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A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

  • Xibin Zhang

    ()

  • Robert D. Brooks

    ()

  • Maxwell L. King

    ()

Multivariate kernel regression is an important tool for investigating the relationship between a response and a set of explanatory variables. It is generally accepted that the performance of a kernel regression estimator largely depends on the choice of bandwidth rather than the kernel function. This nonparametric technique has been employed in a number of empirical studies including the state-price density estimation pioneered by Aït-Sahalia and Lo (1998). However, the widespread usefulness of multivariate kernel regression has been limited by the difficulty in computing a data-driven bandwidth. In this paper, we present a Bayesian approach to bandwidth selection for multivariate kernel regression. A Markov chain Monte Carlo algorithm is presented to sample the bandwidth vector and other parameters in a multivariate kernel regression model. A Monte Carlo study shows that the proposed bandwidth selector is more accurate than the rule-of-thumb bandwidth selector known as the normal reference rule according to Scott (1992) and Bowman and Azzalini (1997). The proposed bandwidth selection algorithm is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow-Debreu securities. When applying the proposed method to the S&P 500 index options and the DAX index options, we find that for short-maturity options, the proposed Bayesian bandwidth selector produces an obviously different state-price density from the one produced by using a subjective bandwidth selector discussed in Aït-Sahalia and Lo (1998).

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 11/07.

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Length: 30 pages
Date of creation: Aug 2007
Date of revision:
Handle: RePEc:msh:ebswps:2007-11
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