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Original Articles

Smoothing With Split Linear Fits

John Alan McDonald Department of Statistics, University of Washington, Seattle, WA, 98195
&
Art B. Owen Department of Statistics, Stanford University, Stanford, CA, 94305
Pages 195-208 | Published online: 23 Mar 2012

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Qianyi Li, Jianbo Li, Yongran Cheng & Riquan Zhang. (2023) Curve fitting and jump detection on nonparametric regression with missing data. Journal of Applied Statistics 50:4, pages 963-983.
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Guo-Xiang Liu, Meng-Meng Wang, Xiu-Li Du, Jin-Guan Lin & Qi-Bing Gao. (2018) Jump-detection and curve estimation methods for discontinuous regression functions based on the piecewise B-spline function. Communications in Statistics - Theory and Methods 47:23, pages 5729-5749.
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Anna Gloria Billé, Roberto Benedetti & Paolo Postiglione. (2017) A two-step approach to account for unobserved spatial heterogeneity. Spatial Economic Analysis 12:4, pages 452-471.
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Wenlin Dai & Tiejun Tong. (2014) Variance estimation in nonparametric regression with jump discontinuities. Journal of Applied Statistics 41:3, pages 530-545.
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JohnH.J. Einmahl & Maria Gantner. (2012) The Half-Half Plot. Technometrics 54:2, pages 138-146.
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L. Desmet & I. Gijbels. (2011) Curve Fitting Under Jump and Peak Irregularities Using Local Linear Regression. Communications in Statistics - Theory and Methods 40:22, pages 4001-4020.
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Jaehee Kim & Jeffrey D. Hart. (2011) A change-point estimator using local Fourier series. Journal of Nonparametric Statistics 23:1, pages 83-98.
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I. Gijbels & A.-C. Goderniaux. (2005) Data-Driven Discontinuity Detection in Derivatives of a Regression Function. Communications in Statistics - Theory and Methods 33:4, pages 851-871.
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I. Gijbels & A-C. Goderniaux. (2004) Bootstrap test for change-points in nonparametric regression. Journal of Nonparametric Statistics 16:3-4, pages 591-611.
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Jochen Einbeck & Göran Kauermann. (2003) Online monitoring with local smoothing methods and adaptive ridging . Journal of Statistical Computation and Simulation 73:12, pages 913-929.
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Peihua Qiu. (2003) A jump-preserving curve fitting procedure based on local piecewise-linear kernel estimation . Journal of Nonparametric Statistics 15:4-5, pages 437-453.
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Ruey-Ching Hwang. (2002) A NEW VERSION OF THE LOCAL CONSTANT M-SMOOTHER. Communications in Statistics - Theory and Methods 31:5, pages 833-848.
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Anestis Antoniadis & Irène Gijbels. (2002) Detecting Abrupt Changes by Wavelet Methods. Journal of Nonparametric Statistics 14:1-2, pages 7-29.
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C.T. Jose & B. Ismail. (2001) Nonparametric inference on jump regression surface. Journal of Nonparametric Statistics 13:6, pages 791-813.
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C.T. Jose & B. Ismall. (1999) Change points in nonparametric regresion functions. Communications in Statistics - Theory and Methods 28:8, pages 1883-1902.
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C.K. Chu, I.K. Glad, F. Godtliebsen & J.S. Marron. (1998) Edge-Preserving Smoothers for Image Processing. Journal of the American Statistical Association 93:442, pages 526-541.
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Peihua Qiu & Brian Yandell. (1998) Local Polynomial Jump-Detection Algorithm in Nonparametric Regression. Technometrics 40:2, pages 141-152.
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Peihua Qiu & Brian Yandell. (1997) Jump Detection in Regression Surfaces. Journal of Computational and Graphical Statistics 6:3, pages 332-354.
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Ja-Yong Koo. (1997) Spline Estimation of Discontinuous Regression Functions. Journal of Computational and Graphical Statistics 6:3, pages 266-284.
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Jianbin Chen & Igor Zurbenko. (1997) Nonparametric boundary detection. Communications in Statistics - Theory and Methods 26:12, pages 2999-3014.
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C. T. Jose & B. Ismail. (1997) Estimation of jump points in nonparametric regression through residual analysis. Communications in Statistics - Theory and Methods 26:11, pages 2583-2607.
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Thomas Lindh & Tomas Lindstrom. (1997) Structural breaks in financial share, savings and growth in OECD: 1960-92. Applied Economics 29:1, pages 33-41.
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C.K. Chu. (1994) Estimation of change-points in a nonparametric regression function through kernel density estimation. Communications in Statistics - Theory and Methods 23:11, pages 3037-3062.
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Peihua Qiu. (1994) Estimation of the number of jumps of the jump regression functions. Communications in Statistics - Theory and Methods 23:8, pages 2141-2155.
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J. S. Wu & C. K. Chu. (1993) Modification for boundary effects and jump points in nonparametric regression. Journal of Nonparametric Statistics 2:4, pages 341-354.
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Peter Hall & D.M. Titterington. (1992) Edge-Preserving and Peak-Preserving Smoothing. Technometrics 34:4, pages 429-440.
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W. Härdle, P. Hall & J.S. Marron. (1992) Regression Smoothing Parameters that are not Far from their Optimum. Journal of the American Statistical Association 87:417, pages 227-233.
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Finbarr O'sullivan. (1987) Comment. Journal of the American Statistical Association 82:400, pages 1051-1055.
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Articles from other publishers (22)

Jaehee Kim. (2022) Multiple change-point estimation in spectral representation. Communications for Statistical Applications and Methods 29:1, pages 807-830.
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Jaehee Kim. (2022) Multiple change-point estimation in spectral representation. Communications for Statistical Applications and Methods 29:1, pages 127-150.
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Yicheng Kang, Yueyong Shi, Yuling Jiao, Wendong Li & Dongdong Xiang. (2021) Fitting jump additive models. Computational Statistics & Data Analysis 162, pages 107266.
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Yicheng Kang, Xiaodong Gong, Jiti Gao & Peihua Qiu. (2019) Errors‐in‐variables jump regression using local clustering. Statistics in Medicine 38:19, pages 3642-3655.
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Zhiming Xia & Peihua Qiu. (2015) Jump information criterion for statistical inference in estimating discontinuous curves. Biometrika 102:2, pages 397-408.
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怡然 李. (2015) A Jump-Preserving Curve Regression Procedure Based on Bilateral Kernel Estimation. Statistical and Application 04:04, pages 335-347.
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Jae-Hee Kim. (2012) Multiple Structural Change-Point Estimation in Linear Regression Models. Communications for Statistical Applications and Methods 19:3, pages 423-432.
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Jib Huh. (2010) Detection of a change point based on local-likelihood. Journal of Multivariate Analysis 101:7, pages 1681-1700.
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Quanxi Shao, Zhanling Li & Zongxue Xu. (2009) Trend detection in hydrological time series by segment regression with application to Shiyang River Basin. Stochastic Environmental Research and Risk Assessment 24:2, pages 221-233.
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Irène Gijbels. (2008) Smoothing and preservation of irregularities using local linear fitting. Applications of Mathematics 53:3, pages 177-194.
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Jung-Huei Lin, Tzu-Kuei Chang & Chih-Kang Chu. (2006) ON STUDY OF A MODIFIED LOCAL CONSTANT $M$-SMOOTHER. Taiwanese Journal of Mathematics 10:6.
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I. R. Sánchez-Borrego, M. D. Martínez-Miranda & A. González-Carmona. (2006) Local linear kernel estimation of the discontinuous regression function. Computational Statistics 21:3-4, pages 557-569.
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W. John Braun & Li-Shan Huang. (2005) Kernel spline regression. Canadian Journal of Statistics 33:2, pages 259-278.
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Irène Gijbels, Peter Hall & Aloïs Kneip. (2016) Interval and band estimation for curves with jumps. Journal of Applied Probability 41:A, pages 65-79.
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Irène Gijbels, Peter Hall & Aloïs Kneip. (2016) Interval and band estimation for curves with jumps. Journal of Applied Probability 41:A, pages 65-79.
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I. Gijbels. 2003. Recent Advances and Trends in Nonparametric Statistics. Recent Advances and Trends in Nonparametric Statistics 183 201 .
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