Asymptotic equivalence of locally stationary processes and bivariate Gaussian white noise
局部平稳过程与二维高斯白噪声的渐近等价性
We consider a general class of statistical experiments, in which an n-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be well-approximable in a linear space of lower dimension Kn with eigenvalues uniformly bounded away from zero and infinity. We prove asymptotic equivalence of this experiment and a class of Kn-dimensional Gaussian models with informative expectation in Le…