Browsing by Subject "Random variables"
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Item Open Access Analysis of cross-correlations between financial markets after the 2008 crisis(Elsevier BV, 2013) Sensoy, A.; Yuksel, S.; Erturk, M.We analyze the cross-correlation matrix C of the index returns of the main financial markets after the 2008 crisis using methods of random matrix theory. We test the eigenvalues of C for universal properties of random matrices and find that the majority of the cross-correlation coefficients arise from randomness. We show that the eigenvector of the largest deviating eigenvalue of C represents a global market itself. We reveal that high volatility of financial markets is observed at the same times with high correlations between them which lowers the risk diversification potential even if one constructs a widely internationally diversified portfolio of stocks. We identify and compare the connection and cluster structure of markets before and after the crisis using minimal spanning and ultrametric hierarchical trees. We find that after the crisis, the co-movement degree of the markets increases. We also highlight the key financial markets of pre and post crisis using main centrality measures and analyze the changes. We repeat the study using rank correlation and compare the differences. Further implications are discussed.Item Open Access Detection of compound structures by region group selection from hierarchical segmentations(IEEE, 2016-07) Akçay, H. Gökhan; Aksoy, SelimDetection of compound structures that are comprised of different arrangements of simpler primitive objects has been a challenging problem as commonly used bag-of-words models are limited in capturing spatial information. We have developed a generic method that considers the primitive objects as random variables, builds a contextual model of their arrangements using a Markov random field, and detects new instances of compound structures through automatic selection of subsets of candidate regions from a hierarchical segmentation by maximizing the likelihood of their individual appearances and relative spatial arrangements. In this paper, we extend the model to handle different types of primitive objects that come from multiple hierarchical segmentations. Results are shown for the detection of different types of housing estates in a WorldView-2 image. © 2016 IEEE.Item Open Access An inequality on guessing and its application to sequential decoding(IEEE, 1995) Arıkan, ErdalLet (X,Y) be a pair of discrete random variables with X taking values from a finite set. Suppose the value of X is to be determined, given the value of Y, by asking questions of the form 'is X equal to x?' until the answer is 'yes'. Let G(x|y) denote the number of guesses in any such guessing scheme when X=x, Y=y. The main result is a tight lower bound on nonnegative moments of G(X|Y). As an application, lower bounds are given on the moments of computation in sequential decoding. In particular, a simple derivation of the cutoff rate bound for a single-user channels is obtained, and the previously unknown cutoff rate region of multi-access channels is determined.Item Open Access An inequality on guessing and its application to sequential decoding(Institute of Electrical and Electronics Engineers, 1996-01) Arikan, E.Let (X,Y) be a pair of discrete random variables with X taking one of M possible values, Suppose the value of X is to be determined, given the value of Y, by asking questions of the form "Is X equal to x?" until the answer is "Yes". Let G(x|y) denote the number of guesses in any such guessing scheme when X=x, Y=y. We prove that E[G(X|Y)/sup /spl rho//]/spl ges/(1+lnM)/sup -/spl rho///spl Sigma//sub y/[/spl Sigma//sub x/P/sub X,Y/(x,y)/sup 1/1+/spl rho//]/sup 1+/spl rho// for any /spl rho//spl ges/0. This provides an operational characterization of Renyi's entropy. Next we apply this inequality to the estimation of the computational complexity of sequential decoding. For this, we regard X as the input, Y as the output of a communication channel. Given Y, the sequential decoding algorithm works essentially by guessing X, one value at a time, until the guess is correct. Thus the computational complexity of sequential decoding, which is a random variable, is given by a guessing function G(X|Y) that is defined by the order in which nodes in the tree code are hypothesized by the decoder. This observation, combined with the above lower bound on moments of G(X|Y), yields lower bounds on moments of computation in sequential decoding. The present approach enables the determination of the (previously known) cutoff rate of sequential decoding in a simple manner; it also yields the (previously unknown) cutoff rate region of sequential decoding for multiaccess channels. These results hold for memoryless channels with finite input alphabets.Item Open Access Joint mixability of some integer matrices(Elsevier B.V., 2016) Bellini, F.; Karaşan, O. E.; Pınar, M. Ç.We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row sum the matrix has been termed jointly mixable (see e.g. Haus (2015), Wang and Wang (2015), Wang et al. (2013)). We show that the lack of joint mixability (the joint mixability gap) is not significant, i.e., the gap between the minimum maximal row sum and the maximum minimal row sum is either zero or one for a class of integer matrices including binary and complete consecutive integers matrices. For integer matrices where all entries are drawn from a given set of discrete values, we show that the gap can be as large as the difference between the maximal and minimal elements of the discrete set. The aforementioned result also leads to a polynomial-time approximation algorithm for matrices with restricted domain. Computing the gap for a {0,1,2}-matrix is proved to be equivalent to finding column permutations minimizing the difference between the maximum and minimum row sums. A polynomial procedure for computing the optimum difference by solving the maximum flow problem on an appropriate graph is given. © 2016 Elsevier B.V. All rights reserved.Item Open Access On the Hajek projection for truncated and censored data(Scientific Publishers, 1993) Gürler, Ü.; Wang, J.-L.Large sample properties of the product-limit estimators for truncated or censored data are usually achieved via the empirical cumulative hazard function estimators. Hajek projection of the empirical cumulative hazard function estimator is derived for truncated data and expressed for censored data. It turns out that both projections are asymptotically ni-equivalent but not equal to the respective influence curves. Weak convergences of the empirical cumulative hazard processes are deduced accordingly.