• 대한수학회지
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• 제52권2호
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• pp.431-445
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• 2015

Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in $L^p$ for conditionally independent and conditionally identically distributed random variables are established, respectively.

• 대한수학회지
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• 제51권3호
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• pp.609-633
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• 2014

From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

• 대한수학회지
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• 제53권6호
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• pp.1275-1292
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• 2016

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ${\infty}$) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.

• 대한수학회지
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• 제51권1호
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• pp.1-15
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• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

• 대한수학회지
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• 제54권2호
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• pp.441-460
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• 2017

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\mathfrak{F}$-independent random variables sequences, the convergence of sums of $\mathfrak{F}$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.799-808
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• 2011

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_i{\mid}1{\leq}i{\leq}n$} is a conditional associated given $\mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$, $Cov^{\mathcal{F}}$ (f($X_1$, ${\ldots}$, $X_n$), g($X_1$, ${\ldots}$, $X_n$)) ${\geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $\mathcal{F}$-associated random variables.

• 한국지능시스템학회논문지
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• 제17권5호
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• pp.684-690
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• 2007

본 논문은 확률변수들로 이루어진 클러스터의 집합과 확률변수들에 대해 관찰된 데이터가 주어진 상황에서, 클러스터 사이에 존재하는 조건부 확률적 의존의 방향성(directional tendency of conditional dependence in the Bayesian probabilistic graphical model)을 결정하는 방법을 기술한다. 클러스터 사이에 존재하는 조건부 확률적 의존의 방향성을 추정하기 위해 한 클러스터에서 다른 각 클러스터에 가장 가까운 확률변수를 해당 클러스터의 외부연결변수로 결정한다. 외부연결변수들 사이에서의 가장 확률이 높은 조건부 확률적 의존성을 나타내는 방향성 비순환 그래프(directed acyclic graph(DAG))를 찾음으로써, 주어진 클러스터들 사이에 존재하는 조건부 확률적 의존의 방향성을 결정한다. 사용된 방법이 클러스터 사이에 존재하는 조건부 확률적 의존의 방향성을 유의미하게 추정할 수 있음을 실험적으로 보인다.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• 대한전자공학회논문지
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• 제26권9호
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• pp.1299-1307
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• 1989

A Korean syllable is regarded as a random variable according to its probabilistic property in occurrence. A Korean syllable is divided into a 'choseong', a 'jungseong', and a 'jongseong' which are regarded as random variables. From the cumulative freaquency of a Korean syllable all possible joint probabilities and conditional probabilities are computed for the three ramdom variables. From the joint probabilities and the conditional probabilities all possible joint entropies and conditional entropies are computed for the three random varibles. Also all possible average mutual informations are calculated for the three random variables. Average mutual informatin between two random variables hss its biggest value between choseong and jungseong. Average mutual information between a random variable and other two random variables has its biggest value between jungseong and choseong-jongseong.

• Journal of the Korean Data and Information Science Society
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• 제23권2호
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• pp.299-307
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• 2012

데이터마이닝은 주어진 데이터베이스에서 항목간의 흥미로운 관계를 찾아내는 기법으로서 의사결정나무는 데이터마이닝의 대표적인 알고리즘이라고 할 수 있다. 의사결정나무는 관심대상이 되는 집단을 몇 개의 소집단으로 분류하거나 예측을 수행하는 방법이다. 일반적으로 연구자가 의사결정나무 모형을 생성 할 때 모형 생성의 기준 및 입력 변수의 수에 따라 복잡한 모형이 생성되기도 한다. 특히 의사결정나무 모형에서 입력 변수의 수가 많을 경우 생성된 모형은 복잡한 형태가 될 수 있고, 모형 분석이 어려울 수도 있다. 만일 입력변수에서 주변조건부 변수 (매개변수, 외적변수)가 존재한다면 이 입력변수는 직접적인 관련성이 없는 것으로 판단한다. 이에 본 논문에서는 주변조건부 변수를 고려하여 의사결정나무모형을 생성하는 방법을 제시하고 그 효율성을 파악하기 위하여 실제 자료에 적용하고자 한다.