Abstract
This note first establishes the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are long-range dependent Gaussian or a function of such random variables. This result is then used to obtain the large sample distributions of a class of M-estimators of the underlying parameters for a large class of non-linear regression models. The class of estimators includes analogs of the least square, least absolute deviation and the Huber(c) estimators. The note also gives the asymptotic uniform linearity of the residual empirical processes.
Research of this author was also partly supported by the NSF Grant DMS 94–02904.
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© 1996 Springer-Verlag New York, Inc.
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Koul, H.L. (1996). Asymptotics of M-estimators in non-linear regression with long-range dependent errors. In: Robinson, P.M., Rosenblatt, M. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2412-9_20
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DOI: https://doi.org/10.1007/978-1-4612-2412-9_20
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