Gaussian Process Based Bayesian Semiparametric Quantitative Trait Loci Interval Mapping

In linkage analysis, it is often necessary to include covariates such as age or weight to increase power or avoid spurious false positive findings. However, if a covariate term in the model is specified incorrectly (e.g., a quadratic term misspecified as a linear term), then the inclusion of the covariate may adversely affect power and accuracy of the identification of Quantitative Trait Loci (QTL). Furthermore, some covariates may interact with each other in a complicated fashion. We implement semiparametric models for single and multiple QTL mapping. Both mapping methods include an unspecified function of any covariate found or suspected to have a more complex than linear but unknown relationship with the response variable. They also allow for interactions among different covariates. This analysis is performed in a Bayesian inference framework using Markov chain Monte Carlo. The advantages of our methods are demonstrated via extensive simulations and real data analysis

Consistency of error density and distribution function estimators in nonparametric regression

This paper considers the problem of estimating the error density and distribution function in nonparametric regression models. Sufficient conditions are given under which the histogram error density estimator based on nonparametric residuals is uniformly weakly and strongly consistent, and L1-consistent. The uniform consistency with a rate of the nonparametric residual empirical distribution function and the histogram error density estimator is also established.Histogram density estimation Nonparametric residuals Empirical process

Extended Glivenko-Cantelli Theorem in ARCH(p)-time series

In this paper we consider the uniform strong consistency of nonparametric innovation distribution function estimation in ARCH(p)-time series. We obtain the extended Glivenko-Cantelli Theorem for the residual-based empirical distribution function.

A goodness-of-fit test of the errors in nonlinear autoregressive time series models

This paper considers the problem of fitting an error density to the goodness-of-fit test of the errors in a nonlinear autoregressive stationary time series regression model. The test statistic is based on the integrated squared error of the nonparametric error density estimate and the null error density. Without knowing the nonlinear autoregressive function, we can show that the test statistic behaves asymptotically the same as the one based on the true errors.Residuals Error density estimation Stationary process

The L1 strong consistency of ARCH innovation density estimator

In this paper we consider the global property for the innovation density estimator in ARCH time series. For the kernel innovation density estimator based on residuals, we obtain its strong consistency under L1-norm.ARCH-time series Kernel density estimation Strong consistency L1-norm