• Honam Mathematical Journal
• /
• v.34 no.2
• /
• pp.209-217
• /
• 2012

Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.

• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.251-269
• /
• 1994

In this paper we extend Kim and Pollard's cube root asymptotics to other rates of convergence, to establish an asymptotic theory for a multidimensional mode estimator based on uniform kernel with shrinking bandwidths. We obtain rates of convergence depending on shrinking rates of bandwidth and non-normal limit distributions. Optimal decreasing rates of bandwidth are discussed.

• Journal of the Korean Statistical Society
• /
• v.27 no.2
• /
• pp.153-163
• /
• 1998

We investigate density estimation problem in the L$^{\infty}$ norm and show that the iii optimal minimax rates are achieved for smooth classes of weakly dependent stationary sequences. Our results are then applied to give uniform convergence rates for various problems including the Gibbs sampler.

• Journal of the Korean Statistical Society
• /
• v.31 no.3
• /
• pp.359-368
• /
• 2002

Nonparametric kernel regression problem is considered for a stationary dependent sequence ｛(Xi, Yj) 1 j $\geq$ 1 ｝. In particular consistency and rates of convergence are discussed, which gives some useful insight for the effect of dependence for stationary $\alpha$-mixing sequences.

• Journal of the Korean Statistical Society
• /
• v.36 no.3
• /
• pp.367-372
• /
• 2007

Classification as a tool to extract information from data plays an important role in science and engineering. Among various classification methodologies, support vector machine has recently seen significant developments. The central problem this paper addresses is the accuracy of support vector machine. In particular, we are interested in the situations where fast rates of convergence to the Bayes risk can be achieved by support vector machine. Through learning examples, we illustrate that support vector machine may yield fast rates if the space spanned by an adopted kernel is sufficiently large.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.495-510
• /
• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• Journal of the military operations research society of Korea
• /
• v.25 no.2
• /
• pp.97-105
• /
• 1999

When infeasible interior-point methods are applied to large-scale linear programming problems, they become unstable and cannot solve the problems if convergence rates of primal feasibility, dual feasibility and duality gap are not well-balanced. We can balance convergence rates of primal feasibility, dual feasibility and duality gap by introducing control parameters. As a result, the stability and the efficiency of infeasible interior-point methods can be improved.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1275-1292
• /
• 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.

• Journal of the Korean Regional Science Association
• /
• v.32 no.3
• /
• pp.45-62
• /
• 2016

The main purpose of this study is to investigate whether the gap of fiscal self-sufficiency rates of 16 provincial governments in Korea has been narrowed and to suggest some remedies based on the empirical results. The panel data set from 1998 to 2013 is used and pooled OLS and system GMM regression techniques are employed. The fiscal self-sufficiency rates show downward trend and ${\beta}-convergence$ exists in absolute and conditional convergence analysis. The speed of conditional convergence anlysis is proved to be faster than that of absolute analysis. Both metropolitan cities and prefectures show convergence of fiscal self-sufficiency rates. We have found out that in the case of metropolitan cities, the proportion of workers in the tertiary industry has positive effect on fiscal self-sufficiency rates and in the case of prefectures number of cars per capita has positive effect. And in both cases increase in old population has negative effect.

• Journal of the Korean Society of Environmental Restoration Technology
• /
• v.25 no.2
• /
• pp.15-22
• /
• 2022

This study has been conducted to investigate the appropriate mixed sowing rates with white clover (Trifolium repens) and Kentucky bluegrass (Poa pratensis) by evaluating initial growth. Six different mixed sowing rates (CT, Control Trifolium repens; CP, Control Poa pratensis; T1P3, Trifolium repens 1 : Poa pratensis 3; T1P2, Trifolium repens 1 : Poa pratensis 2; T1P1, Trifolium repens 1 : Poa pratensis 1; T2P1, Trifolium repens 2 : Poa pratensis 1; T3P1, Trifolium repens 3 : Poa pratensis 1) with three repetitions were implemented in greenhouse experiment plastic pots (50.5 length × 35.0 width × 8.5 cm height). Plant height, leaf length, leaf width, number of leaves, root length, fresh weight, and dry weight were measured after a week from the germination for three months. Initial growth of Kentucky bluegrass significantly increased as mixed sowing rates with increasing, while that of white clover kept relatively decreasing than that in Control. Initial growth strongly affected sowing mixed rates by Kentucky bluegrass and not by white clover in this experiment, indicating that grasses played a dominant role during initial growth period. However, seeding rates with white clover will be dependent on the use of a turf and the desired green cover. There remains a need to further study of the mechanisms and dynamics of legume and grass competition to underpin sustainable management practices.