• Communications for Statistical Applications and Methods
• /
• v.19 no.3
• /
• pp.333-344
• /
• 2012

We consider some statistical properties of the first order difference-based error variance estimator in nonparametric regression models with a single outlier. So far under an outlier(s) such difference-based estimators has been rarely discussed. We propose the first order difference-based estimator using the leave-one-out method to detect a single outlier and simulate the outlier detection in a nonparametric regression model with the single outlier. Moreover, the outlier detection works well. The results are promising even in nonparametric regression models with many outliers using some difference based estimators.

• Journal of Korean Society for Quality Management
• /
• v.24 no.4
• /
• pp.190-206
• /
• 1996

In case measurements are made on units of production in time order, it is reasonable to expect that the measurement errors will sometimes be first order autocorrelated, and a technique to test such autocorrelation is required to give good control of the productive process. Tool-wear process provide an example for which regression model can sometimes be useful in modeling and controlling the process. For the control of such process, we present a simple method for testing first order autocorrelation in regression errors. The method is based on Bayesian test method via Bayes factor and derived by observing that in general, a Bayes factor can be written as the product of a quantity called the Savage-Dickey density ratio and a correction factor ; both terms are easily estimated from Gibbs sampling technique. Performance of the method is examined by means of Monte Carlo simulation. It is noted that the test not only achieves satisfactory power but eliminates the inconvenience occurred in using the well-known Durbin-Watson test.

• Carbon letters
• /
• v.9 no.3
• /
• pp.181-187
• /
• 2008

Batch sorption experiments were carried out for the removal of metylene blue from its aqueous solution using $H_3PO_4$ activated Acacia arabica carbon (AAC). The prepared activated carbon was characterized and was found as an effective adsorbent material. The operating variables studied were initial metylene blue concentration, AAC concentration and solution pH. AAC activated carbon posses a maximum sorption capacity for the range of initial dye concentrations studied (60~100 mg $L^{-1}$). The sorption kinetics were analyzed using reversible first order kinetics, second order, reversible first order, pseudo-first order, and pseudo-second order model. The sorption data tend to fit very well in pseudo-second order model for the entire sorption time. The average pseudo-second order rate constant, $K_{II}$ and regression coefficient value were determined to be 0.0174 mg $g^{-1}$ $min^{-1}$ and 0.9977. The biosorption process also fit well to reversible I order kinetics with a regression coefficient of 0.9878.

• The Korean Journal of Applied Statistics
• /
• v.14 no.1
• /
• pp.71-80
• /
• 2001

Logistic regression model is one of the most popular linear models for a binary response variable and used for the estimation of probability function. In many practical situations, the probability function can be expressed by a bell shaped curve and such a function can be estimated by a second order logistic regression model. However, when the probability curve is asymmetric, the estimation results using a second order logistic regression model may not be precise because a second order logistic regression model is a symmetric function. In addition, even if a second order logistic regression model is used, the interpretation for the effect of second order term may not be easy. In this paper, in order to alleviate such problems, an estimation method for asymmetric probabiity curve based on a first order logistic regression model and iterative bi-section method is proposed and its performance is compared with that of a second order logistic regression model by a simulation study.

• Asian-Australasian Journal of Animal Sciences
• /
• v.21 no.6
• /
• pp.769-775
• /
• 2008

This study was on the relative net income (RNI) for 18,286 Iranian Holstein cows from 799 herds, with first freshening between 1991 and 2000. Two kinds of production system, which differed mainly in milk pricing system and feed cost, were considered. Four different models adopted from the literature were examined to find the optimum model. They differed by the cost of rearing and growth after first calving and they needed different amounts of economic data at the farm level. Results showed that four measures of RNI were highly correlated (>0.96) and could be used equally to measure lifetime profitability of cows. Therefore, in herds without a regular system for recording economic and management data, use of the simplest model is recommended. Multiple regression analysis revealed that RNI was affected by age at first freshening, milk yield and days of productive life (DPL), regardless of production system, and a similar breeding goal could be defined for the two systems. Multiple regression analysis of RNI showed that in order to obtain an unbiased estimate of economic value for DPL, the per day milk yield, not total lifetime milk yield, should be included in the regression model along with DPL. Regression analysis suggested that it is possible to predict RNI using information on age at first freshening along with the length of first lactation and per day milk yield with a coefficient of determination ranging from 0.44 to 0.47.

• Journal of the Korean Statistical Society
• /
• v.9 no.1
• /
• pp.61-77
• /
• 1980

In response surface experiments, a polynomial model is often used to fit the response surface by the method of least squares. However, if the vectors of predictor variables are multicollinear, least squares estimates of the regression parameters have a high probability of being unsatisfactory. Hoerland Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using "ridge" estimates in place of the least squares estimates. Ridge regrssion theory in literature has been mainly concerned with selection of k for the first order polynomial regression model and the precision of $\hat{\beta}(k)$, the ridge estimator of regression parameters. The problem considered in this paper is that of selecting k of ridge regression for a given polynomial regression model with an arbitrary order. A criterion is proposed for selection of k in the context of integrated mean square error of fitted responses, and illustrated with an example. Also, a type of admissibility condition is established and proved for the propose criterion.criterion.

• Journal of the Korean Statistical Society
• /
• v.26 no.3
• /
• pp.365-382
• /
• 1997

In this paper we study the behaviors of the generalized Durbin-Watson (DW) statistics when the nonstationary seasonal time series regression model is misspecified. It is observed that when the series is seasonally integrated the generalized DW statistic for the seasonal period order autocorrelation converges in probability to zero while teh generalized DW statistic for the first order autocorrelation has nondegenerate asymptotic distribution. When the series is regularly and seasonally integrated the generalized DW for the first order autocorrelation still converges in probability to zero.

• Korean Journal of Artificial Intelligence
• /
• v.10 no.1
• /
• pp.9-14
• /
• 2022

The demand for public bicycles operated by the Seoul Metropolitan Government is increasing every year. The size of the Seoul public bicycle project, which first started with about 5,600 units, increased to 3,7500 units as of September 2021, and the number of members is also increasing every year. However, as the size of the project grows, excessive budget spending and deficit problems are emerging for public bicycle projects, and new bicycles, rental office costs, and bicycle maintenance costs are blamed for the deficit. In this paper, the Azure Machine Learning Studio program and the Boosted Decision Tree Regression technique are used to predict the number of public bicycle rental over environmental factors and time. Predicted results it was confirmed that the demand for public bicycles was high in the season except for winter, and the demand for public bicycles was the highest at 6 p.m. In addition, in this paper compare four additional regression algorithms in addition to the Boosted Decision Tree Regression algorithm to measure algorithm performance. The results showed high accuracy in the order of the First Boosted Decision Tree Regression Algorithm (0.878802), second Decision Forest Regression (0.838232), third Poison Regression (0.62699), and fourth Linear Regression (0.618773). Based on these predictions, it is expected that more public bicycles will be placed at rental stations near public transportation to meet the growing demand for commuting hours and that more bicycles will be placed in rental stations in summer than winter and the life of bicycles can be extended in winter.

• Asian-Australasian Journal of Animal Sciences
• /
• v.31 no.10
• /
• pp.1542-1549
• /
• 2018

Objective: Because lactation periods in dairy cows lengthen with increasing total milk production, it is important to predict individual productivities after 305 days in milk (DIM) to determine the optimal lactation period. We therefore examined whether the random regression (RR) coefficient from 306 to 450 DIM (M2) can be predicted from those during the first 305 DIM (M1) by using a RR model. Methods: We analyzed test-day milk records from 85,690 Holstein cows in their first lactations and 131,727 cows in their later (second to fifth) lactations. Data in M1 and M2 were analyzed separately by using different single-trait RR animal models. We then performed a multiple regression analysis of the RR coefficients of M2 on those of M1 during the first and later lactations. Results: The first-order Legendre polynomials were practical covariates of RR for the milk yields of M2. All RR coefficients for the additive genetic (AG) effect and the intercept for the permanent environmental (PE) effect of M2 had moderate to strong correlations with the intercept for the AG effect of M1. The coefficients of determination for multiple regression of the combined intercepts for the AG and PE effects of M2 on the coefficients for the AG effect of M1 were moderate to high. The daily milk yields of M2 predicted by using the RR coefficients for the AG effect of M1 were highly correlated with those obtained by using the coefficients of M2. Conclusion: Milk production after 305 DIM can be predicted by using the RR coefficient estimates of the AG effect during the first 305 DIM.

• Asian-Australasian Journal of Animal Sciences
• /
• v.29 no.6
• /
• pp.775-781
• /
• 2016

A single trait linear mixed random regression test-day model was applied for the first time for analyzing the first lactation monthly test-day milk yield records in Karan Fries cattle. The test-day milk yield data was modeled using a random regression model (RRM) considering different order of Legendre polynomial for the additive genetic effect (4th order) and the permanent environmental effect (5th order). Data pertaining to 1,583 lactation records spread over a period of 30 years were recorded and analyzed in the study. The variance component, heritability and genetic correlations among test-day milk yields were estimated using RRM. RRM heritability estimates of test-day milk yield varied from 0.11 to 0.22 in different test-day records. The estimates of genetic correlations between different test-day milk yields ranged 0.01 (test-day 1 [TD-1] and TD-11) to 0.99 (TD-4 and TD-5). The magnitudes of genetic correlations between test-day milk yields decreased as the interval between test-days increased and adjacent test-day had higher correlations. Additive genetic and permanent environment variances were higher for test-day milk yields at both ends of lactation. The residual variance was observed to be lower than the permanent environment variance for all the test-day milk yields.