Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions
Statistics and Computing
Bayesian estimation of quantile distributions
Statistics and Computing
Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Likelihood-free Bayesian inference for α-stable models
Computational Statistics & Data Analysis
Model selection in binary and tobit quantile regression using the Gibbs sampler
Computational Statistics & Data Analysis
Simultaneous adjustment of bias and coverage probabilities for confidence intervals
Computational Statistics & Data Analysis
| Hi-index | 0.03 |
In this paper, we present new multivariate quantile distributions and utilise likelihood-free Bayesian algorithms for inferring the parameters. In particular, we apply a sequential Monte Carlo (SMC) algorithm that is adaptive in nature and requires very little tuning compared with other approximate Bayesian computation algorithms. Furthermore, we present a framework for the development of multivariate quantile distributions based on a copula. We consider bivariate and time series extensions of the g-and-k distribution under this framework, and develop an efficient component-wise updating scheme free of likelihood functions to be used within the SMC algorithm. In addition, we trial the set of octiles as summary statistics as well as functions of these that form robust measures of location, scale, skewness and kurtosis. We show that these modifications lead to reasonably precise inferences that are more closely comparable to computationally intensive likelihood-based inference. We apply the quantile distributions and algorithms to simulated data and an example involving daily exchange rate returns.