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The sequential uniform law of large numbers
배종식,김성연 대한수학회 2006 대한수학회보 Vol.43 No.3
LetZn (s;f) = n1 P [ns ]i=1 (f(Xi) Pf) be the sequen-tial empirical process based on the independent and identically dis-tributed random variables. We prove that convergence problemsof sup(s;f) jZn (s;f)j to zero boil down to those of supf jZn (1;f)j.We employ Ottaviani's inequality and the complete convergence toestablish, under bracketing entropy with the second moment, thealmost sure convergence of sup(s;f) jZn (s;f)j to zero.
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The second central limit theorem for martingale difference arrays
배종식,전두배,Shlomo Levental 대한수학회 2014 대한수학회보 Vol.51 No.2
In Bae et al. [2], we have considered the uniform CLT for the martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes majorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.
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Uniform asymptotics in the empirical mean residual life process
배종식,김성은 대한수학회 2006 대한수학회지 Vol.43 No.2
In [5], Csorgo and Zitikis exposed the strong uniform-over-[0 , \infty ) consistency, and weak uniform-over-[0 , \infty) approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Csorgo and Zitikis [5].
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The uniform local asymptotic normality
배종식,김성연 대한수학회 2003 대한수학회보 Vol.40 No.3
We investigate a uniform local asymptotic normality for likelihoodratio processes based on an independent and identicallydistributed local asymptotic problem. Our tool is an empiricalprocess theory.
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Two-step LS-SVR for censored regression
배종식,황창하,심주용 한국데이터정보과학회 2012 한국데이터정보과학회지 Vol.23 No.2
This paper deals with the estimations of the least squares support vector regression when the responses are subject to randomly right censoring. The estimation is performed via two steps - the ordinary least squares support vector regression and the least squares support vector regression with censored data. We use the empirical fact that the estimated regression functions subject to randomly right censoring are close to the true regression functions than the observed failure times subject to randomly right censoring. The hyper-parameters of model which affect the performance of the proposed procedure are selected by a generalized cross validation function. Experimental results are then presented which indicate the performance of the proposed procedure.
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The uniform laws of large numbers for the chaotic logistic map
배종식,황창하,전두배 한국데이터정보과학회 2017 한국데이터정보과학회지 Vol.28 No.6
The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.
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THE UNIFORM CLT FOR MARTINGALE DIFFERENCE ARRAYS UNDER THE UNIFORMLY INTEGRABLE ENTROPY
배종식,전두배,Shlomo Levental 대한수학회 2010 대한수학회보 Vol.47 No.1
In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.
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The uniform consistency of the sample kernel quantile process
배종식,김성연 대한수학회 2004 대한수학회보 Vol.41 No.3
We obtain a kernel quantile process based on the kernel quantileestimator and prove the uniform consistency of the kernelquantile process by developing that of the usual sample quantileprocess. We apply our result to the classical kernel typeprocesses.
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배종식,최형진 강원대학교 기초과학연구소 2007 기초과학연구 Vol.18 No.-
기존의 검색 시스템은 영상 자체로부터 추출된 장면 전환 지점을 인덱싱하여 검색하기 때문에 사용자가 원하는 내용을 직접적으로 검색하기가 어려웠다. 이러한 단점을 보환하기 위하여 본 논문에서는 뉴스 데이터를 구조적으로 분할하고 의미적으로 분류하여 내용별로 세분화하여 검색하는 방법을 제안하고자 한다. 제안 방법에 따라 키 프레임에서 추출된 특징 정보를 사전 지식 청보와 비교하여 뉴스 데이터의 세부 내용을 기사별로 분류하여 검색하는 시스템을 설계하고 구현하였다.
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배종식,남윤성,최형진 강원대학교 기초과학연구소 2003 기초과학연구 Vol.14 No.-
매체가 점차 영상을 담은 멀티미디어로 바뀌고, 디지털화되어 저장, 전송 및 처리되고 있다. 디지털 영상 자료가 대중화됨에 따라 방대한 양의 자료를 효과적으로 이용 및 검색하기 하기 위해 영상 데이터의 색인과정이 필요하다. 영상 데이터에서 자막 프레임은 색인정보로서 중요한 역할을 하고 있다. 영상데이터에서 자막 프레임을 검출하여 색인정보로 활용하고자 한다. 자막이 있는 프레임을 검출하기 위해 히스토그램 비교법을 통하여 키프레임을 추출하고 자막의 특성을 이용하여 자막영역을 검출한다. 검출된 프레임 픽셀의 빈도수를 이용하여 자막 프레임을 검출하는 방법을 제안한다.
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