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Adapting for the missing link. (English) Zbl 0828.62059
Summary: We consider the fitting of generalized linear models in which the link function is assumed to be unknown, and propose the following computational method:
First, estimate regression coefficients using the canonical link. Then, estimate the link via a kernel smoother, treating the direction in the predictor space determined by the regression coefficients as known. Then reestimate the direction using the estimated link and alternate between these two steps. We show that under fairly general conditions, \(n^{1/2}\)-consistent estimates of the direction are obtained. A small Monte Carlo study is presented.

MSC:
62J12 Generalized linear models (logistic models)
62G07 Density estimation
65C99 Probabilistic methods, stochastic differential equations
Software:
LISP-STAT
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