Non-Parametric Estimation of Conditional Densities: A New Method

26 Pages Posted: 8 Dec 2016

See all articles by Håkon Otneim

Håkon Otneim

Norwegian School of Economics (NHH) - Department of Business and Management Science

Dag Tjostheim

University of Bergen - Faculty of Mathematics and Natural Sciences

Date Written: December 7, 2016

Abstract

Let X = (X1,...,Xp) be a stochastic vector having joint density function fX(x) with partitions X1 = (X1,...,Xk) and X2 = (Xk 1,...,Xp). A new method for estimating the conditional density function of X1 given X2 is presented. It is based on locally Gaussian approximations, but simplified in order to tackle the curse of dimensionality in multivariate applications, where both response and explanatory variables can be vectors. We compare our method to some available competitors, and the error of approximation is shown to be small in a series of examples using real and simulated data, and the estimator is shown to be particularly robust against noise caused by independent variables. We also present examples of practical applications of our conditional density estimator in the analysis of time series. Typical values for k in our examples are 1 and 2, and we include simulation experiments with values of p up to 6. Large sample theory is established under a strong mixing condition.

Keywords: Conditional density estimation, local likelihood, multivariate data, crossvalidation

JEL Classification: C13, C14, C22

Suggested Citation

Otneim, Håkon and Tjostheim, Dag, Non-Parametric Estimation of Conditional Densities: A New Method (December 7, 2016). NHH Dept. of Business and Management Science Discussion Paper No. 2016/22, Available at SSRN: https://ssrn.com/abstract=2882022 or http://dx.doi.org/10.2139/ssrn.2882022

Håkon Otneim (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

Dag Tjostheim

University of Bergen - Faculty of Mathematics and Natural Sciences ( email )

Norway

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