Full Likelihood Procedure Research Articles

A full likelihood procedure of exchangeable negative binomials for modelling correlated and overdispersed count data

This paper introduces an exchangeable negative binomial distribution resulting from relaxing the independence of the Bernoulli sequence associated with a negative binomial distribution to exchangeability. It is demonstrated that the introduced distribution is a mixture of negative binomial distributions and can be characterized by infinitely many parameters that form a completely monotone sequence. The moments of the distribution are derived and a small simulation is conducted to illustrate the distribution. For data analytic purposes, two methods, truncation and completely-monotone links, are given for converting the saturated distribution of infinitely many parameters to parsimonious distributions of finitely many parameters. A full likelihood procedure is described which can be used to investigate correlated and overdispersed count data common in biomedical sciences and teratology. In the end, the introduced distribution is applied to analyze a real clinical data of burn wounds on patients.

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCHmodel, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

A Full Likelihood Procedure for Analysing Exchangable Binary Data

A full-likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability. The binomial and beta-binomial models are shown to occur as special cases correspondingly, respectively, to the choice of degenerate and beta-mixing distributions. For a finite exchangeable binary sequence of random variables, expressions for the joint distribution, moments, and correlations of all orders are derived. Maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster. In an application to developmental toxicology data analysis, the procedure introduced is compared with a beta-binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose.