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Automatic spectral density estimation for random fields on a lattice via bootstrap. (English) Zbl 1203.62163

Summary: We consider the nonparametric estimation of spectral densities for second-order stationary random fields on a \(d\)-dimensional lattice. We discuss some drawbacks of standard methods and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. We prove the uniform consistency and study the uniform asymptotic distribution when the optimal smoothing number is estimated from the sampled data.

MSC:

62M15 Inference from stochastic processes and spectral analysis
62M40 Random fields; image analysis
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics

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