Estimation of nonlinear functionals: recent results and open problems
Seminar Room 1, Newton Institute
Abstract: We present a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models based on higher order influence functions. The theory reproduces many previous results, produces new non-root n results, and opens up the ability to perform optimal non-root n inference in complex high dimensional models. We present novel rate-optimal point and intervals estimators for various functionals of central importance to biostatistics in settings in which estimation at the expected root n rate is not possible, owing to the curse of dimensionality. We also show that our higher order influence functions have a multi-robustness property that extends the double robustness property of first order influence functions. Open questions will be discussed
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