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Modal regression using kernel density estimation: a review. (English) Zbl 07910820


MSC:

62-08 Computational methods for problems pertaining to statistics

References:

[1] Attaoui, S. (2014). On the nonparametric conditional density and mode estimates in the single functional index model with strongly mixing data. Sankhya A, 76(2), 356-378. · Zbl 1307.62089
[2] Burman, P., & Polonik, W. (2009). Multivariate mode hunting: Data analytic tools with measures of significance. Journal of Multivariate Analysis, 100(6), 1198-1218. · Zbl 1159.62032
[3] Calonico, S., Cattaneo, M. D., & Farrell, M. H. (2017). On the effect of bias estimation on coverage accuracy in nonparametric inference. Journal of the American Statistical Association. In press.
[4] Chacón, J., & Duong, T. (2013). Data‐driven density derivative estimation, with applications to nonparametric clustering and bump hunting. Electronic Journal of Statistics, 7, 499-532. · Zbl 1337.62067
[5] Chaouch, M., Laïb, N., & Louani, D. (2017). Rate of uniform consistency for a class of mode regression on functional stationary ergodic data. Statistical Methods & Applications, 26(1), 19-47. · Zbl 1397.62146
[6] Chen, Y.‐C. (2017). A tutorial on kernel density estimation and recent advances. Biostatistics & Epidemiology, 1(1), 161-187.
[7] Chen, Y.‐C., Genovese, C. R., Tibshirani, R. J., & Wasserman, L. (2016). Nonparametric modal regression. The Annals of Statistics, 44(2), 489-514. · Zbl 1338.62113
[8] Chen, Y.‐C., Genovese, C. R., & Wasserman, L. (2016). A comprehensive approach to mode clustering. Electronic Journal of Statistics, 10(1), 210-241. · Zbl 1332.62200
[9] Chen, Y.‐C., Genovese, C. R., & Wasserman, L. (2017a). Density level sets: Asymptotics, inference, and visualization. Journal of the American Statistical Association, 112, 1684-1696.
[10] Chen, Y.‐C., Genovese, C. R., & Wasserman, L. (2017b). Statistical inference using the morse‐smale complex. Electronic Journal of Statistics, 11(1), 1390-1433. · Zbl 1362.62078
[11] Cheng, Y. (1995). Mean shift, mode seeking, and clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(8), 790-799.
[12] Collomb, G., Härdle, W., & Hassani, S. (1986). A note on prediction via estimation of the conditional mode function. Journal of Statistical Planning and Inference, 15, 227-236. · Zbl 0614.62045
[13] Comaniciu, D., & Meer, P. (2002). Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(5), 603-619.
[14] Cook, J. R., & Stefanski, L. A. (1994). Simulation‐extrapolation estimation in parametric measurement error models. Journal of the American Statistical Association, 89(428), 1314-1328. · Zbl 0810.62028
[15] Dabo‐Niang, S., & Laksaci, A. (2010). Note on conditional mode estimation for functional dependent data. Statistica, 70(1), 83-94. · Zbl 1453.62441
[16] Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the sems algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39(1), 1-38. · Zbl 0364.62022
[17] Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7(1), 1-26. · Zbl 0406.62024
[18] Einbeck, J., & Tutz, G. (2006). Modelling beyond regression functions: An application of multimodal regression to speed-flow data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 55(4), 461-475. · Zbl 1490.62098
[19] Fan, J., Yao, Q., & Tong, H. (1996). Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika, 83(1), 189-206. · Zbl 0865.62026
[20] Fan, J., & Yim, T. H. (2004). A crossvalidation method for estimating conditional densities. Biometrika, 91(4), 819-834. · Zbl 1078.62032
[21] Fukunaga, K., & Hostetler, L. (1975). The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Transactions on Information Theory, 21(1), 32-40. · Zbl 0297.62025
[22] Genovese, C. R., Perone‐Pacifico, M., Verdinelli, I., & Wasserman, L. (2014). Nonparametric ridge estimation. The Annals of Statistics, 42(4), 1511-1545. · Zbl 1310.62045
[23] Gersho, A., & Gray, R. M. (2012). Vector quantization and signal compression (Vol. 159). Berlin/Heidelberg, Germany: Springer Science & Business Media.
[24] Good, I., & Gaskins, R. (1980). Density estimation and bump‐hunting by the penalized likelihood method exemplified by scattering and meteorite data. Journal of the American Statistical Association, 75(369), 42-56. · Zbl 0432.62024
[25] Graf, S., & Luschgy, H. (2007). Foundations of quantization for probability distributions. New York, NY: Springer.
[26] Hall, P., Minnotte, M. C., & Zhang, C. (2004). Bump hunting with non‐gaussian kernels. The Annals of Statistics, 32(5), 2124-2141. · Zbl 1056.62049
[27] Ho, C.‐s., Damien, P., & Walker, S. (2017). Bayesian mode regression using mixtures of triangular densities. Journal of Econometrics, 197(2), 273-283. · Zbl 1422.62105
[28] Huang, M., Li, R., & Wang, S. (2013). Nonparametric mixture of regression models. Journal of the American Statistical Association, 108(503), 929-941. · Zbl 06224977
[29] Huang, M., & Yao, W. (2012). Mixture of regression models with varying mixing proportions: A semiparametric approach. Journal of the American Statistical Association, 107(498), 711-724. · Zbl 1261.62036
[30] Hyndman, R. J., Bashtannyk, D. M., & Grunwald, G. K. (1996). Estimating and visualizing conditional densities. Journal of Computational and Graphical Statistics, 5(4), 315-336.
[31] Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457-481. · Zbl 0089.14801
[32] Kemp, G. C., & Silva, J. S. (2012). Regression towards the mode. Journal of Econometrics, 170(1), 92-101. · Zbl 1443.62100
[33] Khardani, S., Lemdani, M., & Saïd, E. O. (2010). Some asymptotic properties for a smooth kernel estimator of the conditional mode under random censorship. Journal of the Korean Statistical Society, 39(4), 455-469. · Zbl 1294.62105
[34] Khardani, S., Lemdani, M., & Saïd, E. O. (2011). Uniform rate of strong consistency for a smooth kernel estimator of the conditional mode for censored time series. Journal of Statistical Planning and Inference, 141(11), 3426-3436. · Zbl 1221.62063
[35] Khardani, S., & Yao, A. F. (2017). Non linear parametric mode regression. Communications in Statistics‐Theory and Methods, 46(6), 3006-3024. · Zbl 1395.62195
[36] Krief, J. M. (2017). Semi‐linear mode regression. The Econometrics Journal, 20(2), 149-167. · Zbl 07565913
[37] Lee, M.‐J. (1989). Mode regression. Journal of Econometrics, 42(3), 337-349. · Zbl 0692.62092
[38] Lee, M.‐J. (1993). Quadratic mode regression. Journal of Econometrics, 57(1-3), 1-19. · Zbl 0776.62055
[39] Lee, M.‐J., & Kim, H. (1998). Semiparametric econometric estimators for a truncated regression model: A review with an extension. Statistica Neerlandica, 52(2), 200-225. · Zbl 0946.62096
[40] Li, J., Ray, S., & Lindsay, B. G. (2007). A nonparametric statistical approach to clustering via mode identification. Journal of Machine Learning Research, 8(8), 1687-1723. · Zbl 1222.62076
[41] Lindsay, B. G. (1995). Mixture models: Theory, geometry and applications. NSF‐CBMS regional conference series in probability and statistics (pp. i-163). JSTOR. · Zbl 1163.62326
[42] Loubes, J.‐M., & Pelletier, B. (2017). Prediction by quantization of a conditional distribution. Electronic Journal of Statistics, 11(1), 2679-2706. · Zbl 1366.62098
[43] Manski, C. (1991). Regression. Journal of Economic Literature, 29(1), 34-50.
[44] Nadaraya, E. A. (1964). On estimating regression. Theory of Probability & Its Applications, 9(1), 141-142. · Zbl 0136.40902
[45] Ould‐Saïd, E. (1993). Estimation non paramétrique du mode conditionnel. application à la prévision. Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 316(9), 943-947. · Zbl 0774.62040
[46] Ould‐Saïd, E. (1997). A note on ergodic processes prediction via estimation of the conditional mode function. Scandinavian Journal of Statistics, 24(2), 231-239. · Zbl 0879.60026
[47] Ould‐Saïd, E., & Cai, Z. (2005). Strong uniform consistency of nonparametric estimation of the censored conditional mode function. Nonparametric Statistics, 17(7), 797-806. · Zbl 1079.62051
[48] Quandt, R. E. (1972). A new approach to estimating switching regressions. Journal of the American Statistical Association, 67(338), 306-310. · Zbl 0237.62047
[49] Quandt, R. E., & Ramsey, J. B. (1978). Estimating mixtures of normal distributions and switching regressions. Journal of the American Statistical Association, 73(364), 730-738. · Zbl 0401.62024
[50] Rinaldo, A., & Wasserman, L. (2010). Generalized density clustering. The Annals of Statistics, 38(5), 2678-2722. · Zbl 1200.62066
[51] Sager, T. W., & Thisted, R. A. (1982). Maximum likelihood estimation of isotonic modal regression. The Annals of Statistics, 10(3), 690-707. · Zbl 0491.62035
[52] Sasaki, H., Ono, Y., and Sugiyama, M. (2016). Modal regression via direct log‐density derivative estimation. International conference on neural information processing (pp. 108-116). Springer.
[53] Scott, D. W. (2015). Multivariate density estimation: Theory, practice, and visualization. Hoboken, NJ: John Wiley & Sons. · Zbl 1311.62004
[54] Sheather, S. J. (2004). Density estimation. Statistical Science, 19(4), 588-597. · Zbl 1100.62558
[55] Silverman, B. W. (1986). Density estimation for statistics and data analysis. London, England: Chapman and Hall. · Zbl 0617.62042
[56] Tarter, M. E., & Lock, M. D. (1993). Model‐free curve estimation (Vol. 56). Boca Raton, FL: CRC Press.
[57] Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 411-423. · Zbl 0979.62046
[58] Wang, X., Chen, H., Shen, D., and Huang, H. (2017). Cognitive impairment prediction in Alzheimer’s disease with regularized modal regression. Advances in neural information processing systems (pp. 1447-1457).
[59] Watson, G. S. (1964). Smooth regression analysis. Sankhyā: The Indian Journal of Statistics, Series A, 26(4), 359-372. · Zbl 0137.13002
[60] Wu, C. J. (1983). On the convergence properties of the em algorithm. The Annals of Statistics, 11(1), 95-103. · Zbl 0517.62035
[61] Yao, W., & Li, L. (2014). A new regression model: modal linear regression. Scandinavian Journal of Statistics, 41(3), 656-671. · Zbl 1309.62119
[62] Yao, W., Lindsay, B. G., & Li, R. (2012). Local modal regression. Journal of Nonparametric Statistics, 24(3), 647-663. · Zbl 1254.62059
[63] Zhou, H., & Huang, X. (2016). Nonparametric modal regression in the presence of measurement error. Electronic Journal of Statistics, 10(2), 3579-3620. · Zbl 1357.62185
[64] Zhou, H., & Huang, X. (2017). Bandwidth selection for nonparametric modal regression. Communications in Statistics - Simulation and Computation. In press.
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