摘要:

The mathematical theory of the best linear prediction of stationary time series presumes that the model generating the series, which can be specified by either the autocovariance function or the spectral density, is known. The true model is, of course, not known in practice, and the procedure is to fit a model and predict as if this fitted model were the truth. The question then is one of deciding whether the resulting predictions are about as good as could be gotten if the truth were known. This paper describes a method for assessing the predictions of the fitting model by an analysis of residuals. In particular, it is argued that the traditional tests of hypothesis for white noise are inappropriate if prediction is the goal, and a method is described for determining whether or not the mean square errors of the predictions arising from the fitted model can be measurably reduced.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488843

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The problem of predicting therth ordered observationXrin a sample ofnfrom an exponential distribution, based on the observed values of the firstkordered observations from the sample (k<r≤n), is discussed. It is shown how to find an interval estimate forXr, and the result is used to predict the remaining elapsed time in certain life test experiments involving items whose life times follow an exponential distribution.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488844

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Two of the basic approaches to choosing ann-point experimental design in many industrial situations are (i) to set down a simple factorial or fractional factorial design in the factors being studied, or (ii) to choose a design based on the well-known |X′X| criterion. Experimenters often prefer (i) due to its simplicity; our viewpoint here is that (ii) is much better. We first indicate some situations for which (when all the factors are restricted to a cuboidal region) the factorial approach is optimal, as judged by the |X′X| criterion, but the assumed models are often not sensible ones in practical work. We then examine what (similarly restricted) designs are optimal under the |X′X| criterion for the standard linear models of first and second order; because of the very rapid increase in computational difficulties, we consider only “cube plus star” type designs fork≥ 3 (except fork= 3,n= 10). In spite of computational requirements, we recommend use of the |X′X| criterion in general rather than the indiscriminate use of factorials and we briefly discuss the reasons why, both for linear and nonlinear model situations.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488845

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Healy and Westmacott (1956) gave an iterative missing value procedure in which a simple correction is subtracted from each estimated missing value at each iteration. Experience has however shown that it is advantageous to replace the simple correction by a multiplemof it,m> 1. The multiplierm=n/E, wherenis the number of units andEthe number of error degrees of freedom in the absence of missing values, gives an exact solution in one step for most factorial analyses with one missing value; for other analyses, also, convergence is faster withm=n/Ethan withm= 1.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488846

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Consider a life testing experiment consisting ofnitems, (n– 1) of which have the same expected life while one of them could have a much longer expected life. The standard estimators based on a homogeneous model if used in such a case, would tend to overestimate and result in a large mean squared error (MSE). The present paper considers (n– 1) items having p.d.f. given by l/σ exp (–x/σ) while the remaining one has p.d.f. α/σ exp (–xα/σ), 0 < < 1. We consider estimators of c by linear combinations of the first few order statistics. An optimal estimator is suggested and its MSE is compared with that of the standard estimators. The cases ofn= 3 and 4 are explicitly evaluated.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488847

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The relationship between a controllablexandaresponseycan often be described by the simple linear regression model. In the Linear Calibration Problem in addition tonresponses (y1, …,yn) corresponding to knowns (x1…,xn) there aremfurther responses corresponding to a single unknownx. The problem is to estimate this unknownx.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488848

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Variational methods are applied to the determination of experimental designs for estimation of parameters in nonlinear regression models. The performance of one of the designs is illustrated by a nonlinear equation of Langmuir isotherm type and is shown to be a considerable improvement over nondesigned experiments.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488849

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Two years of irregularly spaced measurements of seawater temperature at 200 feet at a fixed North Pacific Ocean location are considered. The data are heteroscedastic in time and the average path jumps about erratically. We seek points of significant change in the data-generating process and wish to study their nature.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488850

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Craig [1] has given a formula for computing the ASN when binomial double sampling is terminated if too many defectives are found in either sample. An alternative form of that result more adaptable to use with tables is given together with the companion result for the hypergeometric case.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488851

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In a recent stratified sample survey of telephone switchboards, the total sample sizenwas limited in advance to a certain small number. Associated with theith switchboard of typekwas the numberYkiof telephone sets behind it. The main items to be estimated were the means yk, of five designated strata. It was proposed that the sample means ykshould have sampling variances as nearly as possible in a given ratio, so as to reflect different degrees of interest in the various strata. The basic problem considered here is to find an appropriate integer valued allocation of n among the strata.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488852

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor