• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1169-1180
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• 2006

Partial least squares regression (PLS) is a biased, non-least squares regression method and is an alternative to the ordinary least squares regression (OLS) when predictors are highly collinear or predictors outnumber observations. One way to understand the properties of biased regression methods is to know how the estimators shrink the OLS estimator. In this paper, we introduce an expression for the shrinkage factor of PLS and develop a new shrinkage expression, and then prove the equivalence of the two representations. We use two near-infrared (NIR) data sets to show general behavior of the shrinkage and in particular for what eigendirections PLS expands the OLS coefficients.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.251-259
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• 2002

Lagged regressor models with general stationary errors independent of the regressors are considered. The regressor process is unstable having characteristic roots on the unit circle. If the order of the lag matches the number of roots on the unit circle, the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. This result extends the well-known result of Grenander and Rosenblatt (1957) for asymptotic efficiency of the OLSE in deterministic polynomial and/or trigonometric regressor models to a class of models with stochastic regressors.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.143-153
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• 2000

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.85-96
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• 1989

This paper is concerned with the strong consistency of the least squares estimators for the nonlinear regression models. A simple and practical sufficient condition for the strong consistency of the least squares estimators is given. It is also discussed that the extension of the strong consistency to a wide class of regression functions can be established by imposing some condition on the input values. Some examples are given to illustrate the application of main result.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.633-641
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• 2001

The least squares method is usually applied when estimating the parameters in the regression models. However the least square estimator is not very efficient when the distribution of the error is skewed. In this paper, we propose the asymmetric least square estimator for a particular nonlinear time series regression model, and give the simple and practical sufficient conditions for the strong consistency of the estimators.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.651-659
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• 2001

Preference map is a widely used graphical method for the preference data set which is frequently encountered in the field of marketing research. This provides joint configuration usually in two dimensional space between "products" and their "attributes". Whereas the classical preference map adopts the ordinary least squares method in deriving map, the present article suggests the weighted least squares approach providing the better graphical display and interpretation compared to the classical one. Internet search engine data in Korea are analysed for illustration.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1189-1191
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• 2005

This paper introduces the least-squares order-recursive lattice (LSORL) Laguerre smoother that has order-recursive smoothing structure based on the Laguerre signal representation. The LSORL Laguerre smoother gives excellent performance for a channel equalization problem with smaller order of tap-weights than its counterpart algorithm based on the transversal filter structure. Simulation results show that the LSORL Laguerre smoother gives better performance than the LSORL transversal smoother.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.135-138
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• 2005

In this paper, we consider the problem of testing for parameter change in time series models based on a cusum of squares. Although the test procedure is well-established for the mean and variance in time series models, a general parameter case was not discussed in literatures. Therefore, here we develop the cusum of squares type test for parameter change in a more general framework. As an example, we consider the change of the parameters in an RCA(1) model. Simulation results are reported for illustration.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.10a
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• pp.300-305
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• 1998

A method of calculating wear amount which is based on digitally measured surface profile was suggested. The original profile of worn out profile was estimated from its adjacent surface profile by using least squares curve fitting with Fourier series. The approximated curve was well fitted to original surface profile. With this approach, more accurate calculation of the wear amount will be possible.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.983-994
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• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.