摘要:

Balls are drawn one after another fromkcellsC1, …,Ckaccording to the multinomial distribution. Suppose theith cell initially containsNiballs, and sampling stops as soon as any of thekcells, sayCα, empties first. LetXidenote the number of balls taken from cellCi(alli ≠ α) at stopping time. The joint asymptotic (asNi→ ∞) distribution of theXi(i ≠ α) is derived under the most general configuration of the multinomial cell probabilitiesp1, …,pk.Conditions onpiandNiare given under which the asymptotic distribution is shown to be either normal or truncated (restricted) normal. An application of the asymptotic distribution theory forNi=N0(i= 1, …,k) in setting up approximate tests and confidence intervals for the largestpiis also given. Under certain conditions onpiandNiit is shown that the asymptotic probability thatCiempties first is equal to the probability content of a positive orthant under a multivariate normal distribution.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500930

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

The maximum likelihood estimate for the non-centrality parameter of a non-central χ2distribution with two degree of freedom is obtained. This estimate is expressed as a solution of an equation involving Bessel functions of order 0 and 1, of purely imaginary argument, both of which are tabulated. The derivation rests mainly on a lemma dealing with limit and monotonicity properties of a function representable as a quotient of two Bessel functions. An asymptotic result is also given.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500931

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This paper carries on work in [2] and [4] on the asymptotic effects of small specification error in simultaneous equation estimation. The specification errors considered are inherent in the approximate nature of econometric models. It is shown that for any parameter and small enough specification error, the probability limits of two-stage least squares and limited-information maximum-likelihood, while different, lie on the same side of the true parameter value, the difference between them being of the second order of smalls relative to the effects of the specification error on either one of them. A method of consistently estimating the sign of the difference of the effects of specification error on the two estimators is given and a procedure suggested for choosing an estimator to reduce those effects. Two relatively simple examples are worked out.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500932

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Econometric models make extensive use of distributed lag relations of the form

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500933

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Formulas for the variances of weighted least squares estimators calculated with estimated weights based on equal replicate numbers are derived in this paper. Results are obtained for the two cases of multivariate and univariate error distributions.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500934

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

It is shown that in a standard linear regression model ordinary least-squares estimators are best linear unbiased if and only if the errors have the same variance and the same nonnegative coefficient of correlation between each pair.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500935

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Asymptotic variances are derived for estimators of the dummy variate regression model described in [6]. The results are summarized by asymptotic covariance matrices for the regression coefficients, the estimated logarithms of odds givenX, and the estimated probabilities givenX.A two population two variable example illustrates the results.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500936

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Experimental design considerations have been virtually ignored by economists who have conducted computer simulation experiments with models of economic systems. The objective of this paper is to spell out in detail the relationship between existing experimental design techniques and techniques of data analysis and the design of simulation experiments with economic systems. We begin by defining the problem of experimental design as applied to computer simulation experiments. With the aid of an example model, we explore several techniques of data analysis and a number of specific experimental design problems. Although this paper is oriented towards the design of computer simulation experiments in economics, the techniques which are discussed are of a general nature and should be applicable to the design of simulation experiments in other disciplines.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500937

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A nine-equation econometric model of the U. S. textile industry is presented to explain the behavior of the industry during the period 1953 through 1962. The endogenous variables of the model include apparel output and demand, textile mill products output and demand, employment, wages, profit, and investment. A computer program was written to simulate the behavior of the textile industry between 1953 and 1962 on the basis of the behavioral relationships implied by the nine-equation model. Three different techniques were used to compare the simulated data generated by the model of the textile industry with actual observed data—graphical analysis, spectral analysis, and total variance analysis.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500938

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This paper presents a method of constructing conservative joint confidence regions for the parameters of a linear model and the volumes of these regions are compared with the volume of an exact confidence region. Confidence regions on the entire surface are obtained from the confidence region on the parameters. The procedures are illustrated for the case of a simple linear model.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500939

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor