using the statistics of the analysis of variance table only by taking linear combinations of mean squares. A form for the exact distribution function of such a linear combination is given. While not new, this form does not seem to have been sufficiently exploited. Its use is illustrated in finding, by numerical integration, exact probabilities associated with two methods of assigning approximate confidence limits to a positive linear combination of variance components.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482234

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The usual χ2goodness-of-fit criterion is considered when all cells have expectations of one and the cell boundaries are not estimated from the data. This situation arises in the use of a measure of consensus proposed by Coleman [1]. Under these circumstances the criterion reduces to X2= Σt=1Nni2−N, where niis the number of observations in cell i and N is the total number of observations in the sample. The exact distribution of X2is given for N = 1(1)25(5)40, 50. For N≥25, the χ2approximation to the exact distribution of X2errs by less than .007 or 20.3 percent for right-tail areas. For left-tail areas the errors are less than .0165 or 89.9 percent when N≥25.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482235

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Eight nonparametric tests of location are examined in a small sample setting. Power functions are presented for samples drawn from the double exponential distribution. The results provide an example where the asymptotically most powerful rank test (the Mood median test) performs poorly for alternatives which are not very close to the null hypothesis.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482236

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Suppose that X1, ···, Xkare mutually independent observations from populations π1, ···, πkand that Xihas a density fxi(·)(1 ≤ i ≤ k). For i = 1, ···, k let pi= P[Xi> maxj ≠ iXj], and let p[k] = max (p1, ···, pk). Bechhofer and Sobel [4] have proposed a nonparametric selection procedure based on multinomial random variables for the problem of selecting a population which has the highest probability, p[k], of producing the largest observation. (The density fxi(·) may be different for each i(i = 1, ···, k) and unknown.) If the k distribution functions have the same form, differing only in location, a population with the highest probability of yielding the largest observation corresponds to a population with the largest location parameter. This latter situation allows use of certain alternative procedures designed for specific parametric cases, and the present article studies the relative efficiency (in terms of fixed sample sizes required to guarantee a given probability of a correct selection in certain specified parametric subspaces) of the Bechhofer-Sobel procedure with respect to some competing selection procedures. These competitors were designed specifically for the normal case by Bechhofer [2], and for the uniform case by the present author. The relative efficiency of the Bechhofer-Sobel procedure, in the cases studied, ranges from .27 to .74.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482237

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482238

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, (rs)prqs-r/(1 - qs) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML estimator or Weinberg's simple sib method. Its efficiency relative to the ML estimator is better in small than in large samples, ranging from 97 percent to 101 percent for the genetically important cases of p = .25 and .50. Mantel's estimator performs better than the simple sib method as an initial estimator in iterative ML scoring.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482239

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482240

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor