摘要:

Numerical methods of differentiation and for the inversion of generating functions and Laplace transforms, are applied to some estimation problems. One problem considered involves the estimation of probabilities related to compound distributions. LetX1,X2, … be independent random variables with known distributions. Furthermore, letNbe a random variable with an unknown distribution. The problem is to make inferences about the compound random variableZ = X1+X2+ … +XNon the basis ofkindependent observations,N1,N2, …,Nk, onN. Another problem considered involves the estimation of the busy period distribution in a Queueing system with known Poisson arrivals but unknown service distribution, on the basis of independent observationsS1,S2, …,Skof the service time. The method uses a functional equation relating the Laplace transforms of the service time and busy period distributions. The same type of approach can be applied to a variety of estimation problems in Queueing and Renewal theory. Where the distribution of service time is known the method may be viewed as a numerical method for solving functional equations of the type frequently occurring in probability theory.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480675

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

A measure is suggested of the efficiency of a randomized block design for the comparison of two treatments by means of a Wilcoxon-type analysis. It is shown how the efficiency can be estimated from data of a randomized block design.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480676

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Since 1951 the Survey Research Center has conducted surveys of consumer optimism and confidence two to four times a year in an attempt to improve methods of forecasting discretionary spending by consumers. The predictive success of these attitude surveys is tested here in conjunction with a number of financial variables by means of time series regressions covering the years 1952–61.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480677

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

The Fisher informationI(p;f1,f2) for estimating the proportionpin a mixture λ(x) =pf1(x) +(1 −p)f2(x) of two densities is investigated. A general power series expansion is obtained, which is then explored in detail for the case of two exponential densities, and for the case of two normal densities with equal scale. Simple approximations are obtained, for example

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480678

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Quality differences make estimation of price indexes for real properties difficult, but these can be largely avoided by basing an index on sales prices of the same property at different times. The problem of combining price relatives of repeat sales of properties to obtain a price index can be converted into a regression problem, and standard techniques of regression analysis can be used to estimate the index. This method of estimation is more efficient than others for combining price relatives in that it utilizes information about the price index for earlier periods contained in sales prices in later periods. Standard errors of the estimated index numbers can be readily computed using the regression method, and it permits certain effects on the value of real properties to be eliminated from the index.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480679

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

When employed in connection with econometric models that have a sufficiently high degree of cognitive significance (as measured by the extent to which underlying economic premises are actually elucidated into empirically testable implications) qualitative analysis of the exact finite sample distribution functions of GCL estimators of structural parameters finds its paramount use in delimiting the precision with which structural coefficients can be estimated. This kind of qualitative analysis is illustrated here by the GCL estimator of themarginal propensity to consumeappearing in a simple five-equationKeynesianmodel. The precision with which the marginal propensity to consume can be estimated from national income statistics is shown to be related to the values of coefficients of disposable income, long-term rate of interest and high-powered money in the investment, liquidity-preference, and supply of money functions. The mode of this dependence is made explicit in the present article.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480680

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

The finite sample properties of an asymptotically efficient technique (JASA, June, 1962) for estimating coefficients in certain generally encountered sets of regression equations are studied in this paper. In particular, exact first and second moments of the asymptotically efficient coefficient estimator are derived and compared with those of the usual least squares estimator. Further, the exact probability density function of the new estimator is derived and studied as a function of sample size. It is found that the approach to asymptotic normality is fairly rapid and that for a wide range of conditions an appreciable part of the asymptotic gain in efficiency is realized in samples of finite size.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480681

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

The logical implications of certain simple consistency requirements for appraising alternative procedures for seasonal adjustment constitute the first problem considered in this paper. It is shown that any sum preserving technique of seasonal adjustment that satisfies the quite reasonable requirements of orthogonality and idempotency can be executed on the electronic computer by standard least squares regression procedures.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480682

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

The paper compares year-to-year changes in the Wiesenberger Index of Return for investment funds of similar objectives. It is initially shown, using correlation techniques, that there was little consistency in yearly performance of the funds during the period from 1951 to 1960. This result serves as support for the assumption that a fund's relative performance in any one year is strictly a random occurrence. We might, therefore, define a “successful” management as one whose fund will be in the top half of funds with similar objectives with probability of at least .7. It is then shown, using a Bayesian approach, that only 28 funds out of a sample of 128 would have judged themselves superior at odds in excess of even money, with the given criterion.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480683

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor

摘要:

Given a series of quarterly data, estimates may be obtained for both trend and seasonal variation by minimising the sum, or more generally a linear combination, of two sums of squares, one of them based on the second differences between trend values, the other on the deviations of the observations from seasonally corrected trend values. Exact solutions are obtained for 8 and 12 observations, and an approximate solution applicable to longer time series is given. A numerical example is supplied, and the procedure outlined here is compared with the moving average method.

ISSN:0162-1459    

DOI:10.1080/01621459.1963.10480684

出版商:Taylor & Francis Group    

年代:1963

数据来源: Taylor