Nonparametric Logistic Regression: Reproducing Kernel Hilbert Spaces and Strong Convexity
نویسندگان
چکیده
We study maximum penalized likelihood estimation for logistic regression type problems. The usual difficulties encountered when the log-odds ratios may become large in absolute value are circumvented by imposing a priori bounds on the estimator, depending on the sample size (n) and smoothing parameter. We pay for this in the convergence rate of the mean integrated squared error by a factor logn. When the “true” log odds ratios are bounded, these factors logn disappear. The main technical tools employed are reproducing kernel Hilbert spaces and convexity inequalities.
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