摘要:

Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrixAis given, and the statistician wants to compute thepth power ofA, wherepis a fractional or negative number; that is, a matrixR, such thatR1/p=A. He can often get a satisfactory approximation toApby using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500913

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Under the assumptions of a linear model with independent residuals, the elements of an orthonormal basis of the corresponding error space can be used to construct normality tests, variance homogeneity tests, and variance estimators. In comparison with other available methods, this theoretically simple approach is more generally applicable, and also yields specific improvements in some particular cases. Some constructions and applications of orthonormal bases of error spaces are presented and discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500914

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Analysis of covariance, with a single covariable in a randomized block design, is reconsidered in terms of structural regression. In practice, the covariable is often times uncontrolled, both in the experiment and in repeated sampling, and may follow a linear model as does the variable of interest. If the covariable is unaffected by treatments, then the covariable model may contain a block effect through no treatment effect. When such a model is adequate, the treatment contrast precision can be increased relative to the precision obtained through the standard method of covariance analysis. If, however, treatments affect the covariable, then a treatment effect is included in the model for the covariable. When this covariable model is adequate and when simplifying assumptions are valid, estimates can be given of direct and indirect treatment effects on the variable of interest.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500915

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function forallvalues of the independent variable have not utilized such constraints; the usual basis for such bands has been the multiple comparison procedure of Scheffé which places no constraints at all upon the independent variables. Any procedure utilizing constraints will necessarily yield a uniform improvement over the method of Scheffé' (assuming both methods are applicable) in the sense of yielding narrower bands for a given confidence probability. In the present paper a non-trivial lower bound is obtained for the confidence probability associated with a multiple comparison procedure appropriate to the case where it can be assumed that each independent variable must be of specified sign; this includes, as a subclass, polynomial regression on a non-negative independent variable. This result gives a basis for a multiple comparison procedure less conservative than that of Scheffé when both are applicable. Implementation of the procedure requires the percentage points of a heretofore untabulated distribution. Tables of percentage points of this distribution appropriate to linear combinations of two, three, or four parameters are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500916

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

If, in using the Wilcoxon signed-rank test, the ranks corresponding to zero differences are deleted, the usual formula for the critical ratio used with the normal approximation must be modified. This note gives the required modification.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500917

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Introduction to Probability Theory and Its Applications, Vol. II,William Feller.New York: John Wiley and Sons, 1966. Pp. xviii, 626. $12.00. Reviewed by Joshua Chover

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500918

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This article has no abstract

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500892

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor