Owen (1988) showed that the non-parametric empirical likelihood ratio under a linear constrain has an asymptotic chi-square distribution, same as in the paramet-ric case. This fact can be used to form (non-parametric, asymptotic) conndence intervals. We suggest here to use the non-parametric version of the Pearson's chi-square statistic instead of the likelihood ratio to form conndence interval...

We consider nonlinear models with an independent variable that is measured with error. The measurement error can be correlated with the true value, i.e. the measurement error is allowed to be nonclassical. We show that we can use a control variate estimator to estimate the parameters of interest. If we are prepared to make an assumption of the joint distribution of the first-stage and measureme...

We consider estimation of linear functionals of the error distribution for two regression models: parametric and nonparametric, and for two types of errors: independent of the covariate and centered (type I), and conditionally centered given the covariate (type II). We show that the residual-based empirical estimators for the nonparametric type I model remain efficient in the type II model. For...

Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is ...

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem. The performance of the res...

This paper presents new biostatistical methods for the analysis of microbiome data based on a fully parametric approach using all the data. The Dirichlet-multinomial distribution allows the analyst to calculate power and sample sizes for experimental design, perform tests of hypotheses (e.g., compare microbiomes across groups), and to estimate parameters describing microbiome properties. The us...

drop plate technique has a priority and preference compared with the spread plate procedure, because of less time, quantity of media, effort requirement, little incubator space, and less labor intensive. the objective of this research was to compare the accuracy and fidelity of drop plate method vs. spread plate method by parametric and nonparametric statistical tests. for bacterial enumeration...

Bayesian semi-parametric inference is considered for a log-linear model. This model consists of a parametric component for the regression coeecients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coeecients and a mixture-of-Dirichlet-processes prior on the unknown error distribution. A Markov ch...

In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. Through this copula we can extend the Marshall-Olkin distribution in order to construct several bivariate survival functions. The cumulative distrib...