Cumulative α-Jensen–Shannon measure of divergence: Properties and applicationsRiyahi, H.; Baratnia, M.; Doostparast, M.
doi: 10.1080/03610926.2023.2238861pmid: N/A
Abstract The problem of quantifying the distance between distributions arises in various fields, including cryptography, information theory, communication networks, machine learning, and data mining. In this article, the analogy with the cumulative Jensen–Shannon divergence, defined in Nguyen and Vreeken (2015), we propose a new divergence measure based on the cumulative distribution function and call it the cumulative α-Jensen–Shannon divergence, denoted by CJS ( α ) . Properties of CJS ( α ) are studied in detail, and also two upper bounds for CJS ( α ) are obtained. The simplified results under the proportional reversed hazard rate model are given. Various illustrative examples are analyzed.
Hamming distances of tight orthogonal arraysPang, Shanqi; Chen, Mengqian; Zhang, Xiao
doi: 10.1080/03610926.2023.2239395pmid: N/A
Abstract Orthogonal arrays (OAs) are widely applied in the statistical design of experiments. The Hamming distances of OAs play an increasingly important role in various areas; however, it is difficult to use Hamming distances, especially for tight and mixed orthogonal arrays (MOAs). For example, two OAs with the same parameters may have distinct Hamming distances due to their different structures and constructions. In addition, studies on Hamming distances of tight OAs are scant, with the exception of a study indicating that a tight symmetrical OA of strength 2 has a constant Hamming distance. In this article, we calculate Hamming distances for high-strength OAs, including all tight symmetrical OAs of strength 3, 4, and 5. Interestingly, the Hamming distances do not depend on the constructions or structures of the arrays. Additionally, we study the Hamming distances of several classes of MOAs of strength 2 and 3, some of which are not related to the structures of the arrays.
Estimating transition intensity rate on interval-censored data using semi-parametric with EM algorithm approachQian, Chen; Srivastava, Deo Kumar; Pan, Jianmin; Hudson, Melissa M.; Rai, Shesh N.
doi: 10.1080/03610926.2023.2239397pmid: 39100716
Abstract Phase IV clinical trials are designed to monitor long-term side effects of medical treatment. For instance, childhood cancer survivors treated with chest radiation and/or anthracycline are often at risk of developing cardiotoxicity during their adulthood. Often the primary focus of a study could be on estimating the cumulative incidence of a particular outcome of interest such as cardiotoxicity. However, it is challenging to evaluate patients continuously and usually, this information is collected through cross-sectional surveys by following patients longitudinally. This leads to interval-censored data since the exact time of the onset of the toxicity is unknown. Rai et al. computed the transition intensity rate using a parametric model and estimated parameters using maximum likelihood approach in an illness-death model. However, such approach may not be suitable if the underlying parametric assumptions do not hold. This manuscript proposes a semi-parametric model, with a logit relationship for the treatment intensities in two groups, to estimate the transition intensity rates within the context of an illness-death model. The estimation of the parameters is done using an EM algorithm with profile likelihood. Results from the simulation studies suggest that the proposed approach is easy to implement and yields comparable results to the parametric model.
Further results on laws of large numbers for the array of random variables under sub-linear expectationHu, Feng; Fu, Yanan; Gao, Miaomiao; Zong, Zhaojun
doi: 10.1080/03610926.2023.2239400pmid: N/A
Abstract– Motivated by risk measure, super-hedge pricing, and modeling uncertainty in finance, Shige Peng established the theory of sub-linear expectation. In this article, we derive two results of laws of large numbers in the framework of sub-linear expectations. One is the strong law of large numbers for the array of random variables, which satisfies non identical distributed and exponential negatively dependent under sub-linear expectation. The other is the weak law of large numbers for the array of random variables, which satisfies non identical distributed and Φ -negatively dependent under sub-linear expectation. These results include and extend some existing results.
A new method of testing mutual independenceGuo, Xiangyu; Zhu, Fukang
doi: 10.1080/03610926.2023.2239402pmid: N/A
Abstract Testing independence between two or more random variables or random vectors receives a lot of attention in the literature. A new test statistic is proposed based on the consistency of the sample distance multivariance to test mutual independence. The bootstrap method is used to obtain the critical value of the test statistic. The simulation results show that our method performs well in the low-dimensional and large-sample cases and gives reasonable results in some cases where other tests do not work. Three real examples are analyzed to show the usefulness of the new test statistic.
Consistent ridge estimation for replicated ultrastructural measurement error modelsÜstündağ Şiray, Gülesen
doi: 10.1080/03610926.2023.2239403pmid: N/A
Abstract The presence of measurement errors in data and multicollinearity among the explanatory variables have negative effects on the estimation of regression coefficients. Within this respect, the motivation of this article is to examine measurement errors and multicollinearity problems simultaneously. In this paper, by utilizing three different forms of corrected score functions three consistent ridge regression estimators are proposed. Theoretical comparisons of these new estimators are examined by implementing the mean squared error criterion. Large sample properties of these estimators are investigated without assuming any distributional assumption. Two numerical examples are presented using real data sets and also a simulation study is performed. The findings indicate that the newly proposed three estimators outperform the existing estimators by the criterion of mean squared error.
A novel sample variance formula and Sv-plot3 for testing hypothesesWijesuriya, Uditha Amarananda
doi: 10.1080/03610926.2023.2239965pmid: N/A
Abstract Sample variance plots, also called Sv-plots, Sv-plot1 and 2, illustrate the deviations from the sample variance, identifying properties of the distribution. Sv-plot2 is exceptionally appealing in testing hypotheses outperforming both histogram and boxplot. In this work, a novel form of independent deviation is introduced, exploring its properties for normally distributed data. The relationship among these deviations, sample average, and variance is established. Further, a novel formula for sample variance is derived. Besides these results, a statistical plot, Sv-plot3 is innovated, that detects outliers, including characteristics of the data distribution such as symmetry and skewness. Remarkably, Sv-plot3 can also be employed to illustrate testing hypotheses over single and two population means comparable to Sv-plot2. Finally, simulated data with hypothetical examples are utilized for illustrations of Sv-plot3. As an efficient graphical tool, Sv-plot3 competitively contributes an attractive visualization for identifying distributional characteristics and testing hypotheses.