摘要:

X1,X2, …, are independent and identically distributed, the common distribution known except for the value of a parameter θ. The problem is to find a test ofH–1:θ = θ–1againstH1.θ=θ1, with pre-assigned error probabilities α, β, and which minimizes the maximum expected sample size (the maximum taken with respect to θ). For the cases where α = β and θ is the mean of a normal distribution, and where α = β and θ is a binomial probability and θ–1+ θ1= 1, a computational scheme for finding such a test is described.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500543

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Calculational short cuts for Kendall's tau and average tau and for Hays' average tau with a criterion ranking (τC) are shown. The short cuts are based mainly on counting “inversions” in the ordering ofnobjects by a given judge, and summing overmjudges, rather than counting agreements for a given object-pair and summing over object-pairs. The sum of the number of inversions thus counted forτChas a limiting normal distribution under the null hypothesis. From this is derived a statistic which approximates the sampling distribution of τC. The approximation is shown to be close even for smallmandn.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500544

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

A curvilinear regression model is treated by linear programming methods, so as to require only mild restrictions on the nature of the non-linearities. Specifically a method is proposed that does not require assuming specific mathematical forms for the regression functions. Restrictive assumptions no stronger than monotonicity or concavity of the forms need be imposed. The linear programming formulations provide fits for the regression functions according to the criteria of minimal sum of absolute deviations and minimal maximum deviation. The alteration needed to employ a least squares fit is also sketched.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500545

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Two important examples of this iterated procedure are given. The first one describes the test of the equality of the means ofmindependent normal distributions having common, but unknown, variance. This test is based on a sequence of Studenttstatistics: the firstttests the equality of the first two means, the secondttests the equality of the first three means (given that the first two means are equal), and so on. Since, under the null hypothesis, these statistics are mutually stochastically independent, it is easy to find the significance level of this procedure. Moreover, a rejection by this iterated scheme provides some reason why allmmeans are not equal. In the second example, the test of the equality ofmindependent distributions is based on a sequence of independent two-sample distribution-free statistics, such as the statistics proposed by Smirnov and Wilcoxon.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500546

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

In this note we present an example where the usual method of obtaining a confidence region for a parameter, namely “inverting” the uniformly most powerful test of a related hypothesis, leads to an interval whose expected length is greater than that obtained by another method of obtaining a confidence interval for the parameter. The implications of this example are then discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500547

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Models are proposed as a basis for unbiased and biased estimation from sample survey data of a regression relation. Unbiased estimates of the variances and covariances of estimates of the regression coefficients are obtained for certain cases but do not appear to exist for all cases. It is suggested that past surveys, conducted mostly to obtain efficiently estimates of means and totals, be analyzed to yield estimates of regression relations, to obtain information needed in designing future surveys, and to test the adequacy of the proposed models.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500548

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

A static equilibrium model is considered in which private employment is a function of output, corporate income tax is a function of net profits, dividends and investment are both functions of net profits after tax, personal income taxes of entrepreneurs and labor are both functions of personal income, and consumption by entrepreneurs and labor are both functions of disposable income. Export, government purchases, interest paid by government, and government employment are parameters.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500549

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

A straightforward procedure is presented which uses the variance formula of a simple estimator to obtain an approximate formula for the variance of a post-stratified estimator. The approximation is the well-known one for the variance of a ratio estimator. The technique is applied to samples which have been selected in stratified and multistage designs and can be extended to other ratio estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500550

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

Several ratio-type estimators in two-phase sampling are presented. One of them is an unbiased estimate and follows direct from the one given by Hartley and Ross for single phase sampling. The paper gives the variances of each of these estimates and discusses the efficiency of the unbiased estimate as compared to the biased estimates. Lastly, the paper gives a numerical illustration and discusses the efficiency of two-phase sampling with respect to single phase sampling under a simple cost function.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500551

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor

摘要:

The principal assumption underlying the model is that Presidential budget recommendations [only for goods and services] are an adequate approximation to Congressional appropriations. This implies that Federal purchases depend on the past stream of budget recommendations. It is suggested that the time shape of this past stream be represented by Koyck and/or Pascal distributed lags. Our best forecasting system, which combines Koyck and Pascal distributions, results in forecast errors of −2.03 per cent for fiscal 1960 and 1.10 per cent for fiscal 1961. We conclude that a distributed lag in budget recommendations for goods and services is extremely useful for forecasting Federal purchases.

ISSN:0162-1459    

DOI:10.1080/01621459.1962.10500552

出版商:Taylor & Francis Group    

年代:1962

数据来源: Taylor