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Bootstrapping least distance estimator in the multivariate regression model

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  • Jhun, Myoungshic
  • Choi, Inkyung

Abstract

The most popular estimation methods in multivariate linear regression are the multivariate least squares estimation and the multivariate least absolute estimation. Each method repeats its univariate estimation method p, the number of response variables, times. Although they are relatively easy to apply, they do not employ the relationship between response variables. This study considers the multivariate least distance estimator of Bai et al. (1990) that accounts for this relationship. We confirm its relative efficiency with respect to the multivariate least absolute estimator under the multivariate normal distribution and contaminated distribution. However, the asymptotic inference of the multivariate least distance estimator is shown to perform poorly in certain circumstances. We suggest the bootstrap method to infer the regression parameters and confirm its viability using Monte Carlo studies.

Suggested Citation

  • Jhun, Myoungshic & Choi, Inkyung, 2009. "Bootstrapping least distance estimator in the multivariate regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4221-4227, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4221-4227
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    References listed on IDEAS

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    1. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
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    Cited by:

    1. Sooncheol Sohn & Byoung Jung & Myoungshic Jhun, 2012. "Permutation tests using least distance estimator in the multivariate regression model," Computational Statistics, Springer, vol. 27(2), pages 191-201, June.

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