Quantile regression approach to conditional mode estimation

Ota, Hirofumi; Kato, Kengo; Hara, Shodo

doi:10.1214/19-ejs1607

Cited by 29 publications

(15 citation statements)

References 60 publications

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“…The consistency of the MLR even for data with skewed conditional distributions makes the MLR a promising approach to analyzing them; refer, for example, to an application to cognitive impairment prediction [6] and analysis of economic data [7], [8]. Thus studies of the MLR and related areas are currently ongoing from various viewpoints [8]- [10]. This paper will be published in the proceedings of the 18th IEEE International Conference on Machine Learning and Applications -ICMLA 2019.…”

Section: Imentioning

confidence: 99%

Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm

Yamasaki

Tanaka

2019

2019 18th IEEE International Conference on Machine Learning and Applications (ICMLA)

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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.

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Section: Imentioning

confidence: 99%

Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm

Yamasaki

Tanaka

2019

2019 18th IEEE International Conference on Machine Learning and Applications (ICMLA)

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“…Due to such reasons, we have experienced much development of modal regression recently. Especially, with the distinguished characteristics of modal regression (such as robustness and better prediction performance (shorter prediction interval)), the idea of linear modal regression was subsequently extended by many researchers such as Yao and Xiang (2016), Zhou and Huang (2016), Chen et al (2016), Krief (2017), Chen (2018), Li and Huang (2019), Ota et al (2019), Kemp et al (2020), among others.…”

mentioning

confidence: 99%

Modal regression for fixed effects panel data

2021

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Most research on panel data focuses on mean or quantile regression while there is not much research about regression methods based on the mode. In this paper, we propose a new model named fixed effects modal regression for panel data in which we model how the conditional mode of the response variable depends on the covariates, and employ a kernelbased objective function to simplify the computation. The proposed modal regression can complement the mean and quantile regressions, and provide better central tendency measure and prediction performance when the data is skewed. We present a linear dummy modal regression (LDMR) method and a pseudo-demodeing two-step (PDTS) method to estimate the proposed modal regression. The computations can be easily implemented using a modified modal-expectation-maximization (MEM) algorithm. We investigate the asymptotic properties of the modal estimators under some mild regularity conditions when the number of individuals, N , and the number of time periods, T , go to infinity. The optimal bandwidths with order (N T ) −1/7 are obtained by minimizing the asymptotic weighted mean squared errors. Monte Carlo simulations and two real data analyses of a public capital productivity study and a carbon dioxide (CO 2 ) emissions study are presented to demonstrate the finite sample performance of the newly proposed modal regression.

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“…For example, in the field of pattern recognition, the mean shift algorithm (Fukunaga & Hostetler, 1975) is one of the most popular methods for density-based clustering, which is nothing but the multiple mode estimation method (Cheng, 1995). Regression toward the mode (Lee, 1989;Kemp & Silva, 2012) has been attracting the interest of many statisticians and is an active area of research (Yao & Li, 2014;Ota, Kato, & Hara, 2019;Sando, Akaho, Murata, & Hino, 2019). Chacón (2020) provided a recent comprehensive review on the use of mode, and our work provides a novel example of the use of the mode for PCA.…”

Section: Introductionmentioning

confidence: 94%

Modal Principal Component Analysis

Sando

Hino

2020

Neural Computation

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Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.

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Quantile regression approach to conditional mode estimation

Cited by 29 publications

References 60 publications

Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm

Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm

Modal regression for fixed effects panel data

Modal Principal Component Analysis

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