Empirical Likelihood Inference for the Rao‐Hartley‐Cochran Sampling Design

The Hartley‐Rao‐Cochran sampling design is an unequal probability sampling design which can be used to select samples from finite populations. We propose to adjust the empirical likelihood approach for the Hartley‐Rao‐Cochran sampling design. The approach proposed intrinsically incorporates sampling weights, auxiliary information and allows for large sampling fractions. It can be used to construct confidence intervals. In a simulation study, we show that the coverage may be better for the empirical likelihood confidence interval than for standard confidence intervals based on variance estimates. The approach proposed is simple to implement and less computer intensive than bootstrap. The confidence interval proposed does not rely on re‐sampling, linearization, variance estimation, design‐effects or joint inclusion probabilities.     

A class of partially linear transformation models for recurrent gap times

In this article, we propose a general class of partially linear transformation models for recurrent gap time data, which extends the linear transformation models by incorporating non linear covariate effects and includes the partially linear proportional hazards and the partially linear proportional odds models as special cases. Both global and local estimating equations are developed to estimate the parametric and non parametric covariate effects, and the asymptotic properties of the resulting estimators are established. The finite-sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a clinic study on chronic granulomatous disease is provided.     

Rank repeated measures analysis of covariance

When analyzing a response variable at the presence of both factors and covariates, with potentially correlated responses and violated assumptions of the normal residual or the linear relationship between the response and the covariates, rank-based tests can be an option for inferential procedures instead of the parametric repeated measures analysis of covariance (ANCOVA) models. This article derives a rank-based method for multi-way ANCOVA models with correlated responses. The generalized estimating equations (GEE) technique is employed to construct the proposed rank tests. Asymptotic properties of the proposed tests are derived. Simulation studies confirmed the performance of the proposed tests.     

Closed-form likelihood estimation for one type of affine point processes

ABSTRACT

This paper presents a closed-form likelihood approximation for one type of affine point processes widely used in financial credit risk models. We proceed by first conjecturing the concrete series form of the transition density, verifying our postulation and then establishing the related coefficients by means of Kolmogorov equations. The asymptotic properties of the maximum-likelihood estimators (MLEs) are given in the end.     

Comparative Study of Generalized Estimating Equations and Logistic Regressions on Different Sample Sizes and Correlation Levels

In this study, it was aimed to determine accuracy of generalized estimating equations versus logistic regressions on different correlation levels and sample sizes. For this aim, two methods were compared with different sample sizes 10, 25, 50 and 100 and correlation levels 0.0, 0.3, 0.5 and 0.8. Result of this study showed that using generalized estimating equations could be preferred versus logistic regression when the sample size is over than 25 and correlation level is higher than 0.3 on data taken from studies with repeated measurements, but logistic regression could be better when the autocorrelations do not exist.     

A comparison study on modeling of clustered and overdispersed count data for multiple comparisons

Data collected in various scientific fields are count data. One way to analyze such data is to compare the individual levels of the factor treatment using multiple comparisons. However, the measured individuals are often clustered – e.g. according to litter or rearing. This must be considered when estimating the parameters by a repeated measurement model. In addition, ignoring the overdispersion to which count data is prone leads to an increase of the type one error rate. We carry out simulation studies using several different data settings and compare different multiple contrast tests with parameter estimates from generalized estimation equations and generalized linear mixed models in order to observe coverage and rejection probabilities. We generate overdispersed, clustered count data in small samples as can be observed in many biological settings. We have found that the generalized estimation equations outperform generalized linear mixed models if the variance-sandwich estimator is correctly specified. Furthermore, generalized linear mixed models show problems with the convergence rate under certain data settings, but there are model implementations with lower implications exists. Finally, we use an example of genetic data to demonstrate the application of the multiple contrast test and the problems of ignoring strong overdispersion.     

On the use of quasi-likelihood for estimation in hidden-Markov random fields

This paper illustrates the use of quasi-likelihood methods of inference for hidden Markov random fields. These are simple to use and can be employed under circumstances where only the model form and its covariance structure are specified. In particular they can be used to derive the same estimating equations as the E-M algorithm or change of measure methods, which make full distributional assumptions.     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.     

Seemingly unrelated systems of econometric equations

A generalization of Zellner's SUR model is derived for sets of seemingly unrelated systems of econometric equations. The resulting structural form – worked out for a set of Cowles Commission-type simultaneous equations systems – is general enough to include any SUR-type or panel-type specification of systems of econometric equations with contemporaneously correlated errors. Maximum estimation efficiency is obtained by treating all the individual subsystems at once rather than in a subsystem-by-subsystem fashion.