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New estimation and inference procedures for a single-index conditional distribution model

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  • Chiang, Chin-Tsang
  • Huang, Ming-Yueh

Abstract

This article employs a more flexible single-index regression model to characterize the conditional distribution. The pseudo least integrated squares approach is proposed to estimate the index coefficients. As shown in the numerical results, our estimator outperforms the existing ones in terms of the mean squared error. Moreover, we provide the generalized cross-validation criteria for bandwidth selection and utilize the frequency distributions of weighted bootstrap analogues for the estimation of asymptotic variance and the construction of confidence intervals. With a defined residual process, a test rule is built to check the correctness of an applied single-index conditional distribution model. To tackle the problem of sparse variables, a multi-stage adaptive Lasso algorithm is developed to enhance the ability of identifying significant variables. All of our procedures are found to be easily implemented, numerically stable, and highly adaptive to a variety of data structures. In addition, we assess the finite sample performances of the proposed estimation and inference procedures through extensive simulation experiments. Two empirical examples from the house-price study in Boston and the environmental study in New York are further used to illustrate applications of the methodology.

Suggested Citation

  • Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:271-285
    DOI: 10.1016/j.jmva.2012.04.003
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    References listed on IDEAS

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    Cited by:

    1. Weiyu Li & Valentin Patilea, 2018. "A dimension reduction approach for conditional Kaplan–Meier estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 295-315, June.
    2. Li, Weiyu & Patilea, Valentin, 2017. "A new minimum contrast approach for inference in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 47-59.
    3. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear-Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 396-424, June.
    4. Shu Yang & Yunshu Zhang, 2023. "Multiply robust matching estimators of average and quantile treatment effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 235-265, March.
    5. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    6. Chin-Tsang Chiang & Shao-Hsuan Wang & Ming-Yueh Huang, 2018. "Versatile estimation in censored single-index hazards regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 523-551, June.
    7. Shih‐Wei Chen & Chin‐Tsang Chiang, 2018. "General single‐index survival regression models for incident and prevalent covariate data and prevalent data without follow‐up," Biometrics, The International Biometric Society, vol. 74(3), pages 881-890, September.

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