• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.57-72
• /
• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.

• Honam Mathematical Journal
• /
• v.28 no.2
• /
• pp.279-290
• /
• 2006

In this paper, we introduced a new notion of conditionally weakly positive quadrant dependence(CWPQD) between two random variables and the partial ordering of CWPQD is developed to compare pairs of CWPQD random vectors. Some properties and closure under certain statistical operations are derived.

• Communications for Statistical Applications and Methods
• /
• v.27 no.2
• /
• pp.163-175
• /
• 2020

We consider a wide class of general weakly-dependent processes, called ψ-weak dependence, which unify almost all weak dependence structures of interest found in statistics under natural conditions on process parameters, such as mixing, association, Bernoulli shifts, and Markovian sequences. For detecting the tail behavior of the weakly dependent processes, change point tests are developed by means of cumulative sum (CUSUM) statistics with the empirical distribution functions of sample extremes. The null limiting distribution is established as a Brownian bridge. Its proof is based on the ψ-weak dependence structure and the existence of the phantom distribution function of stationary weakly-dependent processes. A Monte-Carlo study is conducted to see the performance of sizes and powers of the CUSUM tests in GARCH(1, 1) models; in addition, real data applications are given with log-returns of financial data such as the Korean stock price index.

• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.223-238
• /
• 1994

A random vector $\b{X} = (X_1,\cdots,X_n)$ is weakly associated if and only if for every pair of partitions $\b{X}_1 = (X_{\pi(1)},\cdots,X_{\pi(k)}), \b{X}_2 = (X_{\pi(k+1),\cdots,X_{\pi(n)})$ of $\b{X}, P(\b{X}_1 \in A, \b{X}_2 \in B) \geq P(\b{X}_1 \in A)\b{P}(\b{X}_2 \in B)$ whenever A and B are open upper sets and $\pi$ is a permutation of ${1,\cdots,n}$. In this paper, we develop notions of weak positive dependence, which are weaker than a positive version of negative association (weak association) but stronger than positive orthant dependence by arguments similar to those of Shaked. We also illustrate some concepts of a particular interest. Various properties and interrelationships are derived.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.649-662
• /
• 1999

A random vector =(X1,…, Xn) is conditionally weakly associated if and only if for every pair of partitions 1=(X$\pi$(k+1),…,X$\pi$(k)), 2=(X$\pi$(k+1),…,X$\pi$(n)) of P(1$\in$A│2$\in$B, $\theta$$\in$I) $\geq$P$\in$A│$\theta$$\in$I whenever A and B are open upper sets and $\pi$ is any permutation of {1,…,n}. In this note we develop some concepts of conditional positive dependence, which are weaker than conditional weak association but stronger than conditional positive orthant dependence, by requiring the above inequality to hold only for some upper sets and applying the arguments in Shaked (1982).

• Communications for Statistical Applications and Methods
• /
• v.5 no.1
• /
• pp.193-203
• /
• 1998

In this paper, we introduce a new concept of the multivariate positive dependence. This concept is weaker than the positive orthant dependence. Some basic properties and preservation results are presented.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.553-564
• /
• 1998

In this paper we introduce a new concept of more weakly quadrant dependence of hitting times of stochastic processes. This concept is weaker than the more positively quadrant dependence of hitting times of stochastic processes. This concept is weaker than the more positively quadrant dependence and it is closed under some statistical operations of weakly positive quadrant dependence(WPQD) ordering.

• Communications for Statistical Applications and Methods
• /
• v.13 no.3
• /
• pp.513-524
• /
• 2006

In this paper, we introduce a new notions of conditionally weak dependence and we study their properties, preservation of the conditionally weak independent and positive and negative quadrant dependent(CWQD) property under mixtures, limits, closure under convex combinations, and their interrelationships. Furthermore, we extend multivariate stochastic dependence to stronger conditions of dependence.

• Communications for Statistical Applications and Methods
• /
• v.7 no.3
• /
• pp.845-858
• /
• 2000

In this paper new results are obtained for multivariate processes which help us to identify weak negative orthant dependent(WNOD) structures among hitting times of the processes. Furthermore, an approach to derive dependence properties among the processes is proposed and a partial solution to the question tat what kinds of the dependence properties, when they are imposed on processes, are reflected as analogous properties of corresponding hitting times is give. Examples are given to illustrate these concepts.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.755-768
• /
• 1997

In this paper we introduce a new concept of negative dependence of multivariate random variables. This concept is weaker than the negative orthant dependence(NOD) but it enjoys some properties and preservation results of NOD.