This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Hillier, Grant
Kan, Raymond
Wang, Xiaolu

Additional information is available for the following registered author(s):

Abstract

The top-order zonal polynomials Ck(A), and top-order invariant polynomials Ck1, , Ar) in which each of the partitions of ki, i = 1, see, for example, Phillips (1980, Econometrica 48, 861 398; 1985, International Economic Review 26, 21 896), Hillier (1985, Econometric Theory 1, 53 28), Hillier and Satchell (1986, Econometric Theory 2, 66 257; 1993, Australian Journal of Statistics 35, 271 570) and Chikuse (1987, Econometric Theory 3, 195 207), numerical evaluation of these invariant polynomials is extremely time consuming. As a result, the value of invariant polynomials has been largely confined to analytic work on distribution theory. In this paper we present new, very much more efficient, algorithms for computing both the top-order zonal and invariant polynomials. These results should make the theoretical results involving these functions much more valuable for direct practical study. We demonstrate the value of our results by providing fast and accurate algorithms for computing the moments of a ratio of quadratic forms in normal random variables.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://journals.cambridge.org/abstract_S0266466608090075
File Format: text/html
File Function: link to article abstract page
Download Restriction: no

Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 01 (February)
Pages: 211-242
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:211-242_09

Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Email:
Web page: http://journals.cambridge.org/jid_ECT

For technical questions regarding this item, or to correct its listing, contact: (Mike Eden).

Related research
Keywords:

Other versions of this item:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hillier, Grant H & Kinal, Terrence W & Srivastava, V K, 1984. "On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation," Econometrica, Econometric Society, vol. 52(1), pages 185-202, January. [Downloadable!] (restricted)
  2. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-95, July. [Downloadable!] (restricted)
    Other versions:
  3. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-78, May. [Downloadable!] (restricted)
  4. Ghazal, G. A., 1996. "Recurrence formula for expectations of products of quadratic forms," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 101-109, April. [Downloadable!] (restricted)
  5. Hillier, Grant, 2001. "THE DENSITY OF A QUADRATIC FORM IN A VECTOR UNIFORMLY DISTRIBUTED ON THE n-SPHERE," Econometric Theory, Cambridge University Press, vol. 17(01), pages 1-28, February. [Downloadable!]
    Other versions:
  6. Smith, Murray D., 1989. "On the expectation of a ratio of quadratic forms in normal variables," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 244-257, November. [Downloadable!] (restricted)
  7. Chikuse, Yasuko, 1987. "Methods for Constructing Top Order Invariant Polynomials," Econometric Theory, Cambridge University Press, vol. 3(02), pages 195-207, April. [Downloadable!]
  8. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February. [Downloadable!] (restricted)
    Other versions:
  9. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May. [Downloadable!] (restricted)
  10. De Gooijer, Jan G., 1980. "Exact moments of the sample autocorrelations from series generated by general arima processes of order (p, d, q), d=0 or 1," Journal of Econometrics, Elsevier, vol. 14(3), pages 365-379, December. [Downloadable!] (restricted)
  11. Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annales d'Economie et de Statistique, ADRES, issue 4, pages 05, Octobre-D. [Downloadable!]
  12. Phillips, P. C. B., 1984. "The exact distribution of exogenous variable coefficient estimators," Journal of Econometrics, Elsevier, vol. 26(3), pages 387-398, December. [Downloadable!] (restricted)
    Other versions:
  13. Giovanni Forchini, . "The Exact Cumulative Distribution Function of a Ratio of Quadratic Forms in Normal Variables with Application to the AR(1) Model," Discussion Papers 01/02, Department of Economics, University of York. [Downloadable!]
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors," CeMMAP working papers CWP14/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Statistics
Access and download statistics

Did you know? IDEAS also computes impact factors for journals and working paper series.

This page was last updated on 2009-11-24.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.