• 호남수학학술지
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• 제34권2호
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• pp.209-217
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• 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
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• 제24권1호
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• pp.219-224
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• 1995

A central limit theorem with random indices is obtained for stattionary martingale difference sequences.

• Journal of the Korean Physical Society
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• 제73권10호
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• pp.1589-1595
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• 2018

Similarity index measures the topological proximity of node pairs in a complex network. Numerous similarity indices have been defined and investigated, but the dependency of structure on the performance of similarity indices has not been sufficiently investigated. In this study, we investigated the relationship between the performance of similarity indices and structural properties of a network by employing a two-state random network. A node in a two-state network has binary types that are initially given, and a connection probability is determined from the state of the node pair. The performances of similarity indices are affected by the number of links and the ratio of intra-connections to inter-connections. Similarity indices have different characteristics depending on their type. Local indices perform well in small-size networks and do not depend on whether the structure is intra-dominant or inter-dominant. In contrast, global indices perform better in large-size networks, and some such indices do not perform well in an inter-dominant structure. We also found that link prediction performance and the performance of similarity are correlated in both model networks and empirical networks. This relationship implies that link prediction performance can be used as an approximation for the performance of the similarity index when information about node type is unavailable. This relationship may help to find the appropriate index for given networks.

• 호남수학학술지
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• 제33권2호
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• pp.163-171
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• 2011

In this paper we provide extensions of the Marcinkiewicz Zygmund laws of large numbers for i.i.d random variables with multidimensional indices to the case of negatively dependent random fields.

• Transactions on Electrical and Electronic Materials
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• 제15권3호
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• pp.125-129
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• 2014

A dataset can be clustered by merging the bucket indices that come from the random projection of locality sensitive hashing functions. It should be noted that for this to work the merging interval must be calculated first. To improve the feasibility of large scale data clustering in high dimensional space we propose an enhanced Locality Sensitive Hashing Clustering Method. Firstly, multiple hashing functions are generated. Secondly, data points are projected to bucket indices. Thirdly, bucket indices are clustered to get class labels. Experimental results showed that on synthetic datasets this method achieves high accuracy at much improved cluster speeds. These attributes make it well suited to clustering data in high dimensional space.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.417-425
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• 2008

For stationary m-dimensional martingale difference sequences we prove the random functional central limit theorems and propose an almost sure consistent estimator for the limiting covariance matrix.

• Fisheries and Aquatic Sciences
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• 제21권8호
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• pp.24.1-24.9
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• 2018

The Korean bottom trawl survey has been deployed on a regular basis for about the last decade as part of groundfish stock assessments. The regularity indicates that they sample groundfish once per grid cell whose sides are half of one latitude and that of one longitude, respectively, and whose inside is furthermore divided into nine nested grids. Unless they have a special reason (e.g., running into a rocky bottom), their sample location is at the center grid of the nine nested grids. Given data collected by the survey, we intended to show how to appropriately estimate not only the survey index of a fish stock but also its uncertainty. For the regularity reason, we applied the systematic sampling theory for the above purposes and compared its results with a reference, which was based on the simple random sampling. When using the survey data about 11 fish stocks, collected by the spring and fall surveys in 2014, the survey indices of those stocks estimated under the systematic sampling were overall more precise than those under the simple random sampling. In estimates of the survey indices in number, the standard errors of those estimates under the systematic sampling were reduced from those under the simple random sampling by 0.23~27.44%, while in estimates of the survey indices in weight, they decreased by 0.04~31.97%. In bias of the estimates, the systematic sampling was the same as the simple random sampling. Our paper is first in formally showing how to apply the systematic sampling theory to the actual data collected by the Korean bottom trawl surveys.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.504-512
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• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

• Journal of the Korean Statistical Society
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• 제25권1호
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• pp.153-159
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• 1996

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

• 천문학논총
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• 제30권2호
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• pp.433-437
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• 2015

We show the results of a time series analysis of the long-term light curves of four blazars. 3C 279, 3C 345, 3C 446, and BL Lacertae. We used densely sampled light curves spanning 32 years at three frequency bands (4.8, 8, 14.5 GHz), provided by the University of Michigan Radio Astronomy Observatory monitoring program. The spectral indices of our sources are mostly flat or inverted (-0.5 < ${\alpha}$ < 0), which is consistent with optically thick emission. Strong variability was seen in all light curves on various time scales. From the analyses of time lags between the light curves from different frequency bands and the evolution of the spectral indices with time, we find that we can distinguish high-peaking flares and low-peaking flares according to the Valtaoja et al. classification. The periodograms (temporal power spectra) of the light curves are in good agreement with random-walk power-law noise without any indication of (quasi-)periodic variability. We note that random-walk noise light curves can originate from multiple shocks in jets. The fact that all our sources are in agreement with being random-walk noise emitters at radio wavelengths suggests that such behavior is a general property of blazars. We are going to generalize our approach by applying our methodology to a much larger blazar sample in the near future.