() and Dag Tjøstheim
Håkon Otneim: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Dag Tjøstheim: Dept. of Mathematics, University of Bergen, Postal: University of Bergen , Department of Mathematics, Johannes Bruns gate 12, N-5008 Bergen, Norway
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.
25 pages, December 7, 2016
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