Joint probability density function estimation by spectral estimate methods

The estimation of probability density functions (PDFs) of a given random variable (r.v.) is involved in topics related to codification, speech or whenever a short record of data is available but a greater amount is needed. Existing methods go from the so-called minimum description-length method, up to others based on the maximisation of the differential entropy imposing constraints on the moments of the r.v. In this paper we propose to estimate a PDF function by means of spectral estimate methods, since the positiveness and the real character of any PDF function allow us to deal with it as a power spectrum density function. Particularly, the minimum variance method is focused on because it can be generalised to multidimensional problems, being used in this paper to estimate the joint-PDF function of a multidimensional r.v.