NONPARAMETRIC-ESTIMATION OF GENERALIZED COVARIANCES BY MODELING ONLINE DATA

Structural analysis of data displaying trends may be performed with th e help of generalized increments, the variance of these increments bri ng a function of a generalized covariance. Generalized covariances are estimated primarily by parametric methods (i. e., methods searching f or the best coefficients of a predetermined function), bur also may be completed by one known nonparametric alternative. In this paper, a ne w nonparametric method is proposed. It is founded on the following pri nciples: (1) least-squares residues are generalized increments; and (2 ) the generalized covariance is not a unique function, bur a family of functions (the system is indeterminate). The method is presented in a general context of a k order trend in R(d), although the full solutio n is given only for k = 1 in R'. In R', higher order trends may be dev eloped easily with the equations included in this paper. For higher di mensions in space, the problem is more complex, but a research approac h is proposed. The method is tested on soil pH data and compared to a parametric and nonparametric method.