• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.179-187
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• 2013

Bates and Watts (1981) have discussed the problems of reparameterizing nonlinear models in obtaining accurate linear approximation confidence regions for the parameters. A similar problem exists with computing confidence curves for fitted values or predictions. The statistical behavior of fitted values does not depend on the parameterization. Thus, as long as the intrinsic curvature is small, standard Wald intervals for fitted values are likely to be sufficient. Accuracy of linear approximation for fitted values is investigated using confidence curves.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.401-419
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• 2024

Let K, H, K_II and H_II be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface T_γ(α) with the radius γ along a timelike curve α(s) in Minkowski 3-space E³₁. We prove that T_γ(α) must be a (K, H)-Weingarten surface and a (K, H)-linear Weingarten surface. We also show that T_γ(α) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y) ∈ {(K, K_II), (K, H_II), (H, K_II), (H, H_II), (K_II , H_II)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y)-linear Weingarten type, (X, Y, Z)-linear Weingarten type and (K, H, K_II, H_II)-linear Weingarten type along a timelike curve in E³₁, where (X, Y, Z) ∈ {(K, H, K_II), (K, H, H_II), (K, K_II, H_II), (H, K_II, H_II)}.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.637-644
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• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.131-136
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• 2011

The original Bates-Watts framework applies only to the complete parameter vector. Thus, guidelines developed in that framework can be misleading when the adequacy of the linear approximation is very different for different subsets. The subset curvature measures appear to be reliable indicators of the adequacy of linear approximation for an arbitrary subset of parameters in nonlinear models. Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. The accuracy of outlier tests is investigated using subset curvatures.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.271-284
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• 2012

Let M be a linear Weingarten spacelike hypersurface in a locally symmetric Lorentz space with R = aH + b, where R and H are the normalized scalar curvature and the mean curvature, respectively. In this paper, we give some conditions for the complete hypersurface M to be totally umbilical.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.913-917
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• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-477
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• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Journal of Multimedia Information System
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• v.2 no.1
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• pp.171-178
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• 2015

This article describes 3 dimensional (3D) face recognition system using histogram of oriented gradients (HOG) based on face curvature. The surface curvatures in the face contain the most important personal feature information. In this paper, 3D face images are recognized by the face components: cheek, eyes, mouth, and nose. For the proposed approach, the first step uses the face curvatures which present the facial features for 3D face images, after normalization using the singular value decomposition (SVD). Fisherface method is then applied to each component curvature face. The reason for adapting the Fisherface method maintains the surface attribute for the face curvature, even though it can generate reduced image dimension. And histogram of oriented gradients (HOG) descriptor is one of the state-of-art methods which have been shown to significantly outperform the existing feature set for several objects detection and recognition. In the last step, the linear discriminant analysis is explained for each component. The experimental results showed that the proposed approach leads to higher detection accuracy rate than other methods.

• Korean Journal of Optics and Photonics
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• v.18 no.1
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• pp.19-23
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• 2007

We derived analytically the generalized curvature linear equation useful in the initial optical design of a two-mirror system with finite object distance, including an infinite object distance from paraxial ray tracing and Seidel third order aberration theory for coma coefficient. These aberration coefficients for finite object distance were described by the curvature, the inter-mirror distance, and the effective focal length. The analytical equations were solved by using a computer with a numerical analysis method. Two useful linear relationships, determined by the generalized curvature linear equations relating the curvatures of the two mirrors, for the cancellation of each aberration were shown in the numerical solutions satisfying the nearly zero condition ($<10^{-10}$) for each aberration coefficient. These equations can be utilized easily and efficiently at the step of initial optical design of a two-mirror system with finite object distance.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.237-250
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• 2002

Motivated by Cook's (1986) assessment of local influence by investigating the curvature of a surface associated with the overall discrepancy measure, this paper extends this idea to the linear regression model with AR(p) disturbances. Diagnostic for the linear regression models with AR(p) disturbances are discussed when simultaneous perturbations of the response vector are allowed. For the derived criterion, numerical studies demonstrate routine application of this work.