Nonparametric modal regression based on orthogonal series estimation

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Abstract

In this paper, we proposed an orthogonal series nonparametric modal regression (OS-NMR) method for estimating the conditional mode under a unimodal setting. The unknown modal regression function was approximated by a truncated expansion of orthogonal basis functions, which represents the nonparametric component through a finite-dimensional coefficient vector. These coefficients were estimated using a kernel-density-based modal regression criterion and computed by the modal expectation-maximization (MEM) algorithm. Compared with local polynomial modal regression, the proposed method provides a global approximation and avoids repeated pointwise estimation. The orthogonal structure further separates coefficient estimation error from truncation approximation error, which makes the theoretical arguments clearer and more tractable. We established the convergence rate and asymptotic normality of the proposed estimator, and evaluated its finite-sample performance through simulations and a real data application.

Keywords

orthogonal series expansion / modal regression / MEM algorithm / kernel density estimation / mode

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