The covariance function estimation based on the constrained B-spline smoothing method

Abstract

Covariance functions play a key role in describing signal time-domain characteristics and spatial correlation structures. In recent years, the nonparametric estimation of covariance functions has been studied extensively.However, the positive definiteness cannot be guaranteed for most nonparametric covariance function estimations. In order to overcome the difficulties, in the context of stationary random processes, this paper first studies the asymptotic properties of the unconstrained B-spline covariance function estimator, based on which, the asymptotic 性质 of the constrained B-spline covariance estimator is established. Numerical results of the simulation experiments indicate that the proposed constrained B-spline estimator has an excellent performance of the positive definiteness and AMSE (average mean squared error).Finally, the proposed positive definite covariance estimator is computed for the Canadian temperature data and the Australian electricity demands data.