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Department: search.filters.department.Department of MathematicsSubject: search.filters.subject.Statistics

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    On regular embedding of H-designs into G-designs
    (Utilitas Mathematica, 2013) Quattrocchi, Gaetano; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432
    The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-i-design with k blocks, say H-1, H-2, ...H-k is embedded in a G-design if for every H-i, there exists a distinct block, say G(i), in the G-design that embeds H-i. If G(i) are all isomorphic for 1 <= i <= k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.
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    An investigation of new graph invariants related to the domination number of random proximity catch digraphs
    (Springer, 2012) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Proximity catch digraphs (PCDs) are a special type of proximity graphs based on proximity maps which yield proximity regions. PCDs are defined using the relative allocation of points from two or more classes in a region of interest and have applications in various fields. We introduce some auxiliary tools for PCDs and graph invariants related to the domination number of the PCDs and investigate their probabilistic properties. We consider the cases in which the vertices of the PCDs come from uniform and non-uniform distributions in the region of interest. We also provide some of the newly defined proximity maps as illustrative examples.
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    Segregation indices for disease clustering
    (Wiley-Blackwell, 2014) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Spatial clustering has important implications in various fields. In particular, disease clustering is of major public concern in epidemiology. In this article, we propose the use of two distance-based segregation indices to test the significance of disease clustering among subjects whose locations are from a homogeneous or an inhomogeneous population. We derive the asymptotic distributions of the segregation indices and compare them with other distance-based disease clustering tests in terms of empirical size and power by extensive Monte Carlo simulations. The null pattern we consider is the random labeling (RL) of cases and controls to the given locations. Along this line, we investigate the sensitivity of the size of these tests to the underlying background pattern (e.g., clustered or homogenous) on which the RL is applied, the level of clustering and number of clusters, or to differences in relative abundances of the classes. We demonstrate that differences in relative abundances have the highest influence on the empirical sizes of the tests. We also propose various non-RL patterns as alternatives to the RL pattern and assess the empirical power performances of the tests under these alternatives. We observe that the empirical size of one of the indices is more robust to the differences in relative abundances, and this index performs comparable with the best performers in literature in terms of power. We illustrate the methods on two real-life examples from epidemiology. Copyright (c) 2013 John Wiley & Sons, Ltd.
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    On the use of nearest neighbor contingency tables for testing spatial segregation
    (Springer, 2010) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    For two or more classes (or types) of points, nearest neighbor contingency tables (NNCTs) are constructed using nearest neighbor (NN) frequencies and are used in testing spatial segregation of the classes. Pielou's test of independence, Dixon's cell-specific, class-specific, and overall tests are the tests based on NNCTs (i.e., they are NNCT-tests). These tests are designed and intended for use under the null pattern of random labeling (RL) of completely mapped data. However, it has been shown that Pielou's test is not appropriate for testing segregation against the RL pattern while Dixon's tests are. In this article, we compare Pielou's and Dixon's NNCT-tests; introduce the one-sided versions of Pielou's test; extend the use of NNCT-tests for testing complete spatial randomness (CSR) of points from two or more classes (which is called CSR independence, henceforth). We assess the finite sample performance of the tests by an extensive Monte Carlo simulation study and demonstrate that Dixon's tests are also appropriate for testing CSR independence; but Pielou's test and the corresponding one-sided versions are liberal for testing CSR independence or RL. Furthermore, we show that Pielou's tests are only appropriate when the NNCT is based on a random sample of (base, NN) pairs. We also prove the consistency of the tests under their appropriate null hypotheses. Moreover, we investigate the edge (or boundary) effects on the NNCT-tests and compare the buffer zone and toroidal edge correction methods for these tests. We illustrate the tests on a real life and an artificial data set.
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    The full metamorphosis of lambda-fold block designs with block size four into lambda-fold kite systems
    (Utilitas Mathematica Publishing, 2013) N/A; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432
    Let(X,B)be a λ-fold block design with block size 4. If a path of length two is removed from each block of B the resulting collection of kites K is a partial λ-fold kite system(X,K). If the deleted edges can be arranged into a collection of kites D,then(X,K ∪ D)is a λ-fold kite system [5]. Now for each block 6 ∈ B let {P1(6),P 2(b),P3(b)} be a partition of b into paths of length two and define for each i = 1,2,3, sets Ki and Di as follows: for each b ∈ B,put the kite b\Pi(b)in Ki and the two edges belonging to the path Pi(b)in Di. If the edges in Di can be arranged into a collection of kites Di * then Mi =(X,Ki∪Di *)is a λ-fold kite system,called the ith metamorphosis of(X,B). The full metamorphosis is the set of three metamorphoses {M 1,M2,M3}. We give a complete solution of the following problem: for which n and A does there exist a λ-fold block design with block size 4 having a full metamorphosis into a λ-fold kite system?
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    The metamorphosis of lambda-fold block designs with block size four into maximum packings of lambda K-n with kites
    (Util Math Publ Inc, 2005) N/A; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    Let (X, B) be a lambda-fold block design with block size four and define sets B(K) and E(K-4 \ K) as follows: for each block b is an element of B, remove a path of length two, obtain a kite (a triangle with a tail), and place the kites in B(K) and the paths of length 2 in E(K-4 \ K). If we can reassemble the edges belonging to E(K-4 \ K) into a collection of kites E(K) with leave L, then (X, B(K) boolean OR E(K), L) is a packing of lambda K-n with kites. If vertical bar L vertical bar is as small as possible, then (X, B(K) boolean OR E(K), L) is called a metamorphosis of the lambda-fold block design (X, B) into a maximum packing of lambda K-n with kites. In this paper we give a complete solution of the metamorphosis problem for lambda-fold block designs with block size four into a maximum packing of lambda K-n with kites for all lambda. That is, for each lambda we determine the set of all n such that there exists a lambda-fold block design of order n having a metamorphosis into a maximum packing of lambda K-n with kites.
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    Overall and pairwise segregation tests based on nearest neighbor contingency tables
    (Elsevier, 2009) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Multivariate interaction between two or more classes (or species) has important consequences in many fields and may cause multivariate clustering patterns such as spatial segregation or association. The spatial segregation occurs when members of a class tend to be found near members of the same class (i.e., near conspecifics) while spatial association occurs when members of a class tend to be found near members of the other class or classes. These patterns can be studied using a nearest neighbor contingency table (NNCT). The null hypothesis is randomness in the nearest neighbor (NN) structure, which may result from - among other patterns - random labeling (RL) or complete spatial randomness (CSR) of points from two or more classes (which is called the CSR independence, henceforth). New versions of overall and cell-specific tests based on NNCTs (i.e., NNCT-tests) are introduced and compared with Dixon's overall and cell-specific tests and various other spatial clustering methods. Overall segregation tests are used to detect any deviation from the null case, while the cell-specific tests are post hoc pairwise spatial interaction tests that are applied when the overall test yields a significant result. The distributional properties of these tests are analyzed and finite sample performance of the tests are assessed by an extensive Monte Carlo simulation study. Furthermore, it is shown that the new NNCT-tests have better performance in terms of Type I error and power estimates. The methods are also applied on two real life data sets for illustrative purposes. (c) 2008 Elsevier B.V. All rights reserved.
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    A comparison of analysis of covariate-adjusted residuals and analysis of covariance
    (Taylor & Francis Inc, 2009) Goad, Carla L.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Various methods to control the influence of a covariate on a response variable are compared. These methods are ANOVA with or without homogeneity of variances (HOV) of errors and Kruskal-Wallis (K-W) tests on (covariate-adjusted) residuals and analysis of covariance (ANCOVA). Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set ignoring the treatment levels or factors. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and covariate means are equal for all treatments. Empirical size and power performance of the methods are compared by extensive Monte Carlo simulations. We manipulated the conditions such as assumptions of normality and HOV, sample size, and clustering of the covariates. The parametric methods on residuals and ANCOVA exhibited similar size and power when error terms have symmetric distributions with variances having the same functional form for each treatment, and covariates have uniform distributions within the same interval for each treatment. In such cases, parametric tests have higher power compared to the K-W test on residuals. When error terms have asymmetric distributions or have variances that are heterogeneous with different functional forms for each treatment, the tests are liberal with K-W test having higher power than others. The methods on covariate-adjusted residuals are severely affected by the clustering of the covariates relative to the treatment factors when covariate means are very different for treatments. For data clusters, ANCOVA method exhibits the appropriate level. However, such a clustering might suggest dependence between the covariates and the treatment factors, so makes ANCOVA less reliable as well.
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    On the modeling of CO2 EUA and CER prices of EU-ETS for the 2008-2012 period
    (Wiley, 2016) Gürler, Ülkü; Yenigün, Deniz; Berk, Emre; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131
    Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions. One of the most important implications of carbon trading for industrial systems is the risk of uncertainty about the prices of carbon allowance permits traded in the carbon markets. In this paper, we consider stochastic and time series modeling of carbon market prices and provide estimates of the model parameters involved, based on the European Union emissions trading scheme carbon allowances data obtained for 2008-2012 period. In particular, we consider fractional Brownian motion and autoregressive moving average-generalized autoregressive conditional heteroskedastic modeling of the European Union emissions trading scheme data and provide comparisons with benchmark models. Our analysis reveals evidence for structural changes in the underlying models in the span of the years 2008-2012. Data-driven methods for identifying possible change-points in the underlying models are employed, and a detailed analysis is provided. Our analysis indicated change-points in the European Union Allowance (EUA) prices in the first half of 2009 and in the second half of 2011, whereas in the Certified Emissions Reduction (CER) prices three change-points have appeared, in the first half of 2009, the middle of 2011, and in the second half of 2012. These change-points seem to parallel the global economic indicators as well.
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    Class-specific tests of spatial segregation based on nearest neighbor contingency tables
    (Wiley, 2009) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    The spatial interaction between two or more classes might cause multivariate clustering patterns such as segregation or association, which can be tested using a nearest neighbor contingency table (NNCT). The null hypothesis is randomness in the nearest neighbor structure, which may result from random labeling (RL) or complete spatial randomness of points from two or more classes (which is henceforth called CSR independence). We consider Dixon's class-specific segregation test and introduce a new class-specific test, which is a new decomposition of Dixon's overall chi-squared segregation statistic. We analyze the distributional properties and compare the empirical significant levels and power estimates of the tests using extensive Monte Carlo simulations. We demonstrate that the new class-specific tests have comparable performance with the currently available tests based on NNCTs. For illustrative purposes, we use three example data sets and provide guidelines for using these tests.