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The residual process for non-linear regression

Published online by Cambridge University Press:  14 July 2016

Ian B. MacNeill  and
V. K. Jandhyala
Ian B. MacNeill*
Affiliation:
The University of Western Ontario
V. K. Jandhyala*
Affiliation:
The University of Western Ontario
*
∗ Postal address: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Canada N6A 5B9.
∗ Postal address: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Canada N6A 5B9.
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Abstract

Limit processes for sequences of partial sums of non-linear regression residuals are obtained under assumptions on regressor functions imposed by Jennrich (1969). The limit process and covariance kernel are calculated explicitly for functions of exponential type.

Keywords

WEAK CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 957 - 963
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Grant support for this research was provided by the Natural Sciences and Engineering Research Council of Canada.

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Jennrich, R. I. (1969) Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40, 633–643.Google Scholar
MacNeill, I. B. (1978a) Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times. Ann. Statist. 6, 422–433.Google Scholar
MacNeill, I. B. (1978b) Limit processes for sequences of partial sums of regression residuals. Ann. Prob. 6, 695–698.Google Scholar