Note on asymptotic behavior of spatial sign autocovariance matrices

A Note on the Asymptotic Behavior of Conditional Extremes

Suppose (X1,Zl)"'" (Xn,Zn) are LLd. as (X,Z). Let Mn,k be the maximum of all Z. 's for which X. is among the k-nearest neighbors of X=xO' It is shown that M k has the lI , same asymptotic distribution as the maximum of k LLd. copies of the random variable Z given X=xO' Hence, the asymptotic results for Li.d. observations are applicable to this· situation as well. Key' words: nearest neighbor, c...

Banding Sample Autocovariance Matrices of Stationary Processes

We consider estimation of covariance matrices of stationary processes. Under a short-range dependence condition for a wide class of nonlinear processes, it is shown that the banded covariance matrix estimates converge in operator norm to the true covariance matrix with explicit rates of convergence. We also establish the consistency of the estimate of the inverse covariance matrix. These result...

On singular value distribution of large-dimensional autocovariance matrices

Erratum to "Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes"

The covariance structure of spatial Gaussian predictors aka Kriging predictors is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically...

Discussion of “ High - dimensional autocovariance matrices and optimal linear prediction ” ∗ , †

First, we would like to congratulate Prof. McMurry and Prof. Politis for their thought-provoking paper on the optimal linear prediction based on full time series sample (hereafter, referred as [MP15]). [MP15] considered the one-step optimal linear predictor X∗ n+1 = ∑n i=1 φi(n)Xn+1−i of a univariate time series X1, . . . , Xn in the ` 2 sense which is given by the solution of the Yule-Walker e...