• East Asian mathematical journal
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• 제6권2호
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• pp.133-144
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• 1990

In 1982, N. Miller [5] showed a weighted $L^p$ boundedness theorem for pseudo differential operators with symbols $S^0_{1.0}$. In this paper, we shall prove the pointwise estimates, in terms of the Fefferman, Stein sharp function and Hardy Littlewood maximal function, for pseudo differential operators with reduced symbols and show a weighted $L^p$-boundedness for pseudo differential operators with symbol in $S^m_{\rho,\delta}$, 0{$\leq}{\delta}{\leq}{\rho}{\leq}1$, ${\delta}{\neq}1$, ${\rho}{\neq}0$ and $m=(n+1)(\rho-1)$.

• 대한수학회논문집
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• 제23권1호
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• pp.49-59
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• 2008

In this paper, we prove the sharp estimates for multilinear commutator related to Littlewood-Paley operator. By using the sharp estimates, we obtained the weighted $L^p$-norm inequality for the multilinear commutator for 1 < p < $\infty$.

• 응용통계연구
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• 제26권5호
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• pp.697-712
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• 2013

다시점 자료 연구에서 일반화추정방정식은 가상관행렬을 잘못 가정하더라도 모수의 일치추정량을 도출하므로 많이 이용된다. 하지만, 결측 체계가 완전임의결측이 아닌 경우에는 편의추정량을 제공하고, 시간-종속적 공변량이 포함된 경우에는 가상관행렬에 따라 회귀계수 추정값이 다르게 도출될 수 있는 문제점이 있다. 결측 체계가 임의결측인 경우에 발생하는 문제를 해결하기 위해 가중 방법과 다중대체 방법을 사용하는 것이 제안되었다. 본 논문에서는 시간-종속적 공변량이 포함된 이분형 반복측정자료를 GEE를 이용하여 분석할 때 다양한 결측 체계에서 일반화추정방정식 방법, 가중 방법, 다중대체 방법의 회귀계수 추정에 대한 로버스트성과 정확성을 모의실험을 통하여 비교해 보았다. 세 가지 방법 모두에서 시간-종속적 공변량의 회귀계수가 시간-독립적 공변량의 회귀계수에 비해 가상관행렬에 따라 추정값의 차이가 크게 나타났다. 다른 두 방법에 비해 다중대체 방법이 가상관행렬의 형태에 대해 더 로버스트하고 편의도 작은 추정치를 도출하였다.

• ETRI Journal
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• 제33권1호
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• pp.27-31
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• 2011

This paper addresses estimating the frequency of a cisoid in the presence of white Gaussian noise, which has numerous applications in communications, radar, sonar, and instrumentation and measurement. Due to the nonlinear nature of the frequency estimation problem, there is threshold effect, that is, large error estimates or outliers will occur at sufficiently low signal-to-noise ratio (SNR) conditions. Utilizing the ideas of averaging to increase SNR and weighted linear prediction, an optimal frequency estimator with smaller threshold SNR is developed. Computer simulations are included to compare its mean square error performance with that of the maximum likelihood (ML) estimator, improved weighted phase averager, generalized weighted linear predictor, and single weighted sample correlator as well as Cramer-Rao lower bound. In particular, with smaller computational requirement, the proposed estimator can achieve the same threshold and estimation performance of the ML method.

• Journal of the Korean Data and Information Science Society
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• 제15권1호
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• pp.227-237
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• 2004

In this paper we presented a Bayesian inference approach for estimating the location and scale parameters of the lognormal distribution using iterative Gibbs sampling algorithm. We also presented estimation of location parameter by two non iterative methods, importance sampling and weighted bootstrap assuming scale parameter as known. The estimates by non iterative techniques do not depend on the specification of hyper parameters which is optimal from the Bayesian point of view. The estimates obtained by more sophisticated Gibbs sampler vary slightly with the choices of hyper parameters. The objective of this paper is to illustrate these tools in a simpler setup which may be essential in more complicated situations.

• 대한수학회논문집
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• 제33권2호
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 추계학술대회
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• pp.161-169
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• 2005

In this paper we propose a fuzzy c-regression model based on weighted least squares support vector machine(LS-SVM), which can be used to detect outliers in the switching regression model while preserving simultaneous yielding the estimates of outputs together with a fuzzy c-partitions of data. It can be applied to the nonlinear regression which does not have an explicit form of the regression function. We illustrate the new algorithm with examples which indicate how it can be used to detect outliers and fit the mixed data to the nonlinear regression models.

• 대한수학회지
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• 제61권2호
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• pp.207-226
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• 2024

In this paper, the weighted L^p boundedness of multilinear commutators and multilinear iterated commutators generated by the multilinear singular integral operators with generalized kernels and BMO functions is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels under certain conditions.

• 대한수학회보
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• 제57권4호
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• pp.851-864
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• 2020

This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol σ belonging to the Hörmander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the C_p estimates for the corresponding multilinear pseudo-differential operators are also obtained.

• East Asian mathematical journal
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• 제33권1호
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• pp.37-44
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• 2017

We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.