Abstract
We present some upper bounds on the rate of convergence in the central limit theorem for normalized least square estimates (LSE) in a spherical regression model with long range dependence (LRD) stationary errors. The used method is based on the asymptotic analysis of orthogonal expansion of non-linear functionals of homogeneous isotropic Gaussian random fields and on the Kolmogorov distance. The theory have many applications in science for instance in evaluating the COBE data.
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