• Title, Summary, Keyword: mean of the squared functions

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An estimator of the mean of the squared functions for a nonparametric regression

  • Park, Chun-Gun
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.3
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    • pp.577-585
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    • 2009
  • So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.

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Minimum Mean Squared Error Invariant Designs for Polynomial Approximation

  • Joong-Yang Park
    • Communications for Statistical Applications and Methods
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    • v.2 no.2
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    • pp.376-386
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    • 1995
  • Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

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On Estimating Magnitude-Squared Coherence Functions Using Frequency-Domain Adaptive Digital Filters (주파수 영역 적응 디지탈 필터를 이용한 Magnitude-Squared Coherence 함수 추정)

  • Kim, D.N.;Cha, I.W.;Youn, D.H.
    • The Journal of the Acoustical Society of Korea
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    • v.7 no.2
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    • pp.39-50
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    • 1988
  • It is proposed to use a pair of frequency-domain adaptive digital filters to estimate the magnitude squared coherence (MSC) functions of two signals. Such a method requires less computations than the LMS-MSC algorithm in which the least mean square (LMS) algorithm is applied in the time domain to compute the coefficients of a pair of adaptive digital filters. The frequency-domain adaptive digital filtering algorithms considered in this paper include the constrained frequency domain LMS (CFLMS) and the unconstrained frequency domain LMS (UFLMS) algorithms. The performance of the proposed methods are compared with those of the LMS-MSC algorithm.

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Estimation for Exponential Distribution Based on Multiply Type-II Censored Samples

  • Kang, Suk-Bok
    • 한국데이터정보과학회:학술대회논문집
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    • pp.203-210
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    • 2004
  • When the available sample is multiply Type-II censored, the maximum likelihood estimators of the location and the scale parameters of two- parameter exponential distribution do not admit explicitly. In this case, we propose some estimators which are linear functions of the order statistics and also propose some estimators by approximating the likelihood equations appropriately. We compare the proposed estimators by the mean squared errors.

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Sensitivity Approach of Sequential Sampling Using Adaptive Distance Criterion (적응거리 조건을 이용한 순차적 실험계획의 민감도법)

  • Jung, Jae-Jun;Lee, Tae-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.9
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    • pp.1217-1224
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    • 2005
  • To improve the accuracy of a metamodel, additional sample points can be selected by using a specified criterion, which is often called sequential sampling approach. Sequential sampling approach requires small computational cost compared to one-stage optimal sampling. It is also capable of monitoring the process of metamodeling by means of identifying an important design region for approximation and further refining the fidelity in the region. However, the existing critertia such as mean squared error, entropy and maximin distance essentially depend on the distance between previous selected sample points. Therefore, although sufficient sample points are selected, these sequential sampling strategies cannot guarantee the accuracy of metamodel in the nearby optimum points. This is because criteria of the existing sequential sampling approaches are inefficient to approximate extremum and inflection points of original model. In this research, new sequential sampling approach using the sensitivity of metamodel is proposed to reflect the response. Various functions that can represent a variety of features of engineering problems are used to validate the sensitivity approach. In addition to both root mean squared error and maximum error, the error of metamodel at optimum points is tested to access the superiority of the proposed approach. That is, optimum solutions to minimization of metamodel obtained from the proposed approach are compared with those of true functions. For comparison, both mean squared error approach and maximin distance approach are also examined.

Estimation of Spatial Coherency Functions for Kriging of Spatial Data (공간데이터 크리깅 적용을 위한 공간상관함수 추정)

  • Bae, Tae-Suk
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.34 no.1
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    • pp.91-98
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    • 2016
  • In order to apply Kriging methods for geostatistics of spatial data, an estimation of spatial coherency functions is required priorly based on the spatial distance between measurement points. In the study, the typical coherency functions, such as semi-variogram, homeogram, and covariance function, were estimated using the national geoid model. The test area consisting of 2°×2° and the Unified Control Points (UCPs) within the area were chosen as sampling measurements of the geoid. Based on the distance between the control points, a total of 100 sampling points were grouped into distinct pairs and assigned into a bin. Empirical values, which were calculated with each of the spatial coherency functions, resulted out as a wave model of a semi-variogram for the best quality of fit. Both of homeogram and covariance functions were better fitted into the exponential model. In the future, the methods of various Kriging and the functions of estimated spatial coherency need to be studied to verify the prediction accuracy and to calculate the Mean Squared Prediction Error (MSPE).

Contour Plots of Objective Functions for Feed-Forward Neural Networks

  • Oh, Sang-Hoon
    • International Journal of Contents
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    • v.8 no.4
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    • pp.30-35
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    • 2012
  • Error surfaces provide us with very important information for training of feed-forward neural networks (FNNs). In this paper, we draw the contour plots of various error or objective functions for training of FNNs. Firstly, when applying FNNs to classifications, the weakness of mean-squared error is explained with the viewpoint of error contour plot. And the classification figure of merit, mean log-square error, cross-entropy error, and n-th order extension of cross-entropy error objective functions are considered for the contour plots. Also, the recently proposed target node method is explained with the viewpoint of contour plot. Based on the contour plots, we can explain characteristics of various error or objective functions when training of FNNs proceeds.

An Integrated Sequential Inference Approach for the Normal Mean

  • Almahmeed, M.A.;Hamdy, H.I.;Alzalzalah, Y.H.;Son, M.S.
    • Journal of the Korean Statistical Society
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    • v.31 no.4
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    • pp.415-431
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    • 2002
  • A unified framework for statistical inference for the mean of the normal distribution to derive point estimates, confidence intervals and statistical tests is proposed. This optimal design is justified after investigating the basic information and requirements that are possible and impossible to control when specifying practical and statistical requirements. Point estimation is only credible when viewed in the larger context of interval estimation, since the information required for optimal point estimation is unspecifiable. Triple sampling is proposed and justified as a reasonable sampling vehicle to achieve the specifiable requirements within the unified framework.

On the Interpolation Using Neural Network (신경회로망을 이용한 내삽법에 관하여)

  • 문용호;김유신;손경식
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.18 no.7
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    • pp.907-912
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    • 1993
  • In this Paper we have proposed a new method to implement the interpolation of the functions, using a neural network. The architecture of neural network is a three-layer perceptron and the training algorithm is a modified error back propagation algorithm adding neurons to hidden layer. The interpolated functions are sin(7 X), 3rd order polynomial 0.5$\times$3_2$\times$2+X+2.5 and rectangular pulse 0.99 U (X-0.2) -0.99 U(X-0.8) +0.01, where U(X) is the unit step. The root mean squred errors of the interpolated functions are 0.00258, 0.00164 and 0.00116 respectively.

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A Two Sample Test for Functional Data

  • Lee, Jong Soo;Cox, Dennis D.;Follen, Michele
    • Communications for Statistical Applications and Methods
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    • v.22 no.2
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    • pp.121-135
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    • 2015
  • We consider testing equality of mean functions from two samples of functional data. A novel test based on the adaptive Neyman methodology applied to the Hotelling's T-squared statistic is proposed. Under the enlarged null hypothesis that the distributions of the two populations are the same, randomization methods are proposed to find a null distribution which gives accurate significance levels. An extensive simulation study is presented which shows that the proposed test works very well in comparison with several other methods under a variety of alternatives and is one of the best methods for all alternatives, whereas the other methods all show weak power at some alternatives. An application to a real-world data set demonstrates the applicability of the method.