Fast estimation of matrix exponential spatial models

Lecture 6: Matrix Exponential Spatial models

A Matrix Exponential Spatial Specification

We introduce the matrix exponential as a way of modelling spatially dependent data. The matrix exponential spatial specification simplifies the loglikelihood allowing a closed form solution to the problem of maximum likelihood estimation, and greatly simplifies Bayesian estimation of the model. The matrix exponential spatial specification can produce estimates and inferences similar to those fr...

Fast computation of the matrix exponential for a Toeplitz matrix

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for example as the result of discretizing integral equations with a time invariant kernel. In this case it is not obvious how to take advantage of t...

Whittle Estimation of Exponential Volatility Models

The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Among many models of interest, this class includes one-shock models, such as the EGARCH model of Nelson (1991), and two-shock models, such as the SV model of Taylor (1986). The variable of interest might not have finite fractional moment of an...

Fast Adaptive Estimation of Log-additive Exponential Models in Kullback-leibler Divergence

We study the problem of nonparametric estimation of density functions with aproduct form on the domain4 ={(x1, . . . , xd) ∈ R, 0 ≤ x1 ≤ · · · ≤ xd ≤ 1}. Such densitiesappear in the random truncation model as the joint density function of observations. Theyare also obtained as maximum entropy distributions of order statistics with given marginals.We propose an estimation met...