• Communications for Statistical Applications and Methods
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• 제22권1호
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• pp.81-93
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• 2015

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.

• Journal of the Korean Statistical Society
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• 제27권1호
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• pp.113-132
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• 1998

In this paper, we consider a minimum distance (M.D.) estimation based on kernels for U-statistics. We use Cramer-von Mises type distance function which measures the discrepancy between U-empirical distribution function(d.f.) and modeled d.f. of kernel. In the distance function, we allow various integrating measures, which can be finite, $\sigma$-finite or discrete. Then we derive the asymptotic normality and study the qualitative robustness of M. D. estimates.

• Journal of the Korean Statistical Society
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• 제31권1호
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• pp.109-120
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• 2002

In this paper, we show the weak convergence of U-empirical processes for two sample problem. We use the result to show the asymptotic normality for the generalized dodges-Lehmann estimates with the Bahadur representation for quantifies of U-empirical distributions. Also we consider the asymptotic normality for the test statistics in a simple way.

• 대한수학회보
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• 제60권6호
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• pp.1523-1537
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• 2023

Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.

• International Journal of Reliability and Applications
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• 제16권2호
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• pp.113-122
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• 2015

In this paper, we introduce U-statistics approach to generalized Hollander-Proschan test for new better than used (NBUE) alternative. We prove, the proposed test is equivalent to test was introduced by Anis and Mitra (2011) and includes test was introduced by Hollander Proschan (1975). Also, the asymptotic properties are studied. The powers of our test are estimated. The Pitman asymptotic efficiencies of proposed test are also calculated. Finally, the test is applied to some real data.

• 대한수학회지
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• 제47권6호
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• pp.1317-1328
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• 2010

In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

• 응용통계연구
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• 제34권5호
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• pp.849-861
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• 2021

본 논문은 확률적 자료연계 방법의 기본 개념과 이론적 모형을 소개하고, 실제 통계청 데이터를 사용하여 확률적 자료연계가 진행되는 과정과 원리를 보여준다. 먼저 확률적 자료연계와 결정적 자료연계와의 차이를 간단히 알아보고, 확률적 자료연계 방법론의 토대가 되는 Fellegi-Sunter 모형의 기본 구성과 관련된 모수(m-확률, u-확률), 가중치, 매치여부 판정기준에 대해 기술한다. 그리고 통계청 등록센서스와 인구총조사 자료를 이용하여 그 모형을 적용한 자료연계가 이루어지는 구체적인 과정에 대해 설명하고, 이를 통해 얻어진 연계 결과의 정확성을 살펴본다.

• Journal of the Korean Statistical Society
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• 제33권4호
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• pp.353-365
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• 2004

In this paper, we define the weighted U-empirical process for simple linear model and show the weak convergence to a Gaussian process under some conditions. Then we illustrate the usage of our result with examples. In the appendix, we derive the variance of the weighted U-empirical distribution function.

• 응용통계연구
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• 제24권2호
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• pp.279-292
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• 2011

합리적인 보험료를 책정하기 위해 사용되는 신뢰도 이론은 보험통계학의 중요한 주요 이론 가운데 하나이다. 본 논문에서는 신뢰도 이론의 기본 개념과 함께 유효대수 법칙, 제곱근 법 칙, B$\"{u}$hlmann 신뢰도, B$\"{u}$hlmann 신뢰도, B$\"{u}$hlmann-Straub 신뢰도 등을 소개하였다. 또한 이러한 방법들에 근거하여 새로운 보험료를 실제 자료를 시용하여 예측하였다. 결론적으로, 유효대수 법칙이 가장 정확한 예측력을 보였다.

• 대한수학회지
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• 제53권1호
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• pp.201-215
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Kirchhoff-type equations $\[a+b\({\int}_{{\mathbb{R}}^N}({\mid}{\nabla}u{\mid}^2+V(x){\mid}u{\mid}^2)dx\)\][-{\Delta}u+V(x)u]=f(x,u)$, in ${\mathbb{R}}^N$. Under certain assumptions on V and f, some new criteria on the existence and multiplicity of nontrivial solutions are established by the Morse theory with local linking and the genus properties in critical point theory. Some results from the previously literature are significantly extended and complemented.