• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.549-561
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• 2008

In this paper, we construct a pair of Wolfe type second order symmetric dual problems, in which each component of the objective function contains support function and is, therefore, nondifferentiable. For this problem, we validate weak, strong and converse duality theorems under bonvexity - boncavity assumptions. A second order self duality theorem is also proved under additional appropriate conditions.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1381-1395
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• 2009

Mixed type second order dual to the non-differentiable problem containing support functions is formulated and duality theorems are proved under generalized second order convexity conditions. It is pointed out that the mixed type duality results already reported in the literature are the special cases of our results.

• 한국음향학회:학술대회논문집
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• 한국음향학회 2002년도 하계학술발표대회 논문집 제21권 1호
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• pp.41-44
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• 2002

Blind source separation (BSS) is a fundamental problem that is encountered in many practical applications. In most existing methods, stationary sources are considered higher-order statistics is necessary either explicitly or implicitly. But, many natural signals are nonstationary, and it is possible to perform BSS using only second-order statistics. Our method is based on only second order statistics. The algorithms are developed using the gradient descent method in orthogonality constraint and their performance is confirmed by numerical experiments.

• 대한수학회보
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• 제45권1호
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• pp.75-93
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• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.95-100
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• 2005

In this paper a class of multifactor designs for estimating the slope of second order response surface regression models with correlated errors is considered. General conditions for second order slope rotatability over all directions and also with respect to the maximum directional variance in case of k=2 have been derived assuming errors have a general correlated error structure. And we consider the measures for evaluating slope rotatability with correlated errors similar to in case of uncorrelated error structures.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.557-578
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• 2007

In Response Surface Methodology (RSM), rotatability is a natural and highly desirable property. For second order general correlated regression model, the concept of robust rotatability was introduced by Das (1997). In this paper a new measure of robust rotatability for second order response surface designs with correlated errors is developed and illustrated with an example. A comparison is made between the newly developed measure with the previously suggested measure by Das (1999).

• 한국통신학회논문지
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• 제21권2호
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• pp.357-364
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• 1996

이 논문에서는 고차통계값을 쓰지 않고 비최소 위상 FIR 시스템을 미상 식별(blind identification)할 수 있는 새로운 방법을 제안한다. 제안하는 방법은 2차 백색 신호의 절대평균으로 그 신호의 고차 백색성 여부를 판단할 수 있다는 관찰에서 얻어진다. 제안한 방법은 고차통계값을 쓰는 방법의 새로운 대안이 될 수 있다. 컴퓨터 모의실험을 통해서, 절대평균이 정확히 추정됨을 알 수 있었고 제안한 방법이 고차통계값을 쓰는 방법의 여러 단점을 해결할 수 있음을 보였다.

• 한국음향학회지
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• 제16권6호
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• pp.25-35
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• 1997

음성 신호 처리에 널리사용되어 온 2차 통계에 의한 음성 분석 방법은 잡음 환경에서 성능이 크게 저하되는 단점을 지닌다. 이에 반하여 고차 통계 방법은 Gaussian 잡음 등을 억제하는 특성을 가지고 있어서 잡음 환경에 상대적으로 강인한 음성 특징 추출을 가능하게 한다. 본 논문에서는 고차 통계에 의한 음성 분석 방법을 이용하여 백색 및 유색 잡음 환경에서의 문맥 독립형(text-independent) 화자식별 시스템을 제안하고, 기존의 2차 통계에 의한 방식과 성능을 비교하였다. 본 논문에서의 화자식별 시스템은 벡터 양자화 방법에 기반을 두고 있으며, 고차 통계 방법에 의한 유성음/무성음 판별을 통해 non-Gaussian 특징을 가지면서도 화자 정보가 집중되어 있는 유성음 부분에 대해서만 음성 특징을 추출하여 인식에 사용하였다. 50명의 화자를 대상으로 한 화자식별 실험 결과, 고차 통계 방법이 2차 통계에 의한 방법보다 잡음 환경에서 상대적으로 우수한 인식 성능을 나타냄을 확인하였다.

• Journal of the Korean Statistical Society
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• 제35권1호
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• pp.91-103
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• 2006

Yun (2005) introduced an estimator of the second order parameter characterizing the tail behavior of probability distributions and proved its consistency. In this paper we prove its asymptotic normality under a third order condition.