Statistical Methodology最新文献

For comparison of two experimental treatments with a placebo under an incomplete block crossover design, we develop the weighted-least-squares estimator (WLSE) and the conditional maximum likelihood estimator (CMLE) of the relative treatment effects in Poisson frequency data. We further develop the interval estimator based on the WLSE, the interval estimator based on the CMLE, the interval estimator based on the conditional-likelihood-ratio test and the interval estimator based on the exact conditional distribution. Using Monte Carlo simulations, we find that all interval estimators developed here can perform well in a variety of situations. The exact interval estimator derived here can be especially of use when both the number of patients and the mean number of event occurrences are small in a trial. We use the data taken as part of a double-blind randomized crossover trial comparing salbutamol and salmeterol with a placebo with respect to the number of exacerbations in asthma patients to illustrate the use of these estimators.

A new stochastic order called dynamic cumulative residual quantile entropy (DCRQE) order is established. Some characterizations of the new order are investigated. Closure and reversed closure properties of the DCRQE order are obtained. Applications of the DCRQE ordering in characterizing the proportional hazard rate model and the $k$-record values model are considered.

In medical diagnostics, the ROC curve is the graph of sensitivity against 1-specificity as the diagnostic threshold runs through all possible values. The ROC curve and its associated summary indices are very useful for the evaluation of the discriminatory ability of biomarkers/diagnostic tests with continuous measurements. Among all summary indices, the area under the ROC curve (AUC) is the most popular diagnostic accuracy index, which has been extensively used by researchers for biomarker evaluation and selection. Sometimes, taking the actual measurements of a biomarker is difficult and expensive, whereas ranking them without actual measurements can be easy. In such cases, ranked set sampling based on judgment order statistics would provide more representative samples yielding more accurate estimation. In this study, Gaussian kernel is utilized to obtain a nonparametric estimate of the AUC. Asymptotic properties of the AUC estimates are derived based on the theory of U-statistics. Intensive simulation is conducted to compare the estimates using ranked set samples versus simple random samples. The simulation and theoretical derivation indicate that ranked set sampling is generally preferred with smaller variances and mean squared errors (MSE). The proposed method is illustrated via a real data analysis.

Latent class analysis is used to group categorical data into classes via a probability model. Model selection criteria then judge how well the model fits the data. When addressing incomplete data, the current methodology restricts the imputation to a single, pre-specified number of classes. We seek to develop an entropy-based model selection criterion that does not restrict the imputation to one number of clusters. Simulations show the new criterion performing well against the current standards of AIC and BIC, while a family studies application demonstrates how the criterion provides more detailed and useful results than AIC and BIC.

Designing cluster trials depends on the knowledge of the intracluster correlation coefficient. To overcome the issue of parameter dependence, Bayesian designs are proposed for two level models with and without covariates. These designs minimize the variance of the treatment contrast under certain cost constraints. A pseudo Bayesian design approach is advocated that integrates and averages the objective function over a prior distribution of the intracluster correlation coefficient. Theoretical results on the Bayesian criterion are noted when the intracluster correlation follows a uniform distribution. Two data sets based on educational surveys conducted in schools are used to illustrate the proposed methodology.

In this paper we compare the domains of attraction of limit laws of intermediate order statistics under power normalization with those of limit laws of intermediate order statistics under linear normalization. As a result of this comparison, we obtain necessary and sufficient conditions for a univariate distribution function to belong to the domain of attraction for each of the possible limit laws of intermediate order statistics under power normalization.

In this paper, we introduce a stationary first-order integer-valued autoregressive process with geometric–Poisson marginals. The new process allows negative values for the series. Several properties of the process are established. The unknown parameters of the model are estimated using the Yule–Walker method and the asymptotic properties of the estimator are considered. Some numerical results of the estimators are presented with a brief discussion. Possible application of the process is discussed through a real data example.

For estimating a lower restricted parametric function in the framework of Marchand and Strawderman (2006), we show how $(1-\alpha )\times 100\%$ Bayesian credible intervals can be constructed so that the frequentist probability of coverage is no less than $1-\frac{3\alpha }{2}$. As in Marchand and Strawderman (2013), the findings are achieved through the specification of the spending function of the Bayes credible interval and apply to an “equal-tails” modification of the HPD procedure among others. Our results require a logconcave assumption for the distribution of a pivot, and apply to estimating a lower bounded normal mean with known variance, and to further examples include lower bounded scale parameters from Gamma, Weibull, and Fisher distributions, with the latter also applicable to random effects analysis of variance.

The aim of this paper is to propose procedures that test statistical hypotheses locally, that is, assess the validity of a model in a specific domain of the data. In this context, the one and two sample problems will be discussed. The proposed tests are based on local divergences which are defined in such a way as to quantify the divergence between probability distributions locally, in a specific area of the joint domain of the underlined models. The theoretical results are exemplified using simulations and two real datasets.

Integer-valued time series analysis offers various applications in biomedical, financial, and environmental research. However, existing works usually assume no or constant over-dispersion. In this paper, we propose a new model for time series of counts, the autoregressive conditional negative binomial model that has a time-varying conditional autoregressive mean function and heteroskedasticity. The location and scale parameters of the negative binomial distribution are flexible in the proposed set-up, inducing dynamic over-dispersion. We adopt Bayesian methods with a Markov chain Monte Carlo sampling scheme to estimate model parameters and utilize deviance information criterion for model comparison. We conduct simulations to investigate the estimation performance of this sampling scheme for the proposed negative binomial model. To demonstrate the proposed approach in modelling time-varying over-dispersion, we consider two types of criminal incidents recorded by New South Wales (NSW) Police Force in Australia. We also fit the autoregressive conditional Poisson model to these two datasets. Our results demonstrate that the proposed negative binomial model is preferable to the Poisson model.