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.