Estimating SUR Tobit Model while errors are gaussian scale mixtures: with an application to high frequency financial data

This paper examines multivariate Tobit system with Scale mixture disturbances. Three estimation methods, namely Maximum Simulated Likelihood, Expectation Maximization Algorithm and Bayesian MCMC simulators, are proposed and compared via generated data experiments. The chief finding is that Bayesian approach outperforms others in terms of accuracy, speed and stability. The proposed model is also applied to a real data set and study the high frequency price and trading volume dynamics. The empirical results confirm the information contents of historical price, lending support to the usefulness of technical analysis. In addition, the scale mixture model is also extended to sample selection SUR Tobit and finite Gaussian regime mixtures.Tobit; Gaussian mixtures; Bayesian

Statistical post-processing of hydrological forecasts using Bayesian model averaging

Accurate and reliable probabilistic forecasts of hydrological quantities like runoff or water level are beneficial to various areas of society. Probabilistic state-of-the-art hydrological ensemble prediction models are usually driven with meteorological ensemble forecasts. Hence, biases and dispersion errors of the meteorological forecasts cascade down to the hydrological predictions and add to the errors of the hydrological models. The systematic parts of these errors can be reduced by applying statistical post-processing. For a sound estimation of predictive uncertainty and an optimal correction of systematic errors, statistical post-processing methods should be tailored to the particular forecast variable at hand. Former studies have shown that it can make sense to treat hydrological quantities as bounded variables. In this paper, a doubly truncated Bayesian model averaging (BMA) method, which allows for flexible post-processing of (multi-model) ensemble forecasts of water level, is introduced. A case study based on water level for a gauge of river Rhine, reveals a good predictive skill of doubly truncated BMA compared both to the raw ensemble and the reference ensemble model output statistics approach.Comment: 19 pages, 6 figure

Mixed Marginal Copula Modeling

This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density of the observations with respect to a mixed measure. The treatment is quite general, although we focus focus on mixtures of Gaussian and Archimedean copulas. The inference is Bayesian with the estimation carried out by Markov chain Monte Carlo. We illustrate the methodology and algorithms by applying them to estimate a multivariate income dynamics model.Comment: 46 pages, 8 tables and 4 figure

Data augmentation for models based on rejection sampling

We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea, which seems to be missing in the literature, is a simple scheme to instantiate the rejected proposals preceding each data point. The resulting joint probability over observed and rejected variables can be much simpler than the marginal distribution over the observed variables, which often involves intractable integrals. We consider three problems, the first being the modeling of flow-cytometry measurements subject to truncation. The second is a Bayesian analysis of the matrix Langevin distribution on the Stiefel manifold, and the third, Bayesian inference for a nonparametric Gaussian process density model. The latter two are instances of problems where Markov chain Monte Carlo inference is doubly-intractable. Our experiments demonstrate superior performance over state-of-the-art sampling algorithms for such problems.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1311.090

Parameter Estimation for Data with Lower Limit of Detection Values under the Truncated Model – EM Solutions

Computing unbiased parameter estimates from a distribution using a sample with observations appearing below a lower limit of detection (LLOD) can be challenging. Frequently, LLOD observations are excluded from calculations for parameter estimates, or the LLOD observations are replaced with arbitrary values (LLOD, LLOD/2, LLOD/√2) prior to the calculations. Despite the frequent use of these simple approaches, the approaches are known to provide biased parameter estimates. Alternative approaches include implementing a left truncation or left censoring approach. In the first dissertation aim, we will explore and establish a general theoretical relationship between accurately estimating parameters under left truncated and left censored models. Estimation methods under both models require iterative algorithms. The left truncation approach is applied through an Expectation-Maximization (EM) algorithm. While the left censoring approach is implemented by the Newton-Raphson method. We conclude in the first aim that the left truncation and left censoring approaches yielded equivalent parameter estimates. Computationally, we favored the left truncation approach that is implemented through an EM algorithm. The left truncation approach for estimating parameters is utilized in the remaining aims. In the second aim of this dissertation, we propose an EM algorithm for estimating parameters from a normal distribution when there are multiple LLOD values present. The third aim includes solutions to an EM algorithm for estimating bivariate normal distribution parameters. In the third aim, the data under the left truncation approach can be categorized into 24 scenarios. The construction of the EM algorithm includes the scenarios. All dissertation aims are motivated by toxicology and serology data collected in the Systemic Lupus Erythematosus in Gullah Health study