摘要:

Assume that an autoregression generates the basic data but that the observations are an equi-spaced sample of moving sums of the basic data for non-overlapping discrete intervals. Simple least squares estimates of the underlying autoregression are not consistent. It is shown that it is possible to estimate consistently the coefficients of the underlying autoregression based on the equi-spaced sample. These results are equivalent to showing how to interpolate a finite number of missing values between adjacent sample observations if it is assumed that the underlying model is an autoregression of a specified order. It is not possible to interpolate a continuum of missing observations on the basis of an equi-spaced sample; this assertion is equivalent to the aliasing problem well known in spectral analysis. Finally, the analysis is extended to an autoregression including exogenous variables.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482922

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This paper considers the problem of obtaining efficient estimates for the parameters of a system ofMregression equations. The disturbance terms of this system are assumed to be related by both serial and contemporaneous correlation. Under the further assumption that the serial correlation is a first order autoregressive process, the paper develops an estimator that is consistent and has the same asymptotic normal distribution as the Aitken estimator which assumes the covariance matrix to be known. The paper concludes with a discussion of some alternative covariance specifications and points out certain difficulties with the standard single equation procedures for handling auto-regressive schemes.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482923

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A transformation matrix is given for reducing a random sample of sizento a smaller set ofmuncorrelated variables, with the same mean and minimum common variance. This transformation may be applied to the classic Behrens-Fisher problem to obtain a solution similar to Scheffé's. An indication of the loss of information is also given. The transformation is also used to obtain an exact test of whether two regression planes are parallel, when the variances and sample sizes are unequal. Also a test of whether two regression planes are identical, when they are assumed parallel, can be derived easily by this method, and the results are similar to a recent solution by Potthoff. Some possible applications of the transformation to randomization tests concerning means is also given, the idea being to reduce the sample so that the amount of computations required would be feasible.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482924

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

The problem of iterated tests of hypotheses has been treated from the standpoint of multiple decision theory. Under the assumption that there is a UMP test (not necessarily similar) for each component hypothesis, a procedure has been developed which ensures an upper bound for various probabilities of misclassification and which maximizes the probabilities of correct classification in some class.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482925

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

The values of the power of theF-test corresponding to the degrees of freedom (f1,f2) and non-centrality parameter λ are tabulated for Type I error α =0.005, 0.01, 0.025, 0.05, for the following values of the parameters:

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482926

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A stopping rule for the process of sequential sampling inspection of finite lots is obtained which, with confidence 1—α, guarantees a prespecified upper confidence limit on the number of defective items in the uninspected portion of the lot. Usual assumptions of “control” are not invoked here and, in that sense, the plans are called nonparametric.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482927

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A number of tests and estimates for mean life and other parameters derived under the exponential distribution assumption are studied under the alternative condition that the distribution has an increasing (decreasing) failure rate. The tests and estimates considered are, for the most part, based on censored and truncated samples. It is shown that the usual acceptance sampling procedures based on mean life generally favor the producer (consumer) in the IFR (DFR) case. However, acceptance sampling procedures based on theqth quantile tend to favor the consumer in the IFR case whenqis small. The usual estimates for the mean based on the exponential assumption are positively (negatively) biased when the distribution is IFR (DFR). Many of these results hold under the weaker assumption that the distribution has an increasing (decreasing) failure rate on the average.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482928

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

In applied problems one often wishes to compare the mortality experience of two or more groups of individuals who are known not to be comparable with respect to a covariable. This paper presents an approach to this problem by assuming that the force of mortality for each individual is a function of the covariable. Extension to the case where more than one covariable is present is indicated. It is also suggested that the present method is adaptable to an actuarial type analysis.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482929

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This article considers two examples of bivariate extremal distributions when the margins follow the first asymptotic distribution of the largest values. The variables are assumed to be reduced and each distribution contains only one parameter indicating the association between the extremes. The probability and the density functions of these distributions at the characteristic value, median, and mode have been analyzed. A procedure has been developed to estimate the single parameter of the distributions. A criterion for distinguishing between the two bivariate extremal distributions has been worked out. Finally, the various theories developed are applied to a numerical example.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482930

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A bivariate density function, without location parameter, is defined over the range 0< × < y <∞. The marginal distribution ofYis taken to be Stacy's generalized Gamma distribution [10], and the determining conditional distribution ofXis assumed to be the Beta distribution, normalized over the interval 0<x<y.Parameter estimation for the resulting five-parameter bivariate density, from a complete bivariate sample (xi, yi),i= 1, 2, …,n, is indicated. Whenever the parameters of the conditional Beta distribution may be assumed known, a technique for estimating the three parameters of Stacy's distribution from a complete sample of the warning-times,xi,i= 1, 2, …,n, is presented. Measures of the dispersion of the scale parameter estimates, when calculated from the sample of warning-times, are provided. In conclusion, some important special cases of the bivariate density are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482931

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor