Functional regression of continuous state distributions
In this paper, we consider a regression model to study the distributional relationship between economic variables. Unlike the classical regression dealing exclusively with mean relationship, our model can be used to analyze the entire dependent structure in distribution. Technically, we treat density functions as random elements and represent the regression relationship as a compact linear operator in the Hilbert spaces of square integrable functions. We propose a consistent estimation procedure for our model, and develop a test to investigate the dependent structure of moments. An empirical example is provided to illustrate how our methodology can be implemented in practical applications.
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- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Joon Y. Park, 2003.
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Econometric Society, vol. 71(6), pages 1845-1895, November.
- Joon Y. Park, 2000. "Bootstrap Unit Root Tests," Econometric Society World Congress 2000 Contributed Papers 1587, Econometric Society.
- Park, Joon, 2002. "Bootstrap Unit Root Tests," Working Papers 2003-04, Rice University, Department of Economics.
- Mas, André, 2007. "Weak convergence in the functional autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1231-1261, July. Full references (including those not matched with items on IDEAS)
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