Communications in Statistics: Theory and Methods

doi: 10.1080/03610926.2019.1703135pmid: N/A

We, the Author, the Editors and Publishers of Communications in Statistics – Theory and Methods, have retracted the following article:Sungsu Kim (2019) The probable error in the hypothesis test of normal means using a small sample, Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2019.1703135The author has requested to retract this article due to the research presented being invalid. In the article, K1 in (2) is one to one function of the usual tn−1 as shown below. Hence, the tests based on K1 and tn−1 are the same. Likewise, for the two-sample test, K2 in (4) is one to one function of the usual Hence, the tests based on K2 and are the same.There were code-mistakes in obtaining the results in Tables 1–3.We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions.The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as “Retracted.”

Narjis, Ghulam; Shabbir, Javid

doi: 10.1080/03610926.2019.1628992pmid: N/A

AbstractIn this article, we propose a new partial randomized response technique (RRT) model to estimate the mean of the number of persons possessing a rare sensitive attribute using the Poisson distribution. Properties of the proposed partial RRT model have been studied. The utility of proposed partial RRT model under stratification is also explored. Efficiency comparison between proposed partial RRT model is carried out numerically under simple and stratified random sampling.

Grayling, Michael J.; Wason, James M. S.; Mander, Adrian P.

doi: 10.1080/03610926.2019.1628273pmid: 33408437

AbstractWe describe and compare two methods for the group sequential design of two-arm experiments with Poisson distributed data, which are based on a normal approximation and exact calculations respectively. A framework to determine near-optimal stopping boundaries is also presented. Using this framework, for a considered example, we demonstrate that a group sequential design could reduce the expected sample size under the null hypothesis by as much as 44% compared to a fixed sample approach. We conclude with a discussion of the advantages and disadvantages of the two presented procedures.

Li, Huajiang; Zhou, Hong

doi: 10.1080/03610926.2019.1628989pmid: N/A

AbstractWe propose a novel approach named the covering principle to construct multiple testing procedures from the perspective of rejection regions in the sample space, which is different from the closed testing and the partitioning principles working in the parameter space. We prove that multiple testing procedures based on the covering principle strongly control the familywise error rate if the type I error is strongly controlled in each decomposed subfamily. Computer simulation shows that the new method rejects more hypotheses on the primary endpoints in most scenarios compared to both the graphical and the gate-keeping approaches.

Salamanca, Juan Jesús

doi: 10.1080/03610926.2019.1628990pmid: N/A

AbstractWe start with a random variable defined on a complex metric structure. We are interested in obtaining simple tests to determine whether such random variable has a symmetry. More precisely, we consider a Riemannian manifold which admits a symmetry represented by a Killing vector field. In this setting, we take into account a random variable. Our problem is to analyze and test whether such random variable shares the symmetry related to the Killing vector field. In other words, if that random variable possesses such that symmetry. As particular cases, we consider the Euclidean space and the round sphere.

Yang, Yuehan; Yang, Hu

doi: 10.1080/03610926.2019.1628991pmid: N/A

AbstractThis article studies the convergence rates of the adaptive elastic net and proposes a post-selection method. In the low dimensional settings, Zou and Zhou proved the variable selection consistency of the adaptive elastic net. In this article, we show the probability of the adaptive elastic net selecting the wrong variables decays at an exponential rate in the ultra-high dimensional setting. The Irrepresentable condition isn’t necessary according to some appropriate initial estimator. Furthermore, we show that the MSE and bias of the adaptive elastic net may lead to an inferior rate depending on the choice of the tuning parameters. We also prove that there exists a bias of asymptotic normality in the adaptive elastic net. Hence we propose a post-selection procedure, called SSLS (Separate Selection from Least Squares), to improve the bias problem of the adaptive elastic net. It is shown that the SSLS’s bias decays at an exponential rate and it is MSE decays to zero. The variable selection consistency of SSLS implies its asymptotic normality. We show by simulations and financial modeling that the SSLS performs better than the other oracle-like methods.

Zhang, Xuekang; Yi, Haoran; Shu, Huisheng

doi: 10.1080/03610926.2019.1630436pmid: N/A

AbstractThe present article deals with the problem of parametric estimation for certain nonstationary processes driven by α-stable motions. The trajectory fitting method combined with the weighted least squares technique is used to obtain an estimator of the drift parameter. The asymptotic behavior of the weighted trajectory fitting estimator for general weights in non-ergodic case, including consistency and asymptotic distribution.

Boukhari, Fakhreddine

doi: 10.1080/03610926.2019.1630437pmid: N/A

AbstractIn this paper, we establish a weak law of large numbers for a class of weighted sums of random variables introduced by Jajte (2003). The obtained method allows us to deduce a generalized version of the Marcinkiewicz-Zygmund weak law of large numbers and to strengthen several known results, such as those of Gut (2004) and Naderi et al. (2018). Finally, an application to randomly indexed sums is presented.

Ogasawara, Haruhiko

doi: 10.1080/03610926.2019.1630438pmid: N/A

AbstractThe multivariate Markov and multiple Chebyshev inequalities are improved using the partial expectation. The conditions of the strict inequalities between the improved and unimproved bounds of probabilities are given. The known upper bounds of the tail probabilities by the partial moment are derived as special cases of the Markov inequality, whose improved bounds and extensions to multivariate cases using the semicovariances and partial product moment are presented.

Wei, Shengxue; Gan, Xiaoli; Xing, Guodong

doi: 10.1080/03610926.2019.1630439pmid: N/A

AbstractUnder the dependent structure of bivariate Eyraud-Farlie-Gumbel-Morgenstern copula, we present the asymptotics of expected shortfall for portfolio loss as the confidence level tends to one. Additionally, the corresponding asymptotics of spectral risk measure is also given. In order to illustrate the obtained main result, a numerical example and its relevant simulation are carried out.