• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.229-239
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• 2007

We present a diagnostic method for the quasi-likelihood estimators in generalized linear models. Since these estimators can be usually obtained by iteratively reweighted least squares which are well known to be very sensitive to unusual data, a diagnostic step is indispensable to analysis of data. We extend the local influence approach based on the maximum likelihood function to that on the quasi-likelihood function. Under several perturbation schemes local influence diagnostics are derived. An illustrative example is given and we compare the results provided by local influence and deletion.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.197-206
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• 2006

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.4
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• pp.797-802
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• 2010

In this paper, a systematic procedure to design a nonlinear controller for nonlinear active magnetic bearing (AMB) systems is presented. To do this, we effectively convert the AMB system into a polytopic quasi-linear parameter varying (LPV) system, which is a representation of nonlinear state-space models and is described by the convex combination of a set of precisely known vertices. Unlike the existing quasi-LPV systems, the nonlinear weighting functions, which construct the polytopic quasi-LPV model of the AMB system by connecting the vertices, include not only state variables but also the input ones. This allows us to treat the input nonlinearity effectively. By means of the derived polytopic quasi-LPV model and linear matrix inequality (LMI) conditions, nonlinear controller that stabilizes the AMB system is obtained. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.47.2-47.2
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• 2016

The protons and helium ions in the solar wind are observed to possess anisotropic temperature profiles. The anisotropy appears to be limited by various marginal instability conditions. One of the efficient methods to investigate the global dynamics and distribution of various temperature anisotropies in the large-scale solar wind models may be that based upon the macroscopic quasi-linear approach. The present paper investigates the proton and helium ion anisotropy instabilities on the basis of comparison between the quasi-linear theory versus particle-in-cell simulation. It is found that the overall dynamical development of the particle temperatures is quite accurately reproduced by the macroscopic quasi-linear scheme. The wave energy development in time, however, shows somewhat less restrictive comparisons, indicating that while the quasi-linear method is acceptable for the particle dynamics, the wave analysis probably requires higher-order physics, such as wave-wave coupling or nonlinear wave-particle interaction. We carried out comparative studies of proton firehose instability, aperiodic ordinary mode instability, and helium ion anisotropy instability. It was found that the agreement between QL theory and PIC simulation is rather good. It means that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.219-225
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• 1998

The parameters in linear models with censored normal responses are usually estimated by the iterative maximum likelihood and least square methods. However, the iterative least square method is simple but hardly has theoretical justification, and the iterative maximum likelihood estimating equations are complicatedly derived. In this paper, we justify these methods via Wedderburn (1974)'s quasi-likelihood approach. This provides an explicit justification for the iterative least square method and also directly the iterative maximum likelihood method for estimating the regression coefficients.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.773-786
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• 2023

In this paper, we introduce the pseudospectra of bounded linear operators on quasi normed space and study its proprieties. Beside that, we establish the relationship between the pseudospectra of a sequence of bounded linear operators and its limit.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.133-145
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• 2007

Local linear estimator has a number of advantages over the traditional kernel estimators. The better performance near boundaries is one of them. However, local linear estimator can produce erratic result in sparse regions in the realization of the design and to solve this problem much research has been done. Local linear quasi-likelihood estimator has many common properties with local linear estimator, and it turns out that sparse design can also lead local linear quasi-likelihood estimator to erratic behavior in practice. Several methods to solve this problem are proposed and their finite sample properties are compared by the simulation study.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.247-260
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• 1997

The quasi-likelihood models which greatly widened the scope of generalized linear models are widely used in data analysis where a likelihood is not available. Since a quasi-likelihood may not appear to be an ordinary likelihood for any known distribution in the natural exponential family, to fit the quasi-likelihood models the standard statistical packages such as GLIM, GENSTAT, S-PLUS and so on may not directly applied. SAS/IML is very useful for fitting of such models. In this paper, we present simple SAS/IML(version 6.11) program which helps to fit and analyze the quasi-likelihood models applied to the leaf-blotch data introduced by Wedderburn(1974), and the problem with deviance useful generally to model checking is pointed out, and then its solution method is mention through the data analysis based on this quasi-likelihood models checking.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.362-367
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• 1996

In this paper, the eigenstructure of a class of linear time varying systems, termed as linear quasi-time invariant(LQTI) systems, is investigated. A system composed of dynamic devices such as linear time varying capacitors and resistors can be an example of the class. To effectively describe and analyze the LQTI systems, a generalized differential operator G is introduced. Then the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characteristics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. Also the corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency domain analysis of the systems under consideration. As an application example, a LQTI circuit is examined by using the concept of eigenstructure of LQTI system. The LQTI filter processes the sinusoidal signals modulated by some functions.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.541-562
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• 2000

The generalized linear mixed model framework is for handling count-type categorical data as well as for clustered or overdispersed non-Gaussian data, or for non-linear model data. In this study, we review its general formulation and estimation methods, based on quasi-likelihood and Monte-Carlo techniques. The current research areas and topics for further development are also mentioned.