• Journal of the Korean Statistical Society
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• v.10
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• pp.91-96
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• 1981

The development of Minimum Norm Quadratic Unbiased Estimation (MINQUE) has introduced a unified approach for the estimation of variance components in general linear models. The computational problem has been studied by Liu and Senturia (1977) and Goodnight (1978, setting a-priori values to 0). This paper further simplifies the computation and gives efficient and compact computational algorithm for the MINQUE and dispersion matrix in general linear random model.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.4-12
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• 1989

An efficient method for computing minimum norm quadratic unbiased estimates (MINQUE) of variance components in the mixed model is developed. This computing algorithm which used W-matrix saves both storage usage and computing time.

• Journal of the Korean Statistical Society
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• v.9 no.1
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• pp.97-108
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• 1980

Variance components model appears often in designing experiments including time series data analysis. This paper is investigating the properties of the various procedures in estimating variance components for the two-way random model without interaction under normality. In this age of computer-oriented computations, MINQUE is found to be quite practicla because of the robustness with respect to the design configurations and parameters. Also adjusted AOV type estimation procedure is found to yield superior results over the unadjusted one.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.121-130
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• 1993

For the One-way random effects model with unbalanced data, the AOV and MINQUE estimates of variance components are frequently found to be negative. The primary objective of present study is placed on the computation of the probability of the main effect variance component, being negative. The probability of negative estimators from AOV and MINQUE can be obtained by theoretical computation under the normality assumption. It is, however, difficult to compute the probability of negative estimates for these estimators under arbitrary distributions, and hence their probabilities of being negative were computed by simulation experiment in this study. It was shown that there was no significant difference between the theoretical probability under normality and calculated probability by simulation experiment, and that probability of negative estimates decreases as sample size, number of levels and the value of increase.

• The Korean Journal of Applied Statistics
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• v.10 no.1
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• pp.177-187
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• 1997

This article considers the power performance of the tests in unbalanced two way mixed linear models with one fixed factor. The generalized least squares (GLS) F statistic testing no differences among the effects of the levels of the fixed factor is estimated using Henderson's method III, minimum norm quadratic unbiased estimator (MINQUE) with prior guess 1, maximum likelihood (ML) and resticted maximum likelihood (REML). We investigate the power performance of these test statistics. It can be shown, through simulation, that the GLS F statistics using four estimators produce similar type I error rates and power performance.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.35 no.6
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• pp.573-580
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• 2017

Precise stochastic modeling for GPS measurements is one of key factors in adjustment computations for GPS positioning. To analyze the GPS measurement errors, Minimum Norm Quadratic Unbiased Estimators(MINQUE) approach is used in this study to estimate the variance components for measurement types with short-baseline GPS positioning model. The results showed the magnitudes of measurement errors for C1, P2, L1, L2 are 22.3cm, 27.6cm, 2.5mm, 2.2mm, respectively. To reduce the memory usage and computational burden, variance components are also estimated on epoch-by-epoch basis. The results showed that there exists slight differences between the solutions. However, epoch-by-epoch analysis may also be used for most of GPS applications considering the magnitudes of the differences.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.623-632
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• 1998

이원혼합모형에서 고정효과의 추정가능한 함수에 대한 신뢰구간을 구하는 경우에 어떤 분산성분추정량을 선택하는 것이 가장 바람직한가를 모의실험을 통하여 살펴본다 혼합모형에서는 t-분포와 일반화최소제곱추정량을 사용하여 신뢰구간을 구할 수 있는데, 일반적으로 분산성분을 알 수 없기 때문에 분산성분을 반드시 추정하여야만 한다. 이 경우 분산성분의 추정량으로 가장 많이 사용되는 추정량들인 Henderson의 방법 III 추정량, 사전추측값이 1인 MINQUE 추정량, MLE(최우추정량), REMLE(제한최우추정량)를 이용하여 분산행렬을 추정하고, 신뢰구간의 포함범위확률과 평균길이를 모의실험을 통하여 살펴본다. 모의실험의 결과는 4가지 추정량 모두 비슷한 신뢰구간의 포함범위확률과 평균길이를 갖는 것으로 판명되었다.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.457-469
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• 1996

In this paper, we propose a method for an exact test of H : $p_i$ = $r_i$ for all i against K : $p_i$ $\neq$ $r_i$ for some i in an unbalanced random effect linear model, where $p_i$ denotes the ratio of the i-th variance component to the error variance. Then we present a method to test H : $p_i$ $\leq$ r against K : $p_i$> r for some specific i by applying orthogonal projection on the model. We also show that any test statistic that follows an F-distribution on the boundary of the hypotheses is equal to the one given here.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.11-18
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• 2003

Quite often normality assumptions are not satisfied in practical applications. In this paper, an estimated generalized least squares(EGLS) analysis are considered in two way mixed linear models with arbitrary types of distributions for random effects. We investigate the power performance of EGLS analysis based on Henderson's method III, ML, REML and MINQUE(1). The power performances depend on the imbalance of design, on the actual values of ratio of variance components, and on the skewness and kurtosis parameters of the underlying distributions slightly. Results of our limited simulation study suggest that the EGLS F-statistics using four estimators and arbitrary distributions produce similar type I error rates and power performance.

• Horticultural Science & Technology
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• v.35 no.3
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• pp.361-372
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• 2017

Bred and grown around the world, tomato (Solanum spp.) has highly valuable fruits containings various anti-oxidants such as lycopene, flavonoids, glutamine, and ${\beta}-carotene$. Several studies have explored, way in which to enhance the growth, management and quality of tomato, we focus on the management of growth for yield rather than quality. The expression of superior agronomic traits depends on where cultivars are grown. We evaluated 10 cultivars grown in three environment for their lycopene. HTL3137 ($70.48mg{\cdot}kg^{-1}$), which was grown in Yoeju in spring/summer, contained the highest lycopene content, while HTL10256 ($20.9mg{\cdot}kg^{-1}$), which was grown in Suwon in spring/summer, contain the least lycopene.Correlations between color components and lycopene content varied according to growing location and season. In spring/summer-grown tomatoes from Suwon, no significant correlation was observed between any color component (redness [R], greenness [G], blueness [B], luminosity, $L^*$, $a^*$, $b^*$, hue and chroma) and lycopene content. A correlation was observed between B and lycopene content in tomatoes grown in Yeoju during the same season. In tomatoes grown in Yeoju in fall/winter, significant correlations were found between lycopene content and G, luminosity, $L^*$, and hue. Variance in interactions between genotype, environment, and genotype ${\times}$ environment (G ${\times}$ E) using Minimum Norm Quadratic Unbiased Estimate (MINQUE) analysis indicated that lycopene content depends on genotype (51.33%), environment (49.13%), and G ${\times}$ E (21.43%). However, when the Additive Main Effects and Multiplicative Interaction (AMMI) was used, the G ${\times}$ E value was highest.