Sampling Designs for Estimation of a Random Process

(3) the nonparametric case where the macroscopic mean structure m(t) is unknown. N ( t ) is the small-scale random structure which models the temporal dependence and has zero mean and known covariance function R(t, 5 ) = E N ( t ) N ( s ) . The centered process N ( t ) is assumed to have no quadratic mean derivative and the functions m(t) and f , ( t ) are of comparable smoothness with the microscopic purely random part N ( t ) , specifically, m(t) and fi(t) are of the form J,' R(t, s) l l (s)ds .