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Saddlepoint Expansions in Linear Regression

Author

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  • Ivanov, Alexander V.
  • Zwanzig, Silvelyn

Abstract

In this paper sums of independent but not identically distributed m-dimensional vectors are considered. The summands are generated by a random vector multiplied by a deterministic weight matrix which results in a singular covariance matrix. Under general conditions, given separately for the weight matrix and the random vector, saddlepoint approximations to the distribution of the sum are derived. The results are applied to the least squares estimator, the residual sum of squares, and to an F-statistic in linear regression.

Suggested Citation

  • Ivanov, Alexander V. & Zwanzig, Silvelyn, 2002. "Saddlepoint Expansions in Linear Regression," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 183-207, October.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:1:p:183-207
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    References listed on IDEAS

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    1. O. Barndorff-Nielsen & P. Jupp, 1989. "Approximating exponential models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 247-267, June.
    2. Qumsiyeh, Maher B., 1990. "Edgeworth expansion in regression models," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 86-101, October.
    3. Melnick, G.A. & Zwanziger, J., 1995. "State health care expenditures under competition and regulation, 1980 through 1991," American Journal of Public Health, American Public Health Association, vol. 85(10), pages 1391-1396.
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