Estimation of structural mean breaks for long-memory data sets

In long-memory data sets such as the realized volatilities of financial assets, a sequential test is developed for the detection of structural mean breaks. The long memory, if any, is adjusted by fitting an HAR (heterogeneous autoregressive) model to the data sets and taking the residuals. Our test consists of applying the sequential test of Bai and Perron [Estimating and testing linear models with multiple structural changes. Econometrica. 1998;66:47–78] to the residuals. The large-sample validity of the proposed test is investigated in terms of the consistency of the estimated number of breaks and the asymptotic null distribution of the proposed test. A finite-sample Monte-Carlo experiment reveals that the proposed test tends to produce an unbiased break time estimate, while the usual sequential test of Bai and Perron tends to produce biased break times in the case of long memory. The experiment also reveals that the proposed test has a more stable size than the Bai and Perron test. The proposed test is applied to two realized volatility data sets of the S&P index and the Korea won-US dollar exchange rate for the past 7 years and finds 2 or 3 breaks, while the Bai and Perron test finds 8 or more breaks.     

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.     

Letter to the editor comments on Groparu-Cojocaru and Doray (2013)

Although estimating the five parameters of an unknown Generalized Normal Laplace (GNL) density by minimizing the distance between the empirical and true characteristic functions seems appealing, the approach cannot be advocated in practice. This conclusion is based on extensive numerical simulations in which a fast minimization procedure delivers deceiving estimators with values that are quite far away from the truth. These findings can be predicted by the very large values obtained for the true asymptotic variances of the estimators of the five parameters of the true GNL density.     

A probabilistic clustering method for data elements with normal distributed attributes

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.     

Designing a multiple state repetitive group sampling plan based on the coefficient of variation

A multiple state repetitive group sampling (MSRGS) plan is developed on the basis of the coefficient of variation (CV) of the quality characteristic which follows a normal distribution with unknown mean and variance. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which satisfies the given producer's risk and consumer's risk at the same time and minimizes the average sample number required for inspection. The advantages of the proposed MSRGS plan over the existing sampling plans are discussed. Finally an example is given to illustrate the proposed plan.     

Bootstrap approach to test the homogeneity of order restricted mean vectors when the covariance matrices are unknown

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are unknown, arbitrary positive definite and unequal are considered. This problem of testing has been studied to some extent, for example, by Kulatunga and Sasabuchi (1984 Kulatunga, D. D. S., Sasabuchi, S. (1984). A test of homogeneity of mean vectors against multivariate isotonic alternatives. Mem Fac Sci, Kyushu Univ Ser A Mathemat 38:151–161. [Google Scholar]) when the covariance matrices are known and also Sasabuchi et al. (2003 Sasabuchi, S., Tanaka, K., Tsukamodo, T. (2003). Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Annals of Statistics. 31(5):1517–1536.[Web of Science ®] , [Google Scholar]) and Sasabuchi (2007 Sasabuchi, S. (2007). More powerful tests for homogeneity of multivariate normal mean vectors under an order restriction. Sankhya 69(4):700–716. [Google Scholar]) when the covariance matrices are unknown but common. In this paper, a test statistic is proposed and because of the main advantage of the bootstrap test is that it avoids the derivation of the complex null distribution analytically, a bootstrap test statistic is derived and since the proposed test statistic is location invariance the bootstrap p-value defined logical and some steps are presented to estimate it. Our numerical studies via Monte Carlo simulation show that the proposed bootstrap test can correctly control the type I error rates. The power of the test for some of the p-dimensional normal distributions is computed by Monte Carlo simulation. Also, the null distribution of test statistic is estimated using kernel density. Finally, the bootstrap test is illustrated using a real data.     

Bayesian prediction of order statistics with fixed and random sample sizes based on k-record values from Pareto distribution

In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here.     

Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman–Morgan test of homogeneity of two variances. The bias and mean square error of the estimator are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max–min criterion.     

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.