STATISTICAL PROPERTIES OF LINEAR FRACTAL INTERPOLATION FUNCTIONS FOR RANDOM DATA SETS

Abstract

Let [Formula: see text] be an integer greater than or equal to [Formula: see text] and let [Formula: see text] be numbers with [Formula: see text]. Denote that [Formula: see text] is the interval [Formula: see text] and [Formula: see text] is a set of points. Suppose that [Formula: see text] is a random perturbation of [Formula: see text] for [Formula: see text], and we set [Formula: see text]. Let [Formula: see text] and [Formula: see text] be linear fractal interpolation functions on [Formula: see text] corresponding to the set of points [Formula: see text] and [Formula: see text], respectively. The value [Formula: see text] is random for all [Formula: see text]. In this paper, we show that the expectation of [Formula: see text] is [Formula: see text]. We also establish estimations for the variance of [Formula: see text] and the expectation of [Formula: see text].