• The Korean Journal of Applied Statistics
• /
• v.15 no.2
• /
• pp.395-403
• /
• 2002

In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.

• The Korean Journal of Applied Statistics
• /
• v.17 no.1
• /
• pp.61-73
• /
• 2004

Rotation sampling designs may be classified into two categories. The first type uses the same sample unit for the entire life of the survey. The second type uses the sample unit only for a fixed number of times. In both type of designs, the entire sample is partitioned into a finite number(=G) of rotation groups. This paper is generalization of the first type designs. Since the generalized design can be identified by only G rotation groups and recall level 1, we denote this rotation system as l/G rotation design. Under l/G rotation design, variance and mean squared error (MSE) of generalized composite estimator are derived, incorporating two type of biases and exponentially decaying correlation pattern. Compromising MSE's of some selected l/G designs, we investigate design efficiency, design gap effect, ans the effects of correlation and bias.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.5B
• /
• pp.429-435
• /
• 2010

This study proposed a methodology for evaluating the radar rainfall data, whose basic idea is similar to the analysis of variance in statistics. This method enables us to represent separately the error from the bias and that from the data variability. The proposed method was then applied to two storm events for its evaluation. As results, the error from the bias was found to comprises most of the raw radar data error, which becomes significantly decreased in the quality improved cases. On the other hand, the error from the data variability was rather increased due to the quality improvement procedure. The proposed methodology was found to be effective for evaluating the data quality of a storm event for steps of quality improvement, but has a limitation for comparing qualities of storm events. This limitation should be implemented for its general application.

• Journal of the Korean Statistical Society
• /
• v.36 no.1
• /
• pp.57-76
• /
• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.1
• /
• pp.430-437
• /
• 2018

Ultrasonic attenuation is an important parameter in Quantitative Ultrasound and many algorithms have been proposed to improve estimation accuracy and repeatability for multiple independent estimates. In this work, we propose an improved algorithm for estimating ultrasonic attenuation utilizing the optimal frequency compounding technique based on stochastic noise model. We formulate mathematical compounding equations in the AWGN channel model and solve optimization problems to maximize the signal-to-noise ratio for multiple frequency components. Individual estimates are calculated by the reference phantom method which provides very stable results in uniformly attenuating regions. We also propose the guideline to select frequency ranges of reflected RF signals. Simulation results using numerical phantoms show that the proposed optimal frequency compounding method provides improved accuracy while minimizing estimation bias. The estimation variance is reduced by only 16% for the un-compounding case, whereas it is reduced by 68% for the uniformly compounding case. The frequency range corresponding to the half-power for reflected signals also provides robust and efficient estimation performance.

• Journal of the Korean Statistical Society
• /
• v.21 no.2
• /
• pp.187-200
• /
• 1992

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.109.5-109
• /
• 2001

The separation of scintillation phenomena concurrent with rain attenuation phenomena can be accomplished by filtering. Based on the analysis of satellite signal fading during rain, scintillation and rain attenuation phenomena are examined and extracting from raw data by using adaptive IIR high-pass filter and adaptive IIR low-pass filter. Adaptive IIR filter are designed by using the algorithm of Least Mean p-Power (LMP) Error Criterion which have been modified by Quantizing Gradient technique. This algorithm reduces amount of multiplication computational equal to the length of input data. It is prove here that the convergence speed, variance, bias independence on p values. For this application, p=1 is chosen. The procedure of application ...

• Communications for Statistical Applications and Methods
• /
• v.20 no.1
• /
• pp.63-75
• /
• 2013

In this paper, we derive maximum likelihood estimators (MLEs) and approximate maximum likelihood estimators (AMLEs) of unknown parameters in a generalized half logistic distribution under Type-II hybrid censoring. We also obtain approximate confidence intervals using asymptotic variance and covariance matrices based on the MLEs and the AMLEs. As an illustration, we examine the validity of the proposed estimation using real data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE), bias, and length of the approximate confidence interval through a Monte Carlo simulation for various censoring schemes.

• Journal of Periodontal and Implant Science
• /
• v.45 no.1
• /
• pp.2-7
• /
• 2015

A fundamental problem in analyzing complex multilevel-structured periodontal data is the violation of independency among the observations, which is an assumption in traditional statistical models (e.g., analysis of variance and ordinary least squares regression). In many cases, aggregation (i.e., mean or sum scores) has been employed to overcome this problem. However, the aggregation approach still exhibits certain limitations, such as a loss of power and detailed information, no cross-level relationship analysis, and the potential for creating an ecological fallacy. In order to handle multilevel-structured data appropriately, mixed effects models have been introduced and employed in dental research using periodontal data. The use of mixed effects models might account for the potential bias due to the violation of the independency assumption as well as provide accurate estimates.

• Journal of Korean Institute of Industrial Engineers
• /
• v.14 no.2
• /
• pp.91-97
• /
• 1988

In accelerated life testing, a relationship is usually assumed between the stress and a parameter of the lifetime distribution. However, the true relationship is not usually known, and therefore, the experimenter may wish to provide protections against the likely departures from the assumed relationship. This paper considers an accelerated life test in which two stress levels are involved, and the lifetime of each test item at a stress level is assumed to have an independent, identical, exponential distribution. For the case where a first order relationship is assumed while the true one is quadratic, a procedure is developed for allocating test items to stress levels such that the bias and/or the variance of the estimated(log-transformed) mean lifetime at the use condition is minimized.