• 대한수학회지
• /
• 제53권1호
• /
• 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.

• 호남수학학술지
• /
• 제28권2호
• /
• 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
• /
• 제27권2호
• /
• 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
• /
• 제23권2호
• /
• 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.

• 대한수학회지
• /
• 제36권4호
• /
• 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
• /
• 제5권1호
• /
• 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.

• 아태비즈니스연구
• /
• 제15권1호
• /
• pp.335-352
• /
• 2024

Purpose - Low fertility rate is a serious problem, and this study analyzes factors affecting total fertility rate using panel data from 16 metropolitan cities and provinces in Korea from 2000 to 2022. Design/methodology/approach - Estimating the SAR model considering the weak cross-sectional dependence that exists in variables related to the regional total fertility rate, and using the DKSE estimation method considering the strong cross-sectional dependence. Findings - Estimation results considering weak and strong cross-sectional dependence were similar, confirming the robustness of the results. Female labor force participation rate has a positive effect on total fertility rate, and employment rate has no effect. However, the interaction term is a negative (-) sign. Crude marriage rate has a positive effect on total fertility rate, and apartment price has a slightly positive effect. Environmental factor has no effect, and policy factor has a negative effect. Research implications or Originality - In order for an increase in the female labor force participation rate to lead to an increase in the total fertility rate, qualitative improvements in female employment must be made. Financial investment policies for childbirth must increase their effectiveness. The problem of low fertility rate requires not only population policy but also social, economic, cultural, environmental, and policy conditions to be considered.

• Journal of applied mathematics & informatics
• /
• 제5권2호
• /
• 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
• /
• 제13권3호
• /
• 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
• /
• 제7권3호
• /
• 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.