Bootstrap Inference for Quantile-based Modal Regression

In this article, 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 o...

[1]  P. Good Resampling Methods , 1999, Birkhäuser Boston.

[2]  L. Wasserman,et al.  Nonparametric modal regression , 2014, 1412.1716.

[3]  J. Powell,et al.  Censored regression quantiles , 1986 .

[4]  Dinggang Shen,et al.  Regularized Modal Regression with Applications in Cognitive Impairment Prediction , 2017, NIPS.

[5]  M. Rudelson Random Vectors in the Isotropic Position , 1996, math/9608208.

[6]  Moshe Buchinsky CHANGES IN THE U.S. WAGE STRUCTURE 1963-1987: APPLICATION OF QUANTILE REGRESSION , 1994 .

[7]  Z. Ying,et al.  A resampling method based on pivotal estimating functions , 1994 .

[8]  Cun-Hui Zhang,et al.  Beyond Gaussian approximation: Bootstrap for maxima of sums of independent random vectors , 2017, The Annals of Statistics.

[9]  丸山 徹 Convex Analysisの二,三の進展について , 1977 .

[10]  Runze Li,et al.  Local modal regression , 2012, Journal of nonparametric statistics.

[11]  Q. Shao,et al.  A general bahadur representation of M-estimators and its application to linear regression with nonstochastic designs , 1996 .

[12]  Finite sample inference for quantile regression models , 2009 .

[13]  J. Wellner,et al.  Convergence rates of least squares regression estimators with heavy-tailed errors , 2017, The Annals of Statistics.

[14]  R. Koenker,et al.  Regression Quantiles , 2007 .

[15]  Kengo Kato,et al.  Central limit theorems and bootstrap in high dimensions , 2014, 1412.3661.

[16]  G. C. Kemp,et al.  Regression towards the mode , 2012 .

[17]  Roger Koenker,et al.  Quantile regression 40 years on , 2017 .

[18]  S. Walker,et al.  Bayesian mode regression using mixtures of triangular densities , 2017 .

[19]  Christopher R. Genovese,et al.  Revealing components of the galaxy population through non-parametric techniques , 2008, 0809.2800.

[20]  C. Gutenbrunner,et al.  Regression Rank Scores and Regression Quantiles , 1992 .

[21]  A. Yao,et al.  Non linear parametric mode regression , 2017 .

[22]  David H. Autor,et al.  Trends in U.S. Wage Inequality: Revising the Revisionists , 2008, The Review of Economics and Statistics.

[23]  Richard Williams,et al.  Using the Margins Command to Estimate and Interpret Adjusted Predictions and Marginal Effects , 2012 .

[24]  Susanne M. Schennach,et al.  Instrumental Variable Treatment of Nonclassical Measurement Error Models , 2008 .

[25]  W. Yao,et al.  A New Regression Model: Modal Linear Regression , 2014 .

[26]  Yizong Cheng,et al.  Mean Shift, Mode Seeking, and Clustering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Hirofumi Ohta,et al.  Quantile regression approach to conditional mode estimation , 2018, Electronic Journal of Statistics.

[28]  Kengo Kato,et al.  Some new asymptotic theory for least squares series: Pointwise and uniform results , 2012, 1212.0442.

[29]  Victor Chernozhukov,et al.  Conditional Quantile Processes Based on Series or Many Regressors , 2011, Journal of Econometrics.

[30]  G. Tutz,et al.  Modelling beyond regression functions: an application of multimodal regression to speed–flow data , 2006 .

[31]  Bruce Western,et al.  Unions, Norms, and the Rise in U.S. Wage Inequality , 2011 .

[32]  Kengo Kato,et al.  Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings , 2015, 1502.00352.

[33]  Myoung-jae Lee,et al.  QUADRATIC MODE REGRESSION , 1993 .

[34]  Kengo Kato,et al.  Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications , 2017, Probability Theory and Related Fields.

[35]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[36]  Stephen Portnoy,et al.  Censored Regression Quantiles , 2003 .

[37]  Jun Fan,et al.  A Statistical Learning Approach to Modal Regression , 2017, J. Mach. Learn. Res..

[38]  T. Sager,et al.  Maximum Likelihood Estimation of Isotonic Modal Regression , 1982 .

[39]  Masashi Sugiyama,et al.  Modal Regression via Direct Log-Density Derivative Estimation , 2016, ICONIP.

[40]  M.‐J. Lee,et al.  Semiparametric econometric estimators for a truncated regression model: a review with an extension , 1998 .

[41]  P. Hall On convergence rates of suprema , 1991 .

[42]  John Bound,et al.  The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right? , 1988, Journal of Labor Economics.

[43]  A. Munk,et al.  Non‐parametric confidence bands in deconvolution density estimation , 2007 .

[44]  Naomi S. Altman,et al.  Quantile regression , 2019, Nature Methods.

[45]  Kengo Kato,et al.  Detailed proof of Nazarov's inequality , 2017, 1711.10696.

[46]  José E. Chacón,et al.  The Modal Age of Statistics , 2018, International Statistical Review.

[47]  Prachi Shah,et al.  BMC Bioinformatics Methodology article Comparison of mode estimation methods and application in molecular clock analysis , 2003 .

[48]  J. Krief Semi�?Linear Mode Regression , 2017 .

[49]  Yen-Chi Chen Modal regression using kernel density estimation: A review , 2017, 1710.07004.

[50]  Kengo Kato,et al.  Gaussian approximation of suprema of empirical processes , 2012, 1212.6885.

[51]  R. Koenker Quantile Regression: Name Index , 2005 .

[52]  S. Hedges,et al.  Molecular Evidence for the Early Colonization of Land by Fungi and Plants , 2001, Science.

[53]  Weixin Yao,et al.  Nonparametric and Varying Coefficient Modal Regression , 2016, 1602.06609.

[54]  Martin Raab,et al.  "Balls into Bins" - A Simple and Tight Analysis , 1998, RANDOM.

[55]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[56]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[57]  D. Ruppert,et al.  Trimmed Least Squares Estimation in the Linear Model , 1980 .

[58]  Brian T. Maurer Regression. , 2020, JAAPA : official journal of the American Academy of Physician Assistants.