• Communications for Statistical Applications and Methods
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• 제19권2호
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• pp.287-292
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• 2012

Sample periodogram is widely known as an inconsistent estimator for true spectral density. We show that it becomes consistent when the true spectrum at the zero frequency (often known as long-run variance) equals zero. Asymptotic results for consistency of the periodogram as well as the rate of convergence are formally derived.

• Journal of the Korean Statistical Society
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• 제20권1호
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• pp.29-43
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• 1991

Two data-based bandwidth selectors which are optimal in the sense that they achieve n$\^$-$\frac{1}{2}$/ rate of convergence in kernel density estimation are proposed. The proposed bandwidth selectors are constructed by modifying Park and Marron's plug-in method. The first modification is taking Taylor expansion of the mean integrated squared error to two more terms than in the case of plug-in method. The second is estimating more accurately the functionals of the unknown density appeared in the minimizer of the expansion by using higher order kernels. The proposed bandwidth selectors were proved to be optimal in terms of convergence rate. According to small-sample Monte Carlo studies, the proposed bandwidth selectors showed better performance than all the other bandwidth selectors considered in the simulation.

• Communications for Statistical Applications and Methods
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• 제24권5호
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• pp.481-492
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• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.

• Journal of the Korean Statistical Society
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• 제25권4호
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• pp.499-514
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• 1996

Consider an additive regression model of Y on X = (X$_1$,X$_2$,. . .,$X_p$), Y = $sum_{j=1}^pf_j(X_j) + $\varepsilon$$, where $f_j$s are smooth functions to be estimated and $\varepsilon$ is a random error. If $X_j$s are fixed design points, we call it the fixed design additive model. Since the response variable Y is observed at fixed p-dimensional design points, the behavior of the nonparametric regression estimator depends on the design. We propose a fixed design called permutation fixed design, and fit the regression function by the kernel method. The estimator in the permutation fixed design achieves the univariate optimal rate of convergence in mean squared error for any p $\geq$ 2.

• 한국통신학회논문지
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• 제19권5호
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• pp.939-951
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• 1994

최소 평균 제곱(least mean squares) 알고리듬에 기반을 둔 적응 동화기의 수렴속도는 입력신호의 공분산 행렬에 의해 결정된다. 공분산 행렬의 고유값 spread가 1에 가까울때 수렴속도는 매우 빠르다. 본 논문에서는 LMS 기반 적응 동화기의 빠른 수렴을 위해 통계적으로 주어진 채널에 적합한 변형된 기준신호를 제안하였다. 이론적인 분석과 모의실험을 통해 LMS 기반 적응 동화기의 빠른 수렴을 얻는데 이 변형 방법이 효과적임을 알 수 있었다.

• 대한수학회논문집
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• 제22권1호
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• pp.137-143
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• 2007

In this paper, a Berstein-Hoeffding type inequality is established for linearly negative quadrant dependent random variables. A condition is given for almost sure convergence and the associated rate of convergence is specified.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.185-190
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• 2005

For the almost certainly convergent series $S_n$ of independent random variables the limiting behavior of tail series ${T_n}{\equiv}S-S_{n-1}$ is reviewed. More specifically, tail series strong laws of large number and tail series weak laws of large numbers will be introduced, and their relationship will be investigated. Then, the relationship will also be extended to the case of Banach space valued random elements, by investigating the duality between the limiting behavior of the tail series of random variables and that of random elements.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.153-166
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• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

• International Journal of Internet, Broadcasting and Communication
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• 제12권3호
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• pp.125-130
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• 2020

At the end of 1997, the volatility of the exchange rate intensified as the nation's exchange rate system was converted into a free-floating exchange rate system. As a result, managing the exchange rate is becoming a very important task, and the need for forecasting the exchange rate is growing. The exchange rate prediction model using the existing exchange rate prediction method, statistical technique, cannot find a nonlinear pattern of the time series variable, and it is difficult to analyze the time series with the variability cluster phenomenon. And as the number of variables to be analyzed increases, the number of parameters to be estimated increases, and it is not easy to interpret the meaning of the estimated coefficients. Accordingly, the exchange rate prediction model using artificial neural network, rather than statistical technique, is presented. Using DNN, which is the basis of deep learning among artificial neural networks, and LSTM, a recurrent neural network model, the number of hidden layers, neurons, and activation function changes of each model found the optimal exchange rate prediction model. The study found that although there were model differences, LSTM models performed better than DNN models and performed best when the activation function was Tanh.

• Journal of the Korean Statistical Society
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• 제33권4호
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• pp.459-470
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• 2004

We study the approximation of the solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H > 1/2 through discretization of space and time. The rate of convergence of an approximation for Euler scheme is established.