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- W3003529518 abstract "Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: which kernel achieves smaller error? and which kernel is computationally efficient?. First, we show that a Biweight kernel is optimal in the sense of minimizing an asymptotic mean squared error of a resulting MLR parameter. This result is derived from our refined analysis of an asymptotic statistical behavior of MLR. Secondly, we provide a kernel class for which iteratively reweighted least-squares algorithm (IRLS) is guaranteed to converge, and especially prove that IRLS with an Epanechnikov kernel terminates in a finite number of iterations. Simulation studies empirically verified that using a Biweight kernel provides good estimation accuracy and that using an Epanechnikov kernel is computationally efficient. Our results improve MLR of which existing studies often stick to a Gaussian kernel and modal EM algorithm specialized for it, by providing guidelines of kernel selection." @default.
- W3003529518 created "2020-02-07" @default.
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- W3003529518 date "2020-01-29" @default.
- W3003529518 modified "2023-09-23" @default.
- W3003529518 title "Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm" @default.
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- W3003529518 doi "https://doi.org/10.48550/arxiv.2001.11168" @default.
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