• East Asian mathematical journal
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• v.5 no.1
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• 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.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.641-648
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• 2007

We propose the new sampling method, called modified ranked ordering set sampling (MROSS). Kim and Kim (2003) suggested the sign test using the ranked ordering set sampling (ROSS), and showed that the asymptotic relative efficiency (ARE) of ROSS against RSS for sign test increases as sample size does. We propose the estimator for the population mean using MROSS. The relative precision (RP) of estimator of the population mean using MROSS method with respect to the usual estimator using modified RSS is higher, and when the underlying distribution is skewed, the bias of the proposed estimator is smaller than that of several ranked set sampling estimators.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.81-90
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• 1983

The least squares estimator of disturbance variance in a regression model is biased under a serial correlation. Under the assumption of an AR(I), Theil(1971) crudely related the bias with the autocorrelation of the disturbances and the autocorrelation of the explanatory variable for a simple regression. In this paper we derive a relation which relates the bias with the autocorrelation of disturbances and the autocorrelation of explanatory variables for a multiple regression with improved precision.

• Journal of Communications and Networks
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• v.16 no.6
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• pp.583-591
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• 2014

In wireless communications, knowledge of the signal-to-noise ratio is required in diverse communication applications. In this paper, we derive the variance of the maximum likelihood estimator in the data-aided and non-data-aided schemes for determining the optimal shrinkage factor. The shrinkage factor is usually the constant that is multiplied by the unbiased estimate and it increases the bias slightly while considerably decreasing the variance so that the overall mean squared error decreases. The closed-form biased estimators for binary-phase-shift-keying and quadrature phase-shift-keying systems are then obtained. Simulation results show that the mean squared error of the proposed method is lower than that of the maximum likelihood method for low and moderate signal-to-noise ratio conditions.

• The Korean Journal of Applied Statistics
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• v.31 no.3
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• pp.397-408
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• 2018

Various methods for accurate parameter estimation have been developed in a sample survey and it is also common to use a ratio estimator or the regression estimator using auxiliary information. The ratio-type estimator has been used in many recent studies and is known to improve the accuracy of estimation by adjusting the ratio estimator. However, various studies are under way to solve it since the ratio-type estimator is biased. In this study, we propose a generalized ratio-type estimator with a new parameter added to the ratio-type estimator to remove the bias. We suggested a method to apply this result to the parameter estimation under the error assumption of heteroscedasticity. Through simulation, we confirmed that the suggested generalized ratio-type estimator gives good results compared to conventional ratio-type estimators.

• Smart Structures and Systems
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• v.17 no.4
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• pp.647-667
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• 2016

In this paper, dynamic displacement is estimated with high accuracy by blending high-sampling rate acceleration data with low-sampling rate displacement measurement using a two-stage Kalman estimator. In Stage 1, the two-stage Kalman estimator first approximates dynamic displacement. Then, the estimator in Stage 2 estimates a bias with high accuracy and refines the displacement estimate from Stage 1. In the previous Kalman filter based displacement techniques, the estimation accuracy can deteriorate due to (1) the discontinuities produced when the estimate is adjusted by displacement measurement and (2) slow convergence at the beginning of estimation. To resolve these drawbacks, the previous techniques adopt smoothing techniques, which involve additional future measurements in the estimation. However, the smoothing techniques require more computational time and resources and hamper real-time estimation. The proposed technique addresses the drawbacks of the previous techniques without smoothing. The performance of the proposed technique is verified under various dynamic loading, sampling rate and noise level conditions via a series of numerical simulations and experiments. Its performance is also compared with those of the existing Kalman filter based techniques.

• IE interfaces
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• v.22 no.3
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• pp.214-222
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• 2009

In the early design stage, system reliability must be estimated from life testing data at the component level. Previously, a point estimate of system reliability was obtained from the unbiased estimate of the component reliability after assuming that the number of failed components for a given time followed a binomial distribution. For deriving the confidence interval of system reliability, either the lognormal distribution or the normal approximation of the binomial distribution was assumed for the estimator of system reliability. In this paper, a new estimator is used for the component level reliability, which is biased but has a smaller mean square error than the previous one. We propose to use the beta distribution rather than the lognormal or approximated normal distribution for developing the confidence interval of the system reliability. A numerical example based on Monte Carlo simulation illustrates advantages of the proposed approach over the previous approach.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.815-824
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• 2013

Traditional Pearson chi-squared test is not appropriate for the data collected by the complex sample design. When one uses the traditional Pearson chi-squared test to the complex sample categorical data, it may give wrong test results, and the error may occur not only due to the biased variance estimators but also due to the biased point estimators of cell proportions. In this study, the design based consistent Wald test statistics was derived for k-population homogeneity test, and the traditional Pearson chi-squared test statistics was partitioned into three parts according to the causes of error; the error due to the bias of variance estimator, the error due to the bias of cell proportion estimator, and the unseparated error due to the both bias of variance estimator and bias of cell proportion estimator. An analysis was conducted for empirical results of the relative size of each error component to the Pearson chi-squared test statistics. The second year data from the fourth Korean national health and nutrition examination survey (KNHANES, IV-2) was used for the analysis. The empirical results show that the relative size of error from the bias of variance estimator was relatively larger than the size of error from the bias of cell proportion estimator, but its degrees were different variable by variable.