Statistical Methodology最新文献

In this paper, we consider generalized inverted exponential distribution which is capable of modeling various shapes of failure rates and aging criteria. The purpose of this paper is two fold. Based on progressive type-II censored data, first we consider the problem of estimation of parameters under classical and Bayesian approaches. In this regard, we obtain maximum likelihood estimates, and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates under the respective approaches. Second, we consider the problem of prediction of future observations using maximum likelihood predictor, best unbiased predictor, conditional median predictor and Bayes predictor. The associated predictive interval estimates for the censored observations are computed as well. Finally, we analyze two real data sets and conduct a Monte Carlo simulation study to compare the performance of the various proposed estimators and predictors.

In this study a varying-coefficient partially nonlinear model with measurement errors in the nonparametric part is proposed. Based on the corrected profile least-squared estimation methodology, we define the estimates of the unknowns of the current models, and check whether the coefficient functions are a constant or not by using the popular generalized likelihood ratio (GLR) test method. Further, the corresponding asymptotic distribution is established and a bootstrap procedure is also employed to implement the proposed methodology. Simulated and real examples are given to illustrate our proposed methodology.

A flexible class of skew-slash distributions which is a location-scale mixture of skew-elliptically distributed random variable with power of a beta random variable is presented. This family of distributions, which is a generalization of location-scale mixture of normal and beta distributions, contain some existing and important distributions and is appropriate for modeling data with skewness and heavy tail structure. Some distributional properties and the moments of this new family of distributions are obtained. In the special case of location-scale mixture of skew-normal distribution, we estimate the parameters via an EM-type algorithm and a simulation study and an application to real data are provided for illustration. Finally we extend some results to multivariate case.

We derive two new confidence ellipsoids (CEs) and four CE variations for covariate coefficient vectors with nuisance parameters under the seemingly unrelated regression (SUR) model. Unlike most CE approaches for SUR models studied so far, we assume unequal regression coefficients for our two regression models. The two new basic CEs are a CE based on a Wald statistic with nuisance parameters and a CE based on the asymptotic normality of the SUR two-stage unbiased estimator of the primary regression coefficients. We compare the coverage and volume characteristics of the six SUR-based CEs via a Monte Carlo simulation. For the configurations in our simulation, we determine that, except for small sample sizes, a CE based on a two-stage statistic with a Bartlett corrected $(1-\alpha )$ percentile is generally preferred because it has essentially nominal coverage and relatively small volume. For small sample sizes, the parametric bootstrap CE based on the two-stage estimator attains close-to-nominal coverage and is superior to the competing CEs in terms of volume. Finally, we apply three SUR Wald-type CEs with favorable coverage properties and relatively small volumes to a real data set to demonstrate the gain in precision over the ordinary-least-squares-based CE.

The analysis of longitudinal data or repeated measurements is an important and growing area of Statistics. In this context, data come in different formats but typically, they have a hierarchical or multi-level structure including group and subject components, and the main purpose of the analysis is usually to estimate these components from the data. A standard way to perform this estimation is via mixed models. In this paper, we show that the estimated group effects from standard smooth mixed models can deviate systematically from the underlying group mean, leading to wrong conclusions about the data. We then present two ways to avoid such systematic deviations and misinterpretations when fitting flexible mixed models to multi-level data. The first method is a marginal procedure, and the second method is based on the conditional distribution of the subject effects derived from appropriate constraints. Both methods are robust against mis-specification of the covariance structure in the sense that they allow one to resolve the lack of centring found in standard smooth mixed models.

Based on stochastically independent samples with underlying density functions from the same multiparameter exponential family, a weighted version of Matusita’s affinity is applied as test statistic in a homogeneity test of identical densities as well as in a discrimination problem. Asymptotic distributions of the test statistics are stated, and the impact of weights on the deviation of actual and required type I error for finite sample sizes is examined in a simulation study.

In this paper, we derive a measure of discrepancy based on the Gini’s mean difference to test the null hypothesis that two random variables, which are ordered in a variability-type stochastic order, are equally dispersive versus the alternative that one strictly dominates the other. We describe the test, evaluate its performance under a variety of situations and illustrate the procedure with an example using log returns of real data.

The varying coefficient model provides a useful tool for statistical modeling. In this paper, we propose a new procedure for more efficient estimation of its coefficient functions when its errors are serially correlated and modeled as an autoregressive (AR) process. We establish the asymptotic distribution of the proposed estimator and show that it is more efficient than the conventional local linear estimator. Furthermore, we suggest a penalized profile least squares method with the smoothly clipped absolute deviation (SCAD) penalty function to select the order of the AR error process. Simulation evidence shows that significant gains can be achieved in finite samples with the proposed estimation procedure. Moreover, a real data example is given to illustrate the usefulness of the proposed estimation procedure.

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.