An Application of the Orthogonal Series Estimators in the Classification Of Mixed Variables

Suppose we have two general populations π 1 , π 2 . Each object belonging to the population π i , i = 1, 2 is characterized by a random vector X ′ = ( Z ′, Y ′), where Z is discrete and Y is continuous. On a certain element which is a member of a one of the two populations a realization π′ 0 =( z ′ 0 , y ′ 0 ) of the random vector X has been observed and we want to classify that element. One of the possible methods of doing it is to estimate the density functions of X in π 1 and π 2 and construct an estimated classification rule. In this paper the density estimates based on the orthogonal series (Hall, 1983) will be employed and the classification rule will be examined on a practical example.