• 대한수학회지
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• 제58권1호
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.621-640
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• 2022

The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.

• 대한수학회지
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• 제43권6호
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• pp.1169-1181
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• 2006

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

• 대한수학회지
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• 제41권5호
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• pp.883-894
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• 2004

We discuss in this paper the strong convergence for weighted sums of negative associated (in abbreviation: NA) arrays. Meanwhile, the central limit theorem for weighted sums of NA variables and linear process based on NA variables is also considered. As corollary, we get the results on iid of Li et al. ([10]) in NA setting.

• 대한수학회보
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• 제47권3호
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• pp.467-482
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• 2010

For a double array of random elements {$V_{mn};m{\geq}1,\;n{\geq}1$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which $k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i=1}}\sum{{u_n}\atop{i=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in $L_r$ (0 < r < 2). The weak law results provide conditions for $k_{mn}^{-\frac{1}{r}}\sum{{T_m}\atop{i=1}}\sum{{\tau}_n\atop{j=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in probability where {$T_m;m\;{\geq}1$} and {${\tau}_n;n\;{\geq}1$} are sequences of positive integer-valued random variables, {$k_{mn};m{{\geq}}1,\;n{\geq}1$} is an array of positive integers. The sharpness of the results is illustrated by examples.

• Journal of the Korean Statistical Society
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• 제25권2호
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• pp.175-183
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• 1996

Let $S_n,n$ = 1, 2,... denote the partial sums of not necessarily in-dependent random variables. Let N(c) = min${ n ; S_n > c}$, c $\geq$ 0. Theorem 2 states that N (c), (suitably normalized), tends to 0 in p-mean, 1 $\leq$ p < 2, as c longrightarrow $\infty$ under mild conditions, which generalizes earlier result by Gut(1974). The proof follows by applying Theorem 1, which generalizes the known result $E$\mid$S_n$\mid$^p$ = o(n), 0 < p< 2, as n .rarw..inf. to randomly indexed partial sums.

• Journal of information and communication convergence engineering
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• 제9권4호
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• pp.420-423
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• 2011

The paper is devoted to problem of spline modeling of multidimensional signals. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria are which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. In this method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables.

• 한국융합학회논문지
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• 제10권1호
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• pp.205-214
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• 2019

우리나라 정부 당국은 주로 최저가낙찰제도를 이용하여 조달을 시행해왔으나, 과거 일정 시기 동안은 제한적 평균가 낙찰제 경매방식(일명 부찰제)을 이용하여 시설공사부문 조달을 실시했다. 부찰제란 각 입찰자들이 서로 모르게 공급가격을 적어 내면 그 가격을 평균하여 그 평균값에 가장 가까우면서 평균값보다는 낮은 공급가격을 부른 사람이 승자가 되며, 그가 부른 가격에서 낙찰가가 결정되는 제도이다. 본 논문은 제한적 평균가낙찰제 경매방식을 자원배분기구설계(mechanism design)의 관점에서 정형화하고, 고려할 문제를 제시한다. 나아가 ?명의 일반적 상황 하에서 사적 정보를 가지고 있는 입찰자들의 전략을 일양 분포 가정과 선형전략의 가정을 도입하여 구하고, 이를 통해 부찰제 경매방식의 균형을 제시한다. 또한 이러한 균형전략을 최저가낙찰제도와 비교함으로써 우리나라에서 자주 사용되는 두 제도의 효율성과 기대수입의 측면을 살펴본다. 끝으로 부찰제를 실시하는 경매인(정부)의 현실적 목적성이 어느 정도 달성되고 있는가를 비판적으로 고찰한다.