Aggregating classifiers via Rademacher–Walsh polynomials

Methods are proposed to combine several individual classifiers in order to develop more accurate classification rules. The proposed algorithm uses Rademacher–Walsh polynomials to combine M (≥2) individual classifiers in a nonlinear way. The resulting classifier is optimal in the sense that its misclassification error rate is always less than, or equal to, that of each constituent classifier. A number of numerical examples (based on both real and simulated data) are also given. These examples demonstrate some new, and far-reaching, benefits of working with combined classifiers.     

A class of exponential-type ratio estimators of a general parameter

This paper addresses the problem of estimating a general parameter using information on an auxiliary variable X. We have suggested a class of exponential-type ratio estimators for the parameter and its properties are studied. It is identified that the estimators due to Upadhyaya et al. [Journal of Statistical Theory and Practice (2011), 5(2), 285–302] and Yadav and Kadilar [Revista Columbiana de Estadistica, (2013), 36(1), 145–152] are members of the proposed estimator. We have also shown that the suggested estimator is more efficient than the estimators of Upadhyaya et al. (2011 Upadhyaya, L.N., Singh, H.P., Chatterjee, S., Yadav, R. (2011). Improved ratio and product exponential type estimators. J. Stat. Theo. Pract. 5 (2): 285–302.[Taylor &; Francis Online] , [Google Scholar]) and Yadav and Kadilar (2013 Yadav, S.K., Kadilar, C. (2013). Improved exponential type ratio estimator of population variance. Revis. Colum. de Estadist. 36(1): 145–152. [Google Scholar]). Numerical illustration is provided in support of the present study.     

Mean shift and influence measures in linear measurement error models with stochastic linear restrictions

We present influence diagnostics for linear measurement error models with stochastic linear restrictions using the corrected likelihood of Nakamura in 1990. The case deletion and mean shift outlier models are developed to identify outlying and influential observations. We derive a corrected score test statistic for outlier detection based on mean shift outlier models. The analogs of Cook's distance and likelihood distance are proposed to determine influential observations based on case deletion models. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to evaluate the performance of the proposed estimators based on the mean squares error criterion and the score test statistic. Finally, a numerical example is given to illustrate the theoretical results.     

A goodness of fit test for multilevel survival data

No satisfactory goodness of fit test is available for multilevel survival data which occur when survival data are clustered or hierarchical in nature. Hence the aim of this research is to develop a new goodness of fit test for multilevel survival data and to examine the properties of the newly developed test. Simulation studies were carried out to evaluate the type ? error and the power. The results showed that the type I error holds for every combination tested and that the test is powerful against the alternative hypothesis of nonproportional hazards for all combinations tested.     

Nonparametric Shrinkage Estimation for Aalen's Additive Hazards Model

Aalen's nonparametric additive model in which the regression coefficients are assumed to be unspecified functions of time is a flexible alternative to Cox's proportional hazards model when the proportionality assumption is in doubt. In this paper, we incorporate a general linear hypothesis into the estimation of the time‐varying regression coefficients. We combine unrestricted least squares estimators and estimators that are restricted by the linear hypothesis and produce James‐Stein‐type shrinkage estimators of the regression coefficients. We develop the asymptotic joint distribution of such restricted and unrestricted estimators and use this to study the relative performance of the proposed estimators via their integrated asymptotic distributional risks. We conduct Monte Carlo simulations to examine the relative performance of the estimators in terms of their integrated mean square errors. We also compare the performance of the proposed estimators with a recently devised LASSO estimator as well as with ridge‐type estimators both via simulations and data on the survival of primary billiary cirhosis patients.     

Empirical Uncertain Bayes Methods in Area‐level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area‐level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one‐point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area‐level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson‐gamma and the binomial‐beta, and the normal‐normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well‐known expectation‐maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second‐order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.     

On the construction of optimal experimental designs: a penalty approach

Tn optimal experimental design theory there are well-known situations, in which additional constraints are implied to the design set. These constraints destroy in general the simplex structure of the set of feasible points of the design set. Thus the available iteration procedures for the unrestricted case are no longer applicable.

In this paper a penalty approach is suggested which transforms the restricted problem to the unrestricted case and allows the application of well-known algorithms such as the Fedorov-Wynn-type or the projected gradient procedure.     

On sequential closed testing dose groups with a control

Methods for a sequential test of a dose-response effect in pre-clinical studies are investigated. The objective of the test procedure is to compare several dose groups with a zero-dose control. The sequential testing is conducted within a closed family of one-sided tests. The procedures investigated are based on a monotonicity assumption. These closed procedures strongly control the familywise error rate while providing information about the shape of the dose-responce relationship. Performance of sequential testing procedures are compared via a Monte Carlo simulation study. We illustrae the procedures by application to a real data set.     

Modal non‐linear regression in the presence of Laplace measurement error

In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure.     

An improved alternative estimation procedure for current population mean in presence of positively and negatively correlated auxiliary variables in two-occasion rotation patterns

Abstract

The present study confirms the influential role of a positively and a negatively correlated auxiliary variables in enhancing the precision of estimates of current population mean in two occasion rotation (successive) sampling. Exponential-type estimators of current population mean have been proposed for three different situations: (i) the information on a positively correlated auxiliary variable is readily available on both occasions (ii) the information on a negatively correlated auxiliary variable is readily available on both occasions and (iii) the information on both positively and negatively correlated auxiliary variables are readily available on both the occasions. The characteristics of the proposed estimators have been explored and their efficacious performances are compared with the natural and recent contemporary estimators. Optimum replacement strategies of the proposed estimation procedures have been formulated. Simulation and empirical studies are carried out to justify the proposition of the proposed estimators and appropriate recommendations have been put forward to the survey practitioners.