Estimating parameters in the presence of many nuisance parameters

This paper considers estimation of parameters for high-dimensional time series with the presence of many nuisance parameters. In particular we are interested in data consisting of p time series of length n, with p to be as large or even larger than n. Here we consider the composite-likelihood estimation and the profile quasi-likelihood estimation. The asymptotic properties of these methodologies are investigated. Simulations are used to illustrate our both of these methods and explore the performance of these methods.