• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.31-41
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• 1999

We investigate some techniques of iterative refinement of solutions of a nonsingular system Ax = b with A partitioned into blocks using only single precision arithmetic. We prove that iterative refinement improves a blockwise measure of backward stability. Some applications of the results for the least squares problem (LS) will be also considered.

• 대한수학회논문집
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• 제12권3호
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• pp.813-827
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• 1997

Multigrid methods for two first-order system least squares (FOSLS) using bilinear finite elements are developed for the pure traction problem of planar linear elasticity. They are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. In this paper, concentration is given on solving for the gradients of displacement only. Numerical results show that the convergences are uniform even as the material becomes nearly incompressible. Computations for convergence rates are included.

• 한국경영과학회지
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• 제28권3호
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• pp.61-66
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• 2003

In many multiple regression analyses, the “multi-collinearity” problem arises since some independent variables are highly correlated with each other. Practically, the Ridge regression method is often adopted to deal with the problems resulting from multi-collinearity. We propose a better alternative method using iteration to obtain an exact least squares estimator. We prove the solvability of the proposed algorithm mathematically and then compare our method with the traditional one.

• Journal of the Korean Statistical Society
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• 제34권2호
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• pp.109-123
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• 2005

Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.

• Communications for Statistical Applications and Methods
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• 제4권2호
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• pp.353-358
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• 1997

When the disturbances in the linear repression medel are generated by a seasonal autoregressive scheme the Cochrane Orcutt transformation estimator (COTE) is a well known alternative to Generalized Least Squares estimator (GLSE). In this paper it is analyzed in which situation the Ordinary Least Squares estimator (OLSE) is always better than COTE for positive autocorrelation in terms of efficiency which is here defined as the ratio of the total variances.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.183-192
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• 1996

The least squares cross validated bandwidth is the mini-mizer of the corss validation function for choosing the smooth parame-ter of a kernel density estimator. It is a completely automatic method but it requires inordinate amounts of computational time. We present a convenient formula for calculation of the cross validation function when the kernel function is a symmetric polynomial with finite sup-port. Also we suggest an algorithm for finding global minima of the crass validation function.

• 한국음향학회:학술대회논문집
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• 한국음향학회 1987년도 학술발표회 논문집
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• pp.58-60
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• 1987

In this paper, we investigate an infinite impulse response adaptive digital filter based on the nonlinear least-squares algorithm, and compare its convergence speed to that of a self-orthogonalizing IIR ADF which is known to have fastest convergence. By simulation, it is shown that the NLS IIR ADF converges faster than other known IIR ADF's, especially for a low-order case.

• 한국음향학회:학술대회논문집
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• 한국음향학회 1987년도 학술발표회 논문집
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• pp.79-81
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• 1987

In this paper we propose a fast adaptive least squares algorithm for linear phase FIR filters. The algorithm requires 10m multiplications per data point where m is the filter order. Both linear phase cases with constant phase delay and constant group delay are examined. Simulation results demonstrate that the proeposed algorithm is superior to the LMS gradient algorithm and the averaging scheme used for the modified fast Kalman algorithm.

• 대한수학회보
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• 제48권4호
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• pp.839-845
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• 2011

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

• Journal of the Korean Statistical Society
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• 제16권2호
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• pp.80-91
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• 1987

Minimum $L_i$ norm estimation is a robust procedure ins the sense that it leads to an estimator which has greater statistical eficiency than the least squares estimator in the presence of outliers. And the $L_1$ norm estimator has some desirable statistical properties. In this paper a new computational procedure for $L_1$ norm estimation is proposed which combines the idea of reweighted least squares method and the linear programming approach. A modification of the projective transformation method is employed to solve the linear programming problem instead of the simplex method. It is proved that the proposed algorithm terminates in a finite number of iterations.