The normalized importance sampling estimator allows the target density f to be known only up to a multiplicative constant. We indicate how it can be derived by a delta method-based approximation of a Rao-Blackwellized acceptance rejection estimator. Using additional terms in the delta method...

The Asmussen-Kroese Monte Carlo estimators of P(S_n u) and P(S_N u) are known to work well in rare event settings, where S_N is the sum of independent, identically distributed heavy-tailed random variables X_1,...,X_N and N is a non-negative, integer-valued random variable independent of the...

We investigate some estimation and testing issues for a class of high-dimensional near unit root time series models. We first study the asymptotic behavior of the first k largest eigenvalues of the sample covariance matrices of the time series model. Then we propose a new estimator for the...

This paper establishes asymptotic properties for spiked empirical eigenvalues of sample co- variance matrices for high-dimensional data with both cross-sectional dependence and a dependent sample structure. A new finding from the established theoretical results is that spiked empirical...