Functional linear instrumental regression under second order stationarity

Jan Johannes

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arXiv · 1603.01649

Functional linear instrumental regression under second order stationarity

Jan Johannes

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Abstract

We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an endogenous random function X. Assuming second order stationarity jointly for X and W a nonparametric estimator of the functional slope parameter and its derivatives is proposed based on an n-sample of (Y,X,W). In this paper the minimax optimal rate of convergence of the estimator is derived assuming that the slope parameter belongs to the well-known Sobolev space of periodic functions. We discuss the cases that the cross-covariance operator associated to the random functions X and W is finitely, infinitely or in some general form smoothing.

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Jan Johannes. 2016-03-04. Functional linear instrumental regression under second order stationarity. https://arxiv.org/abs/1603.01649

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