• Title, Summary, Keyword: additive function

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A GENERALIZED ADDITIVE-QUARTIC FUNCTIONAL EQUATION AND ITS STABILITY

  • HENGKRAWIT, CHARINTHIP;THANYACHAROEN, ANURK
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1759-1776
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    • 2015
  • We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

The Weight Function in BIRQ Estimator for the AR(1) Model with Additive Outliers

  • Jung Byoung Cheol;Han Sang Moon
    • Proceedings of the Korean Statistical Society Conference
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    • pp.129-134
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    • 2004
  • In this study, we investigate the effects of the weight function in the bounded influence regression quantile (BIRQ) estimator for the AR(1) model with additive outliers. In order to down-weight the outliers of X-axis, the Mallows' (1973) weight function has been commonly used in the BIRQ estimator. However, in our Monte Carlo study, the BIRQ estimator using the Tukey's bisquare weight function shows less MSE and bias than that of using the Mallows' weight function or Huber's weight function.

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Checking the Additive Risk Model with Martingale Residuals

  • Myung-Unn Song;Dong-Myung Jeong;Jae-Kee Song
    • Journal of the Korean Statistical Society
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    • v.25 no.3
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    • pp.433-444
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    • 1996
  • In contrast to the multiplicative risk model, the additive risk model specifies that the hazard function with covariates is the sum of, rather than product of, the baseline hazard function and the regression function of covariates. We, in this paper, propose a method for checking the adequacy of the additive risk model based on partial-sum of matingale residuals. Under the assumed model, the asymptotic properties of the proposed test statistic and approximation method to find the critical values of the limiting distribution are studied. Several real examples are illustrated.

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ALGEBRAIC ENTROPIES OF NATURAL NUMBERS WITH ONE OR TWO PRIME FACTORS

  • JEONG, SEUNGPIL;KIM, KYONG HOON;KIM, GWANGIL
    • The Pure and Applied Mathematics
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    • v.23 no.3
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    • pp.205-221
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    • 2016
  • We formulate the additive entropy of a natural number in terms of the additive partition function, and show that its multiplicative entropy is directly related to the multiplicative partition function. We give a practical formula for the multiplicative entropy of natural numbers with two prime factors. We use this formula to analyze the comparative density of additive and multiplicative entropy, prove that this density converges to zero as the number tends to infinity, and empirically observe this asymptotic behavior.

INTEGRAL OPERATORS FOR OPERATOR VALUED MEASURES

  • Park, Jae-Myung
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.331-336
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    • 1994
  • Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

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A General Semiparametric Additive Risk Model

  • Park, Cheol-Yong
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.2
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    • pp.421-429
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    • 2008
  • We consider a general semiparametric additive risk model that consists of three components. They are parametric, purely and smoothly nonparametric components. In parametric component, time dependent term is known up to proportional constant. In purely nonparametric component, time dependent term is an unknown function, and time dependent term in smoothly nonparametric component is an unknown but smoothly function. As an estimation method of this model, we use the weighted least square estimation by Huffer and McKeague (1991). We provide an illustrative example as well as a simulation study that compares the performance of our method with the ordinary least square method.

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Noise Reduction Approach of Nonlinear Function for a Range Image using 2-D Kalman Filtering Method

  • Katayama, Jun;Sekin, Yoshifumi
    • Proceedings of the IEEK Conference
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    • pp.898-901
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    • 2000
  • A new 2-D block Kalman filtering method which uses a nonlinear function is presented to generate a more accurate filtered estimate of a range image that has been corrupted by additive noise. Novel 2-D block Kalman filtering method is constructed of the conventional method and nonlinear function which utilizes to control estimation error. We show that novel 2-D Kalman filtering method using a nonlinear function is effective at reducing the additive noise, not distorting shape edges.

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On comonotonically additive interval-valued functionals and interval-valued hoquet integrals(I) (보단조 가법 구간치 범함수와 구간치 쇼케이적분에 관한 연구(I))

  • Lee, Chae-Jang;Kim, Tae-Kyun;Jeon, Jong-Duek
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.9-13
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    • 2003
  • In this paper, we will define comonotonically additive interval-valued functionals which are generalized comonotonically additive real-valued functionals in Shcmeildler[14] and Narukawa[12], and study some properties of them. And we also investigate some relations between comonotonically additive interval-valued functionals and interval-valued Choquet integrals on a suitable function space cf.[19,10,11,13].

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Estimation of Covariance Functions for Growth of Angora Goats

  • Liu, Wenzhong;Zhang, Yuan;Zhou, Zhongxiao
    • Asian-Australasian Journal of Animal Sciences
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    • v.22 no.7
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    • pp.931-936
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    • 2009
  • Body weights of 862 Angora goats between birth and 36 months of age, recorded on a semiyearly basis from 1988 to 2000, were used to estimate genetic, permanent environmental and phenotypic covariance functions. These functions were estimated by fitting a random regression model with 6th order polynomial for direct additive genetic and animal permanent environmental effects and 4th and 5th order polynomial for maternal genetic and permanent environmental effects, respectively. A phenotypic covariance function was estimated by modelling overall animal and maternal effects. The results showed that the most variable coefficient was the intercept for both direct and maternal additive genetic effects. The direct additive genetic (co)variances increased with age and reached a maximum at about 30 months, whereas the maternal additive genetic (co)variances increased rapidly from birth and reached a maximum at weaning, and then decreased with age. Animal permanent environmental (co)variances increased with age from birth to 30 months with lower rate before 12 months and higher rate between 12 and 30 months. Maternal permanent environmental (co)variances changed little before 6 months but then increased slowly and reached a maximum at about 30 months. These results suggested that the contribution of maternal additive genetic and permanent environmental effects to growth variation differed from those of direct additive genetic and animal permanent environmental effects not only in expression time, but also in action magnitude. The phenotypic (co)variance estimates increased with age from birth to 36 months of age.

DENSITY SMOOTHNESS PARAMETER ESTIMATION WITH SOME ADDITIVE NOISES

  • Zhao, Junjian;Zhuang, Zhitao
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1367-1376
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    • 2018
  • In practice, the density function of a random variable X is always unknown. Even its smoothness parameter is unknown to us. In this paper, we will consider a density smoothness parameter estimation problem via wavelet theory. The smoothness parameter is defined in the sense of equivalent Besov norms. It is well-known that it is almost impossible to estimate this kind of parameter in general case. But it becomes possible when we add some conditions (to our proof, we can not remove them) to the density function. Besides, the density function contains impurities. It is covered by some additive noises, which is the key point we want to show in this paper.