摘要:

A necessary and sufficient condition is given for the existence of elements in the GOMORY group of cuts with given vanishing coefficients.

ISSN:0047-6277    

DOI:10.1080/02331887308801132

出版商:Akademie-Verlag    

年代:1973

数据来源: Taylor

摘要:

In this paper hitherto existing statements of duality for homogeneous programming will be represented. Then the authors deal with general problems of homogeneous non-linear programming min.withThe degrees of the objectiv function and constraints, all homogenous, may be at choice. For such problems theorems of duality are deducted. Known results have been produced by specialization.

ISSN:0047-6277    

DOI:10.1080/02331887308801133

出版商:Akademie-Verlag    

年代:1973

数据来源: Taylor

摘要:

An efficiency theorem is stated expressing the one-to-one correspondence betwem the linear maximurn-vector problem and the corresponding parametric linear programming problem.

ISSN:0047-6277    

DOI:10.1080/02331887308801134

出版商:Akademie-Verlag    

年代:1973

数据来源: Taylor

摘要:

we extend the theory of principal components to random variabiesXwith values in a separable HILBERT space and prove optima! properties well-known for finite-dimen-sional spaces, Further we give an estimate of the variance operatorDfrom a series of independent, observations and prove the strong consistency if the estimate for nuclearD.In the caseDhas single eigenvalues we find that with probability 1 the limiting properties of the sample principal components computed from such an estimate ofDare those of the exact principal components.

ISSN:0047-6277    

DOI:10.1080/02331887308801137

出版商:Akademie-Verlag    

年代:1973

数据来源: Taylor

摘要:

A theory of model choice in regression analysis is developed, covering tho problems of approximation of regression functions with unknown functional form, of optimal prediction for the realization of some dependend variables, of polynomial and multiple regression. In this (decision theoretical) frame a survey of the known model choice procedures including stepwise procedures and their variants is given. Moreover, several new procedures and variants are described, e.g. BAYEsian, minimax and empirical model choice, global and robust backward elimination or stepwise regression. The procedures of “maximal multiple correlation”“optimal regression” and theCp-criterion of MALLOWS are obtained as special cases of ε-BAYES, BAYES and empirical model choice respectively.Some comparisons of procedures considering the risk function are reported, e.g. under some assumptions the lower global variant of forward selection is better than the choice of the largest model.The parameters of this procedure can be chosen in such a way, that a very small model. The parameters of this procedures can be chosen in such a way, that a very small model is chosen, that approximating an unknown regression function by a linear combination of few given functions.

ISSN:0047-6277    

DOI:10.1080/02331887308801138

出版商:Akademie-Verlag    

年代:1973

数据来源: Taylor