Non linear parametric mode regression

Khardani, Salah; Yao, Anne Françoise

doi:10.1080/03610926.2014.1002940

Cited by 18 publications

(8 citation statements)

References 26 publications

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“…Starting from the pioneering work of Sager and Thisted (1982), there is now a large literature on modal regression. There are two major approaches to estimating the conditional mode comparable to our method; one is linear modal regression where the conditional mode is assumed to be linear in covariates (Lee, 1989(Lee, , 1993Kemp and Santos-Silva, 2012;Yao and Li, 2014), and the other is nonparametric estimation (Yao et al, 2012;Chen et al, 2016); see also Lee and Kim (1998); Manski (1991); Einbeck and Tutz (2006); Sasaki et al (2016); Ho et al (2017); Khardani and Yao (2017); Krief (2017) for alternative methods including semiparametric and Bayesian estimation. Lee (1989Lee ( , 1993 assume symmetry of the error distribution to derive limit theorems for their proposed estimators, but the symmetry assumption implies that the conditional mean, median, and mode coincide, thereby significantly reducing the complexity of estimating the conditional mode.…”

Section: Literature Reviewmentioning

confidence: 99%

Bootstrap inference for quantile-based modal regression

Zhang¹,

Kato²,

Ruppert³

2020

Preprint

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In this paper, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop a novel bootstrap method, which we call the pivotal bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the pivotal * Tao Zhang is partially supported by NSF grant DMS-1952306.

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Section: Literature Reviewmentioning

confidence: 99%

Bootstrap inference for quantile-based modal regression

Zhang¹,

Kato²,

Ruppert³

2020

Preprint

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“…, x n ] T . The optimization problem (26) reduces to the following linear programming problem: min u,v∈R n ,β∈R d…”

Section: (16)mentioning

confidence: 99%

Quantile regression approach to conditional mode estimation

Ota¹,

Kato²,

Hara³

2019

Electron. J. Statist.

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In this paper, we consider estimation of the conditional mode of an outcome variable given regressors. To this end, we propose and analyze a computationally scalable estimator derived from a linear quantile regression model and develop asymptotic distributional theory for the estimator. Specifically, we find that the pointwise limiting distribution is a scale transformation of Chernoff's distribution despite the presence of regressors. In addition, we consider analytical and subsampling-based confidence intervals for the proposed estimator. We also conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimator together with the analytical and subsampling confidence intervals. Finally, we apply the proposed estimator to predicting the net hourly electrical energy output using Combined Cycle Power Plant Data.Date: The first arXiv version:

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“…Parametric unimodal regression forms estimators using Equation ( 7) or its generalizations (Kemp & Silva, 2012;Khardani & Yao, 2017;Krief, 2017;Lee, 1989Lee, , 1993Lee & Kim, 1998;Manski, 1991;Yao & Li, 2014). Parameters estimated through the maximizing criterion in Equation ( 7) are equivalent to those obtained through maximum likelihood estimation.…”

Section: Estimating Unimodal Regressionmentioning

confidence: 99%

Modal regression using kernel density estimation: A review

Chen

2018

WIREs Computational Stats

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We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating the relationship between a response variable and its covariates. Specifically, modal regression summarizes the interactions between the response variable and covariates using the conditional mode or local modes. We first describe the underlying model of modal regression and its estimators based on kernel density estimation. We then review the asymptotic properties of the estimators and strategies for choosing the smoothing bandwidth. We also discuss useful algorithms and similar alternative approaches for modal regression, and propose future direction in this field. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Density Estimation

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Non linear parametric mode regression

Cited by 18 publications

References 26 publications

Bootstrap inference for quantile-based modal regression

Bootstrap inference for quantile-based modal regression

Quantile regression approach to conditional mode estimation

Modal regression using kernel density estimation: A review

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