Maximization of empirical Shannon information in testing significant variables of linear model
Search for an unknown set A,Card(A) = s, of significant variables of a linear model with random IID discrete binary carriers and finitely supported IID noise is studied. Two statistics T1, Ts, based on maximization of Shannon Information (SI) of the corresponding classes of joint empirical inputoutput distributions, are proposed inspired by the related study in Csiszar and Körner (1981). The first one compares sequences of values of each variable and of the output separately. The second one explores the relation between the subsets of the (N x t) design matrix corresponding to each subset of variables of given cardinality and the output sequence. Here N is the number of experiments and t is the total number of variables. Both statistics are shown to be asymptotically as efficient as the MLtest for the corresponding classes of joint empirical distributions in the artificial case when MLtest is applicable: if the unknown parameters bλ, λ Є A, of the model and the distribution of errors are known. Our tests do not require this information. Therefore, they are asymptotically uniformly most efficient in the corresponding classes of tests. The second statistic is shown to provide asymptotically best rate of search for the set A of significant variables when tÇÉ but requires about ts log t cycles of computing. This may appear in accessible for actual computations in some applications. The first statistic requires only t log t cycles of computing operations and provides the best order of magnitude of the characteristics studied for the second class of tests.
Year of publication: 
1998


Authors:  Malyutov, M. ; Sadaka, H. 
Publisher: 
Berlin : Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 
Saved in:
Series:  SFB 373 Discussion Paper ; 1998,2 

Type of publication:  Book / Working Paper 
Type of publication (narrower categories):  Working Paper 
Language:  English 
Other identifiers:  721077196 [GVK] hdl:10419/61266 [Handle] RePEc:zbw:sfb373:19982 [RePEc] 
Source: 
Persistent link: https://www.econbiz.de/10010309878
Saved in favorites
Similar items by person

Maximization of empirical Shannon information in testing significant variables of linear model
Malyutov, M., (1998)

Maximization of Empirical Shannon Information in Testing Significant Variables of Linear Model
Malyutov, M.,

Maximization of empirical shannon information in testing significant variables of linear model
Malyutov, M., (1998)
 More ...