WIAS Preprint No. 420, (1998)

Asymptotic equivalence of spectral density and regression estimation


  • Golubev, Georgii
  • Nussbaum, Michael

2010 Mathematics Subject Classification

  • 62G07 62G20


  • Stationary Gaussian process, spectral density, Le Cam's distance, asymptotic equivalence, local limit theorem, signal in Gaussian white noise


We consider the statistical experiment given by a sample y(1),...,y(n) of a stationary Gaussian process with an unknown smooth spectral density. Asymptotic equivalence with a nonparametric regression in discrete Gaussian white noise is established. The key is a local limit theorem for an increasing number of empirical covariance coefficients.

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