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Publication Metadata only 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/AProximity 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.Publication Metadata only Bayesian analysis of doubly stochastic Markov processes in reliability(Cambridge University Press (CUP), 2021) Ay, Atilla; Soyer, Refik; Landon, Joshua; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631Markov processes play an important role in reliability analysis and particularly in modeling the stochastic evolution of survival/failure behavior of systems. The probability law of Markov processes is described by its generator or the transition rate matrix. In this paper, we suppose that the process is doubly stochastic in the sense that the generator is also stochastic. In our model, we suppose that the entries in the generator change with respect to the changing states of yet another Markov process. This process represents the random environment that the stochastic model operates in. In fact, we have a Markov modulated Markov process which can be modeled as a bivariate Markov process that can be analyzed probabilistically using Markovian analysis. In this setting, however, we are interested in Bayesian inference on model parameters. We present a computationally tractable approach using Gibbs sampling and demonstrate it by numerical illustrations. We also discuss cases that involve complete and partial data sets on both processes.Publication Metadata only Dandelion plot: a method for the visualization of R-mode exploratory factor analyses(Springer Heidelberg, 2014) Çene, Erhan; Sedef, Ahmet; Demir, İbrahim; N/A; Manukyan, Artur; PhD Student; Graduate School of Sciences and Engineering; N/AOne of the important aspects of exploratory factor analysis (EFA) is to discover underlying structures in real life problems. Especially, R-mode methods of EFA aim to investigate the relationship between variables. Visualizing an efficient EFA model is as important as obtaining one. A good graph of an EFA should be simple, informative and easy to interpret. A few number of visualization methods exist. Dandelion plot, a novel method of visualization for R-mode EFA, is used in this study, providing a more effective representation of factors. With this method, factor variances and factor loadings can be plotted on a single window. The representation of both positivity and negativity among factor loadings is another strength of the method.Publication Metadata only Directional clustering tests based on nearest neighbour contingency tables(Taylor & Francis Ltd, 2010) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ASpatial interaction between two or more classes or species has important implications in various fields, and might cause multivariate patterns such as segregation or association. Segregation occurs when members of a class or species are more likely to be found near members of the same class or conspecifics; association occurs when members of a class or species are more likely to be found near members of another class or species. The null patterns considered are random labelling and complete spatial randomness (CSR) of points from two or more classes, which is henceforth called CSR independence. The clustering tests based on nearest neighbour contingency tables (NNCTs) that are in use in the literature are two-sided tests. In this article, we consider the directional (i.e. one-sided) versions of the cell-specific NNCT tests and introduce new directional NNCT tests for the two-class case. We analyse the distributional properties and compare the empirical significant levels and empirical power estimates of the tests using extensive Monte Carlo simulations. We demonstrate that the new directional tests have comparable performance with the currently available NNCT tests in terms of empirical size and power. We use an ecological data set for illustrative purposes and provide guidelines for using these NNCT tests.Publication Metadata only Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity(Elsevier, 2013) Saikkonen, Pentti; Department of Economics; Meitz, Mika; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; N/AWe consider maximum likelihood estimation of a particular noninvertible ARMA model with autoregressive conditionally heteroskedastic (ARCH) errors. The model can be seen as an extension to the so-called all-pass models in that it allows for autocorrelation and for more flexible forms of conditional heteroskedasticity. These features may be attractive especially in economic and financial applications. Unlike in previous literature on maximum likelihood estimation of noncausal and/or noninvertible ARMA models and all-pass models, our estimation theory does allow for Gaussian innovations. We give conditions under which a strongly consistent and asymptotically normally distributed solution to the likelihood equations exists, and we also provide a consistent estimator of the limiting covariance matrix.Publication Metadata only New tests of spatial segregation based on nearest neighbour contingency tables(Wiley, 2010) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AThe spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause segregation or association, which are two major types of spatial patterns between the classes. These patterns can be studied using a nearest neighbour contingency table (NNCT) which is constructed using the frequencies of nearest neighbour types. Three new multivariate clustering tests are proposed based on NNCTs using the appropriate sampling distribution of the cell counts in a NNCT. The null patterns considered are random labelling (RL) and complete spatial randomness (CSR) of points from two or more classes. The finite sample performance of these tests are compared with other tests in terms of empirical size and power. It is demonstrated that the newly proposed NNCT tests perform relatively well compared with their competitors and the tests are illustrated using two example data sets.Publication Metadata only 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; 105131Increased 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.Publication Metadata only Optimal pricing and production policies of a make-to-stock system with fluctuating demand(Cambridge University Press (CUP), 2009) Gayon, Jean-Philippe; Talay-Degirmenci, Isilay; Department of Industrial Engineering; Department of Industrial Engineering; Karaesmen, Fikri; Örmeci, Lerzan; Faculty Member; Faculty Member; Department of Industrial Engineering; College of Engineering; College of Engineering; 3579; 32863We study the effects of different pricing strategies available to a production-inventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are investigated: static pricing, for which only one price is used at all times, environment-dependent pricing, for which price changes with the environment, and dynamic pricing, for which price depends on both the current environment and the stock level. The objective is to find an optimal replenishment and pricing policy under each of these strategies. This article presents some structural properties of optimal replenishment policies and a numerical study that compares the performances of these three pricing strategies.Publication Metadata only Weak convergence to a matrix stochastic integral with stable processes(Cambridge Univ Press, 1997) Department of Economics; Caner, Mehmet; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; N/AThis paper generalizes the univariate results of Chan and Tran (1989, Econometric Theory 5, 354-362) and Phillips (1990, Econometric Theory 6, 44-62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(1) for a random walk with independent and identically distributed errors and for I(1) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. The limit laws are represented by functionals of a stable process. A semiparametric correction is used in order to asymptotically eliminate the ''bias'' term in the limit law. These results are also an extension of the multivariate limit theory for square-integrable disturbances derived by Phillips and Durlauf (1986, Review of Economic Studies 53, 473-495). Potential applications include tests for multivariate unit roots and cointegration.