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Nonparametric Mixture of Regression Models

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  • Mian Huang
  • Runze Li
  • Shaoli Wang

Abstract

Motivated by an analysis of U.S. house price index (HPI) data, we propose nonparametric finite mixture of regression models. We study the identifiability issue of the proposed models, and develop an estimation procedure by employing kernel regression. We further systematically study the sampling properties of the proposed estimators, and establish their asymptotic normality. A modified EM algorithm is proposed to carry out the estimation procedure. We show that our algorithm preserves the ascent property of the EM algorithm in an asymptotic sense. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed estimation procedure. An empirical analysis of the U.S. HPI data is illustrated for the proposed methodology.

Suggested Citation

  • Mian Huang & Runze Li & Shaoli Wang, 2013. "Nonparametric Mixture of Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 929-941, September.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:929-941
    DOI: 10.1080/01621459.2013.772897
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    Cited by:

    1. Jales, Hugo & Jiang, Boqian & Rosenthal, Stuart S., 2023. "JUE Insight: Using the mode to test for selection in city size wage premia," Journal of Urban Economics, Elsevier, vol. 133(C).
    2. Hoshino Tadao & Yanagi Takahide, 2022. "Estimating marginal treatment effects under unobserved group heterogeneity," Journal of Causal Inference, De Gruyter, vol. 10(1), pages 197-216, January.
    3. Sijia Xiang & Weixin Yao, 2020. "Semiparametric mixtures of regressions with single-index for model based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 261-292, June.
    4. Ye, Mao & Lu, Zhao-Hua & Li, Yimei & Song, Xinyuan, 2019. "Finite mixture of varying coefficient model: Estimation and component selection," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 452-474.
    5. Ahonen, Ilmari & Nevalainen, Jaakko & Larocque, Denis, 2019. "Prediction with a flexible finite mixture-of-regressions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 212-224.
    6. Yu, Jing & Nummi, Tapio & Pan, Jianxin, 2022. "Mixture regression for longitudinal data based on joint mean–covariance model," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    7. Sphiwe B. Skhosana & Salomon M. Millard & Frans H. J. Kanfer, 2023. "A Novel EM-Type Algorithm to Estimate Semi-Parametric Mixtures of Partially Linear Models," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    8. Li, Xiongya & Bai, Xiuqin & Song, Weixing, 2017. "Robust mixture multivariate linear regression by multivariate Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 32-39.
    9. Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 65-87, March.
    10. Wang, Shaoli & Yao, Weixin & Huang, Mian, 2014. "A note on the identifiability of nonparametric and semiparametric mixtures of GLMs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 41-45.
    11. Amico, Mailis & Van Keilegom, Ingrid, 2017. "Cure models in survival analysis," LIDAM Discussion Papers ISBA 2017007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Yanyuan Ma & Shaoli Wang & Lin Xu & Weixin Yao, 2021. "Semiparametric mixture regression with unspecified error distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 429-444, June.
    13. Guannan Liu & Wei Long & Bingduo Yang & Zongwu Cai, 2022. "Semiparametric estimation and model selection for conditional mixture copula models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 287-330, March.
    14. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 745-775, September.
    15. Abbas Khalili & Farhad Shokoohi & Masoud Asgharian & Shili Lin, 2023. "Sparse estimation in semiparametric finite mixture of varying coefficient regression models," Biometrics, The International Biometric Society, vol. 79(4), pages 3445-3457, December.
    16. Sijia Xiang & Weixin Yao, 2018. "Semiparametric mixtures of nonparametric regressions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 131-154, February.
    17. Kien C. Tran & Mike G. Tsionas & Emmanuel Mamatzakis, 2020. "Why fully efficient banks matter? A nonparametric stochastic frontier approach in the presence of fully efficient banks," Empirical Economics, Springer, vol. 58(6), pages 2733-2760, June.
    18. Marina Khismatullina & Michael Vogt, 2022. "Multiscale Comparison of Nonparametric Trend Curves," Papers 2209.10841, arXiv.org.

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