• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.327-336
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• 2001

This work concerns estimating a regression function, which is not linear, using aggregate data. In much of the empirical research, data are aggregated for various reasons before statistical analysis. In a traditional parametric approach, a linear estimation of the non-linear function with aggregate data can result in unstable estimators of the parameters. More serious consequence is the bias in the estimation of the non-linear function. The approach we employ is the kernel regression smoothing. We describe the conditions when the aggregate data can be used to estimate the regression function efficiently. Numerical examples will illustrate our findings.

• Korean Journal of Veterinary Research
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• v.50 no.1
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• pp.11-17
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• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.4
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• pp.499-505
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• 2006

Regularlization approach to regression can be easily found in Statistics and Information Science literature. The technique of regularlization was introduced as a way of controlling the smoothness properties of regression function. In this paper, we have presented a new method to evaluate linear and non-linear fuzzy regression model based on Tanaka's model using the idea of regularlization technique. Especially this method is a very attractive approach to model non -linear fuzzy data.

• Asian-Australasian Journal of Animal Sciences
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• v.9 no.4
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• pp.439-447
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• 1996

Monthly test day production for 12,020 records, were collected from six of the largest specialized dairy farms located in central region of the Kingdom of Saudi Arabia. The records described lactating cows in four parities and two seasons of calving. Monthly test day records were fitted using Wood's model $At{{^b}{_e}}^{-ct}$ with multiple and additive error term. Linear and non-linear regression models were used to find the estimates of the parameters necessary to draw the lactation curves. The shape of the lactation curves of different parities showed that third lactation has the heighest peak (43.08 kg) for linear regression model and (42.08 kg) for non-linear regression model. Fourth lactation has the lowest peak (24.00kg) for linear regression model and (25.64 kg) for non-linear regression models. Cows of second and third lactations reached the peak at 58 day for both linear and non-linear regression models. Cows of first lactation were more persistent and had late peak at 68 and 67 days for both models respectively. While, third lactation cows were lower persistent and had early peak at 58 day for both models. Cows calved at winter months have higher starting values (A), higher ascending slope (b) and higher decending slope (c). Least square means of milk yield of the first four parities and for overall data were 6,653, 7,659, 7,482, 6,988 and 7,614 kg respectively. The corresponding lactation period were 358, 367, 350, 363 and 364 days respectively.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.515-524
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• 2007

This paper deals with local linear estimation of fuzzy regression models based on Diamond(1998) as a new class of non-linear fuzzy regression. The purpose of this paper is to introduce a use of smoothing in testing for lack of fit of parametric fuzzy regression models.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.394-394
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• 2000

This Paper proposes a new nonlinear partial least square method that extends the linear PLS. Proposed nonlinear PLS uses self-organizing feature map as PLS outer relation and multilayer neural network as PLS inner regression method.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.773-786
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• 2016

Multiple quantile regression that simultaneously estimate several conditional quantiles of response given covariates can provide a comprehensive information about the relationship between the response and covariates. Some quantile estimates can cross if conditional quantiles are separately estimated; however, this violates the definition of the quantile. To tackle this issue, multiple quantile regression with non-crossing constraints have been developed. In this paper, we carry out a comparison study on several popular methods for non-crossing multiple linear quantile regression to provide practical guidance on its application.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.445-449
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• 2005

Yen et al. [Fuzzy Sets and Systems 106 (1999) 167-177] calculated the fuzzy membership function for the output to find the non-symmetric triangular fuzzy number coefficients of a linear regression model for all given input-output data sets. In this note, we show that the result they obtained in their paper is invalid.

• Journal of Welding and Joining
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• v.17 no.4
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• pp.85-92
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• 1999

In GMAW, the spatter is generated because of the variation of the arc state. If the arc state is quantitatively assessed, the control method to make the spatter be reduced is able to develop. This study was attempted to develop the optimal model that could estimate the arc state quantitatively. To do this, the generated spatters was captured under the limited welding conditions, and the waveforms of the arc voltage and of the welding current were collected. From the collected waveforms, the waveform factors and their standard deviations were produced, and the linear and non-linear regression models constituted using the factors and their standard deviations are proposed to estimate the arc state. the performance test to the proposed models was practiced. Obtained results are as follow. From the results of correlation analysis between the factors and the amount of the generated spatters, the standard deviations of the waveform factors have more the multiple regression coefficients than the waveform factors. Because the correlation coefficient between T and {TEX}$T_{a}${/TEX}, and s[T] and s[{TEX}$T_{a}${/TEX}] was nearly one, it was found that these factors have the same effect to the spatter generation. In the regression models to estimate the arc state, it was fond that the linear and the non linear models were also consisted of similar factors. In addition, the linear regression model was assessed the optimal model for estimating the arc state because the variance of data was narrow and multiple regression coefficient was highest among the models. But in the welding conditions which the amount of the generated spatters were small, it was found that the non linear regression model had better the estimation performance for the spatter generation than the linear.

• Journal of the Korean GEO-environmental Society
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• v.11 no.12
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• pp.63-74
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• 2010

Normally consolidated and slightly overconsolidated soft clay layer is widely distributed in the south coast of Korea. To ensure the efficient and economical construction design of any structure to be built on this soft soil, exhaustive studies related to geotechnical and physical engineering properties are required. In this study, the relationship of the physical properties of southern Gwangyang marine clay in the Korea Peninsula were examined, including natural water content, specific gravity, total unit weight, initial void ratio, liquid limit, plastic limit, and physical properties of activity and soil parameters. For the parameter relationship analysis, the latest relatively reliable data on the large harbor construction work were used, optimum values were deducted with linear regression and non-linear regression between soil parameters, water content or initial void ratio appears to be very large. Moreover, in the linear and involution pattern regression, equal coefficient of determination appeared. The relationship of the different parameters was shown to be excellent in the non-linear regression of involution equation and exponential equation pattern compared with the findings of linear regression analysis.