• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.115-134
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• 1994

Polynomial errors-in-variables model with one predictor variable and one response variable is defined and an estimator of model is derived following the Booth's linear model estimation procedure. Since polynomial model is nonlinear function of the unknown regression coefficients and error-free predictors, it is nonlinear model in errors-in-variables model. As a result of applying linear model estimation method to nonlinear model, some additional assumptions are necessary. Hence, an estimator is derived under the assumption that the error variances are decrasing as sample size increases. Asymptotic propoerties of the derived estimator are provided. A simulation study is presented to compare the small sample properties of the derived estimator with those of OLS estimator.

• Nutrition Research and Practice
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• 제5권4호
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• pp.357-364
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• 2011

Selenium is an antioxidant trace element linked to cardiovascular disease and cancer. Although diet is a major source, relatively little else is known about independent determinants of selenium levels in free-living humans. In this study, we aimed to investigate the independent demographic. lifestyle, and dietary determinants of selenium levels in 1,997 men and 1,905 women in two large prospective U.S. cohorts. Toenail selenium levels were quantified using neutron activation analysis. Diet, geographic residence, demographic, and environmental factors were assessed by validated self-administered questionnaires. Multivariate generalized linear models were conducted to assess the independent relations of these factors with toenail selenium levels, correcting for measurement error in the diet. In multi variable-adjusted analyses, independent predictors of higher selenium were male gender (6.3% higher levels); living in West and Northern-Midwest U.S. regions (8.9% and 7.4% higher than Southern-Midwest regions, respectively); consumption of beef and bread products (between 0.7 - 2.5% higher per daily serving); and selenium supplement use (6.9% higher than non-users); whereas cigarette smoking (5-10% lower than never smokers), older age (0.6% lower per 5 years), and consumption of eggs, white rice, dairy products, coffee, and alcohol (between 0.1 to 2.0% lower per daily serving) were associated with lower selenium. Multiple dietary and non-dietary factors independently predicted selenium levels, suggesting that both consumption and non-dietary processes (e.g.. related to oxidant status) may affect levels. Significant geographic variation in selenium levels exists in the US.

• 천문학회보
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• 제42권2호
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• pp.59.5-60
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• 2017

We present the relationship between vector magnetic field parameters and solar major flare occurrence rate. Based on this, we are developing a forecast model of major flare (M and X-class) occurrence rate within a day using hourly vector magnetic field data of Space-weather HMI Active Region Patch (SHARP) from May 2010 to April 2017. In order to reduce the projection effect, we use SHARP data whose longitudes are within ${\pm}60$ degrees. We consider six SHARP magnetic parameters (the total unsigned current helicity, the total photospheric magnetic free energy density, the total unsigned vertical current, the absolute value of the net current helicity, the sum of the net current emanating from each polarity, and the total unsigned magnetic flux) with high F-scores as useful predictors of flaring activity from Bobra and Couvidat (2015). We have considered two cases. In case 1, we have divided the data into two sets separated in chronological order. 75% of the data before a given day are used for setting up a flare model and 25% of the data after that day are used for test. In case 2, the data are divided into two sets every year in order to reduce the solar cycle (SC) phase effect. All magnetic parameters are divided into 100 groups to estimate the corresponding flare occurrence rates. The flare identification is determined by using LMSAL flare locations, giving more numbers of flares than the NGDC flare list. Major results are as follows. First, major flare occurrence rates are well correlated with six magnetic parameters. Second, the occurrence rate ranges from 0.001 to 1 for M and X-class flares. Third, the logarithmic values of flaring rates are well approximated by two linear equations with different slopes: steeper one at lower values and lower one at higher values. Fourth, the sum of the net current emanating from each polarity gives the minimum RMS error between observed flare rates and predicted ones. Fifth, the RMS error for case 2, which is taken to reduce SC phase effect, are smaller than those for case 1.