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Volume 3
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Stats, Volume 3, Issue 1 (March 2020) – 7 articles

Cover Story (view full-size image): This article proposes evaluating the distribution of distances between points randomly distributed in a compact set, such as point events generated by a homogeneous Poisson process. The distribution of distances between elements is important in situations where the interaction between elements depends on distance. It involves many disciplines, such as statistical physics, biology, ecology, geography, and networking. After a review of solutions proposed in the literature, this article presents a modern, general, and unified resolution method. The method is then applied to typical compact sets: segments, rectangles, disks, spheres, and hyperspheres. The article also highlights various applications of these results, for example, that variance of distances in hyperspheres tends to zero when the space dimension increases.View this paper.
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16 pages, 5036 KiB  
Article
Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia
by Tomislav Malvić, Josip Ivšinović, Josipa Velić, Jasenka Sremac and Uroš Barudžija
Stats 2020, 3(1), 68-83; https://doi.org/10.3390/stats3010007 - 23 Mar 2020
Cited by 11 | Viewed by 3713
Abstract
Interpolation is a procedure that depends on the spatial and/or statistical properties of the analysed variable(s). It is a particularly challenging task for small datasets, such as in those with less than 20 points of data. This problem is common in subsurface geological [...] Read more.
Interpolation is a procedure that depends on the spatial and/or statistical properties of the analysed variable(s). It is a particularly challenging task for small datasets, such as in those with less than 20 points of data. This problem is common in subsurface geological mapping, i.e., in cases where the data is taken solely from wells. Successful solutions of such mapping problems depend on interpolation methods designed primarily for small datasets and the datasets themselves. Here, we compare two methods, Inverse Distance Weighting and the Modified Shepard’s Method, and apply them to three variables (porosity, permeability, and thickness) measured in the Neogene sandstone hydrocarbon reservoirs (northern Croatia). The results show that cross-validation itself will not provide appropriate map selection, but, in combination with geometrical features, it can help experts eliminate the solutions with low-probable structures/shapes. The Golden Software licensed program Surfer 15 was used for the interpolations in this study. Full article
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12 pages, 863 KiB  
Article
Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data
by Dewi Rahardja
Stats 2020, 3(1), 56-67; https://doi.org/10.3390/stats3010006 - 12 Mar 2020
Cited by 3 | Viewed by 2923
Abstract
In sequential tests, typically a (pairwise) multiple comparison procedure (MCP) is performed after an omnibus test (an overall equality test). In general, when an omnibus test (e.g., overall equality of multiple proportions test) is rejected, then we further conduct a (pairwise) multiple comparisons [...] Read more.
In sequential tests, typically a (pairwise) multiple comparison procedure (MCP) is performed after an omnibus test (an overall equality test). In general, when an omnibus test (e.g., overall equality of multiple proportions test) is rejected, then we further conduct a (pairwise) multiple comparisons or MCPs to determine which (e.g., proportions) pairs the significant differences came from. In this article, via likelihood-based approaches, we acquire three confidence intervals (CIs) for comparing each pairwise proportion difference in the presence of over-reported binomial data. Our closed-form algorithm is easy to implement. As a result, for multiple-sample proportions differences, we can easily apply MCP adjustment methods (e.g., Bonferroni, Šidák, and Dunn) to address the multiplicity issue, unlike previous literatures. We illustrate our procedures to a real data example. Full article
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16 pages, 4196 KiB  
Article
On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study
by Sergio Perez-Melo and B. M. Golam Kibria
Stats 2020, 3(1), 40-55; https://doi.org/10.3390/stats3010005 - 10 Mar 2020
Cited by 14 | Viewed by 3679
Abstract
Ridge regression is a popular method to solve the multicollinearity problem for both linear and non-linear regression models. This paper studied forty different ridge regression t-type tests of the individual coefficients of a linear regression model. A simulation study was conducted to [...] Read more.
Ridge regression is a popular method to solve the multicollinearity problem for both linear and non-linear regression models. This paper studied forty different ridge regression t-type tests of the individual coefficients of a linear regression model. A simulation study was conducted to evaluate the performance of the proposed tests with respect to their empirical sizes and powers under different settings. Our simulation results demonstrated that many of the proposed tests have type I error rates close to the 5% nominal level and, among those, all tests except one have considerable gain in powers over the standard ordinary least squares (OLS) t-type test. It was observed from our simulation results that seven tests based on some ridge estimators performed better than the rest in terms of achieving higher power gains while maintaining a 5% nominal size. Full article
(This article belongs to the Section Computational Statistics)
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6 pages, 749 KiB  
Article
New Equivalence Tests for Hardy–Weinberg Equilibrium and Multiple Alleles
by Vladimir Ostrovski
Stats 2020, 3(1), 34-39; https://doi.org/10.3390/stats3010004 - 05 Feb 2020
Cited by 1 | Viewed by 2549
Abstract
We consider testing equivalence to Hardy–Weinberg Equilibrium in case of multiple alleles. Two different test statistics are proposed for this test problem. The asymptotic distribution of the test statistics is derived. The corresponding tests can be carried out using asymptotic approximation. Alternatively, the [...] Read more.
We consider testing equivalence to Hardy–Weinberg Equilibrium in case of multiple alleles. Two different test statistics are proposed for this test problem. The asymptotic distribution of the test statistics is derived. The corresponding tests can be carried out using asymptotic approximation. Alternatively, the variance of the test statistics can be estimated by the bootstrap method. The proposed tests are applied to three real data sets. The finite sample performance of the tests is studied by simulations, which are inspired by the real data sets. Full article
2 pages, 169 KiB  
Editorial
Acknowledgement to Reviewers of Stats in 2019
by Stats Editorial Office
Stats 2020, 3(1), 32-33; https://doi.org/10.3390/stats3010003 - 19 Jan 2020
Cited by 1 | Viewed by 1604
Abstract
The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not [...] Full article
16 pages, 3185 KiB  
Article
General Fitting Methods Based on Lq Norms and their Optimization
by George Livadiotis
Stats 2020, 3(1), 16-31; https://doi.org/10.3390/stats3010002 - 06 Jan 2020
Cited by 4 | Viewed by 2379
Abstract
The widely used fitting method of least squares is neither unique nor does it provide the most accurate results. Other fitting methods exist which differ on the metric norm can be used for expressing the total deviations between the given data and the [...] Read more.
The widely used fitting method of least squares is neither unique nor does it provide the most accurate results. Other fitting methods exist which differ on the metric norm can be used for expressing the total deviations between the given data and the fitted statistical model. The least square method is based on the Euclidean norm L2, while the alternative least absolute deviations method is based on the Taxicab norm, L1. In general, there is an infinite number of fitting methods based on metric spaces induced by Lq norms. The most accurate, and thus optimal method, is the one with the (i) highest sensitivity, given by the curvature at the minimum of total deviations, (ii) the smallest errors of the fitting parameters, (iii) best goodness of fitting. The first two cases concern fitting methods where the given curve functions or datasets do not have any errors, while the third case deals with fitting methods where the given data are assigned with errors. Full article
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15 pages, 1892 KiB  
Article
Distribution of Distances between Elements in a Compact Set
by Solal Lellouche and Marc Souris
Stats 2020, 3(1), 1-15; https://doi.org/10.3390/stats3010001 - 26 Dec 2019
Cited by 16 | Viewed by 2942
Abstract
In this article, we propose a review of studies evaluating the distribution of distances between elements of a random set independently and uniformly distributed over a region of space in a normed R -vector space (for example, point events generated by a homogeneous [...] Read more.
In this article, we propose a review of studies evaluating the distribution of distances between elements of a random set independently and uniformly distributed over a region of space in a normed R -vector space (for example, point events generated by a homogeneous Poisson process in a compact set). The distribution of distances between individuals is present in many situations when interaction depends on distance and concerns many disciplines, such as statistical physics, biology, ecology, geography, networking, etc. After reviewing the solutions proposed in the literature, we present a modern, general and unified resolution method using convolution of random vectors. We apply this method to typical compact sets: segments, rectangles, disks, spheres and hyperspheres. We show, for example, that in a hypersphere the distribution of distances has a typical shape and is polynomial for odd dimensions. We also present various applications of these results and we show, for example, that variance of distances in a hypersphere tends to zero when space dimension increases. Full article
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