• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.103-108
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• 2002

We consider an estimation of discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of a change point and jump size in variance function and then construct an estimator of entire variance function. We examine the rates of convergence of these estimators and give results on their asymptotics. Numerical work reveals that the effectiveness of change point analysis in variance function estimation is quite significant.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.1-23
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• 2006

In this paper we consider an estimation of the discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of the change point in the variance function and then construct an estimator of the entire variance function. We examine the rates of convergence of these estimators and give results for their asymptotics. Numerical work reveals that using the proposed change point analysis in the variance function estimation is quite effective.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.53-68
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• 1999

To improve the slow convergence property of the steepest ascent type algorithm for continuous D-optimal design problems. we develop a new algorithm. We apply the nonlinear system of equations as the necessary condition of optimality and develop the two-point algorithm that solves the problem of clustering. Because of the nature of the steepest coordinate ascent algorithm avoiding the problem of clustering itself helps the improvement of convergence speed. The numerical examples show the performances of the new method is better than those of various steepest ascent algorithms.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.255-269
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• 2004

This paper develops log-density estimation for directional data. The methodology is to use expansions with respect to spherical harmonics followed by estimating the unknown parameters by maximum likelihood. Minimax rates of convergence in terms of the Kullback-Leibler information divergence are obtained.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.877-897
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• 2016

In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.59-78
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• 2004

A regression function in generalized linear model may have a discontinuity/change point at unknown location. In order to estimate the location of the discontinuity point and its jump size, the strategy is to use a nonparametric approach based on one-sided kernel weighted local-likelihood functions. Weak convergences of the proposed estimators are established. The finite-sample performances of the proposed estimators with practical aspects are illustrated by simulated examples.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.105-112
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• 1990

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.281-295
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• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.413-423
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• 2014

In this article we study different properties of the statistically convergent and statistically null sequence classes of fuzzy real numbers with fuzzy metric, like completeness, solidness, sequence algebra, symmetricity and convergence free.

• Journal of the Korea institute for structural maintenance and inspection
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• v.13 no.2 s.54
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• pp.231-242
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• 2009

The baseline distribution of a structure represents the statistical distribution of dynamic response feature from the healthy state of the structure. Generally, damage-sensitive dynamic response feature of a structure manifest themselves near the tail of a baseline statistical distribution. In this regard, some researchers have paid attention to extreme value distribution for modeling the tail of a baseline distribution. However, few researches have been conducted to theoretically understand the extreme value distribution from a perspective of statistical damage assessment. This study investigates the asymptotic convergence of domain of attraction in extreme value distribution through parameter estimation, which is needed for reliable statistical damage assessment. In particular, the asymptotic convergence of a domain of attraction is quantified with respect to the sample size out of which each extreme value is extracted. The effect of the sample size on false positive alarms in statistical damage assessment is quantitatively investigated as well. The validity of the proposed method is demonstrated through numerically simulated acceleration data on a two span continuous truss bridge.