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An optimization interpretation of integration and back‐fitting estimators for separable nonparametric models

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  • J. P. Nielsen
  • O. B. Linton

Abstract

We provide an optimization interpretation of both back‐fitting and integration estimators for additive nonparametric regression. We find that the integration estimator is a projection with respect to a product measure. We also provide further understanding of the back‐fitting method.

Suggested Citation

  • J. P. Nielsen & O. B. Linton, 1998. "An optimization interpretation of integration and back‐fitting estimators for separable nonparametric models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 217-222.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:1:p:217-222
    DOI: 10.1111/1467-9868.00120
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    1. Linton, Oliver & Mammen, Enno & Nielsen, Jens Perch & Tanggaard, Carsten, 1998. "Estimating yield curves by Kernel smoothing methods," SFB 373 Discussion Papers 1999,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Fei Liu & Jiti Gao & Yanrong Yang, 2020. "Time-Varying Panel Data Models with an Additive Factor Structure," Monash Econometrics and Business Statistics Working Papers 42/20, Monash University, Department of Econometrics and Business Statistics.
    3. Linton, Oliver & Mammen, Enno & Nielsen, Jans Perch & Tanggaard, Carsten, 2001. "Yield curve estimation by kernel smoothing methods," Journal of Econometrics, Elsevier, vol. 105(1), pages 185-223, November.
    4. Graciela Boente & Alejandra Martínez, 2017. "Marginal integration M-estimators for additive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 231-260, June.
    5. Lawrence Dacuycuy, 2006. "Explaining male wage inequality in the Philippines: non-parametric and semiparametric approaches," Applied Economics, Taylor & Francis Journals, vol. 38(21), pages 2497-2511.
    6. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    7. Abe, Makoto & Boztuæg, Yasemin & Hildebrandt, Lutz, 2000. "Investigation of the stochastic utility maximization process of consumer brand choice by semiparametric modeling," SFB 373 Discussion Papers 2000,84, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Nathalie Chèze & Jean-Michel Poggi & Bruno Portier, 2003. "Partial and Recombined Estimators for Nonlinear Additive Models," Statistical Inference for Stochastic Processes, Springer, vol. 6(2), pages 155-197, May.
    9. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    10. Degui Li & Oliver Linton & Zudi Lu, 2012. "A Flexible Semiparametric Model for Time Series," Monash Econometrics and Business Statistics Working Papers 17/12, Monash University, Department of Econometrics and Business Statistics.
    11. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    12. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    13. Makoto Abe & Yasemin Boztug & Lutz Hildebrandt, 2004. "Investigating the competitive assumption of Multinomial Logit models of brand choice by nonparametric modeling," Computational Statistics, Springer, vol. 19(4), pages 635-657, December.
    14. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.

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