• Journal of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.327-349
• /
• 2021

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.949-957
• /
• 2005

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

• Communications for Statistical Applications and Methods
• /
• v.7 no.1
• /
• pp.291-296
• /
• 2000

Petrov(1996) examined the connection between general moment conditions and the applicability of the strong law lf large numbers to a sequence of pairwise independnt and identically distributed random variables. In this note wee generalize Theorem 1 of Petrov(1996) and also show that still holds under assumption of pairwise negative quadrant dependence(NQD).

• Communications of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.377-384
• /
• 1998

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.2
• /
• pp.313-318
• /
• 2012

The power inequality ${\prod}_{k=1}^{N}\;{x}_{k}^{x_{k}}\;{\geq}\;{\prod}_{k=1}^{N}\;{p}_{k}^{x_{k}}$ holds for the points $(x_1,{\ldots},x_N),(p_1,{\ldots},p_N)$ of the simplex. We show this using the analytic method combining Frostman's density theorem with the strong law of large numbers.

• Communications of the Korean Mathematical Society
• /
• v.18 no.3
• /
• pp.551-558
• /
• 2003

In this paper we Obtain the Hajeck-Renyi type inequality for the asymptotically almost negatively associated(AANA) random variables and extend some results for negatively associated random variables to the AANA case by applying this inequality.

• Honam Mathematical Journal
• /
• v.33 no.4
• /
• pp.591-602
• /
• 2011

In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on $\mathbb{Z}^2$.

• The Journal of the Korea Contents Association
• /
• v.6 no.5
• /
• pp.29-34
• /
• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• Journal of the Korean Statistical Society
• /
• v.31 no.3
• /
• pp.369-378
• /
• 2002

Strong laws of large numbers for weighted sums of asymptotically almost negatively associated(AANA) sequence are proved by our generalized maximal inequality for AANA random variables at a crucial step.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.511-526
• /
• 2002

In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.