Communications in Statistics: Theory and Methods

Sikolya, Kinga; Baran, Sándor

doi: 10.1080/03610926.2019.1645855pmid: N/A

AbstractPhysics, chemistry, biology or finance are just some examples out of the many fields where complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modeling. They play role e.g. in the description of the motion of a charged test particle in a constant magnetic field or in the study of rotating waves in time-dependent reaction diffusion systems, whereas Kolmogorov used such a process to model the so-called Chandler wobble, the small deviation in the Earth’s axis of rotation. A common problem in these applications is deciding how to choose a set of a sample locations in order to predict a random process in an optimal way. We study the optimal design problem for the prediction of a complex OU process on a compact interval with respect to integrated mean square prediction error (IMSPE) and entropy criteria. We derive the exact forms of both criteria, moreover, we show that optimal designs based on entropy criterion are equidistant, whereas the IMSPE based ones may differ from it. Finally, we present some numerical experiments to illustrate selected cases of optimal designs for small number of sampling locations.

Agami, Sarit; Adler, Robert J.

doi: 10.1080/03610926.2019.1615091pmid: N/A

AbstractTopological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence diagrams. In an earlier article we proposed a parametric representation for the probability distributions of persistence diagrams, and based on it provided a method for their replication. Since the typical situation for big data is that only one persistence diagram is available, these replications allow for conventional statistical inference, which, by its very nature, requires some form of replication. In the current paper we continue this analysis, and further develop its practical statistical methodology, by investigating a wider class of examples than treated previously.

Zhang, Erhua; Wu, Jilin

doi: 10.1080/03610926.2019.1609038pmid: N/A

AbstractThis article proposes a nonparametric test for structural changes in linear regression models that allows for serial correlation, autoregressive conditional heteroskedasticity and time-varying variance in error terms. The test requires no trimming of the boundary region near the end points of the sample period, and requires no prior information on the alternative, what it requires is the transformed OLS residuals under the null hypothesis. We show that the test has a limiting standard normal distribution under the null hypothesis, and is powerful against single break, multiple breaks and smooth structural changes. The Monte Carlo experiment is conducted to highlight the merits of the proposed test relative to other popular tests for structural changes.

Liu, Yang; Zhu, Lin; Liu, Guanfu; Li, Huapeng

doi: 10.1080/03610926.2019.1609039pmid: N/A

AbstractIn continuous-time capture-recapture experiments, individual heterogeneity has a large effect on the capture probability. To account for the heterogeneity, we consider an individual covariate, which is categorical and subject to missing. In this article, we develop a general model to summarize three kinds of missing mechanisms, and propose a maximum likelihood estimator of the abundance. A likelihood ratio confidence interval of the abundance is also proposed. We illustrate the proposed methods by simulation studies and a real data example of a bird species prinia subflava in Hong Kong.

Li, Yuying; Xu, Xiaozhu; Zhang, Haifeng

doi: 10.1080/03610926.2019.1609516pmid: N/A

AbstractIn this paper, we investigate the bases and dimension in finitely generated subsemimodules over commutative semirings. First, we give a sufficient condition for each basis of generated subsemimodule W to have the same number of elements. Particularly, in a cancellative and yoked semiring we show that the dimension of W is well-defined, and there exists a subsemimodule W such that Then we present a series of related properties of free sets in a free generated subsemimodule. Finally, we mainly study some properties of range and kernel of linear transformation for semimodules M, discuss the construction of range and kernel in detail, and present some conditions that the formula in classical linear algebra holds.

Bhushan, Shashi; Pandey, Shailja

doi: 10.1080/03610926.2019.1609518pmid: N/A

AbstractThe present study is an attempt to equip a strategy with a cost-effective computational approach when non response is present under two occasion sampling. We have applied our computational cost strategy over Choudhary et al. (2004)’s non response setup for fixed precision and evaluated cost. In addition, we have also computed variance for some fixed cost. We have discussed the aforementioned procedure for three cases as when there is non response present on both occasions, first occasion and second occasion. A numerical illustration is demonstrated for validation of improved cost methodology where we also work out with optimum unmatched or matched fraction while Choudhary et al. (2004) do not provide the direct optimal result.

Khalili, Atefeh; Eskandari, Farzad

doi: 10.1080/03610926.2019.1609519pmid: N/A

AbstractIn this paper we introduce continuous tree mixture model that is the mixture of undirected graphical models with tree structured graphs and is considered as multivariate analysis with a non parametric approach. We estimate its parameters, the component edge sets and mixture proportions through regularized maximum likalihood procedure. Our new algorithm, which uses expectation maximization algorithm and the modified version of Kruskal algorithm, simultaneosly estimates and prunes the mixture component trees. Simulation studies indicate this method performs better than the alternative Gaussian graphical mixture model. The proposed method is also applied to water-level data set and is compared with the results of Gaussian mixture model.

Thavaneswaran, Aerambamoorthy; Paseka, Alex; Frank, Julieta

doi: 10.1080/03610926.2019.1610443pmid: N/A

AbstractIn this paper, using estimating function approach, a new optimal volatility estimator is introduced and based on the recursive form of the estimator a data-driven generalized EWMA model for value at risk (VaR) forecast is proposed. An appropriate data-driven model for volatility is identified by the relationship between absolute deviation and standard deviation for symmetric distributions with finite variance. It is shown that the asymptotic variance of the proposed volatility estimator is smaller than that of conventional estimators and is more appropriate for financial data with larger kurtosis. For IBM, Microsoft, Apple stocks and SP 500 index the proposed method is used to identify the model, estimate the volatility, and obtain minimum mean square error(MMSE) forecasts of VaR.

Malela-Majika, J.C.; Rapoo, E.M; Mukherjee, A.; Graham, M.A.

doi: 10.1080/03610926.2019.1612914pmid: N/A

AbstractNonparametric statistical process monitoring schemes are robust alternatives to traditional parametric process monitoring schemes, especially when the assumption of normality is invalid or when we do not have enough information about the underlying process distribution. In this paper, we propose to improve the well-known precedence scheme using the 2-of-(h + 1) supplementary runs-rules (where is a nonzero positive integer). The in-control and out-of-control performances of the proposed control schemes are thoroughly investigated using both Markov chain and simulation based approaches. We find that the proposed schemes outperform their competitors in many cases. A real-life example is given to illustrate the design and implementation of the proposed schemes.

Roy, Anuradha; Klein, Daniel

doi: 10.1080/03610926.2019.1612915pmid: N/A

AbstractA new parametric hypothesis test of mean interval for interval-valued data set, which can deal with massive information contained in nowadays massive data “Big data” sets, is proposed. An approach using an orthogonal transformation is introduced to obtain an equivalent hypothesis test of mean interval in terms of the mid-point and mid-range of the interval-valued variable. The new test is very efficient in small interval-valued sample scenarios. Some simulation studies are conducted for the investigation of the sample size and the power of test. The performance of the proposed test is illustrated with two real-life examples.