2 problems

The log-average periodogram is considered for Gaussian time series, with covariance matrices that may be positive semidefinite rather than positive definite. Extension conjecture.…

Let $X_1,X_2,\ldots$ be independent and identically distributed random variables, and define … … where $q=\max\{j:0<\omega_j<\pi\}$. Write $\log^+x=\max\{\log x,0\}$ and let $G$ ha…