• Communications for Statistical Applications and Methods
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• 제24권6호
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Journal of the Korean Data and Information Science Society
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• 제20권2호
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• pp.251-260
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• 2009

이 논문에서는 단순 선형회귀 모형에서 회귀 계수의 최적 추정량을 구할 수 있는 자기공분산에 근거한 추정 방법을 제시하였다. 이 방법이 직관적으로 매혹적이지는 않지만 이 최적 추정량이 해당 회귀 계수의 불편추정량이 된다. 설명변수가 0과 1사이의 균등간격의 값을 가지면, 오차가 자기회귀 이동평균 모형을 따르면 성립하는 조건 하에서 이 최적 추정량이 최소제곱 추정량과 점근적으로 통일한 분포를 가진다는 것을 보였다. 추가적으로 똑같은 조건 하에서 이 최적 추정량이 해당 회귀 계수에 확률상 수렴한다는 것을 자체적으로 입증하였다.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.899-908
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• 2008

If the regression function has jump points, nonparametric estimation method based on local smoothing is not statistically consistent. Therefore, when we estimate regression function, it is quite important to know whether it is reasonable to assume that regression function is continuous. If the regression function appears to have jump points, then we should estimate first the location of jump points. In this paper, we propose a procedure which can do both the testing hypothesis of discontinuity of regression function and the estimation of the number and the location of jump points simultaneously. The performance of the proposed method is evaluated through a simulation study. We also apply the procedure to real data sets as examples.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1204-1209
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• 1990

This paper offers the theory and method for regression analysis of the regression model with operational parameter variables based on the fundamentals of mathematical statistics. Regression coefficients are usually constants related to the problem of regression analysis. This paper considers that regression coefficients are not constants but the functions of some operational parameter variables. This is a kind of method of two-step fitting regression model. The second part of this paper considers the experimental step numbers as recursive variables, the recursive identification with unknown operational parameter variables, which includes two recursive variables, is deduced. Then the optimization and the recursive identification are combined to obtain the sequential experiment optimum design with operational parameter variables. This paper also offers a fast recursive algorithm for a large number of sequential experiments.

• Journal of Oral Medicine and Pain
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• 제10권1호
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• pp.73-89
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• 1985

This study comprised 157 extracted teeth, 73 of the teeth originated from mates and 84 from females, the age range was 12-79 years. The correlation coefficient of each Gustafson's criteria in relation to age was carried out. Age estimation were performed on 157 teeth according to the method by Gustafson and by use of multiple regression, as used by Johanson, after evaluating the six criteria of Gustafson by multiple regression computer analysis. Two prediction formulas and standard deviations were compared with each other. The results were as follows : 1. The author found that six Gustafson's criteria had strong correlation with age except root resorption, and correlation coefficients were r = 0.79 (Transparent dentin), r=0.72 (Secondary dentin), r 0.69 (Periodontal change), r=0.63(Attrition), r = 0.39 (Root resorption), respecti vely. 2. The age estimation formula by Gustafson's method was calculated as follows: Y 8.88 + 3.52X r =0.87, r2 = 0.76, SD = 8.18, F = 483.56, P < 0.01 The age estimation formula by multiple regression was calculated as follows: Y 8.57 + 6.37T + 6.37T + 4.63P + 2.70S + 2.40C + 3.08A + 1.34R r= 0.89, r2 = 0.78, SD = 7.82, F = 91.62, P < 0.01, Durbin-Watson Coefficient = 1.09 3. In comparison of two estimation formulas, the formula by multiple regression, the method of Johanson, was found to be slightly more reliable than Gustafson's method. Gustafson's method SD = 8.18, Multiple regression (Johanson's method) SD = 7.82 4. It was reaffirmed that Gustafson's six criteria could be a independent variable in multiple regression analysis.

• Asian-Australasian Journal of Animal Sciences
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• 제21권7호
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• pp.923-927
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• 2008

The objective of this study was to compare random regression model and multiple trait animal model estimates of the (co) variance of total sperm cells over the active lifetime of AI boars. Data were provided by Smithfield Premium Genetics (Rose Hill, NC). Total number of records and animals for the random regression model were 19,629 and 1,736, respectively. Data for multiple trait animal model analyses were edited to include only records produced at 9, 12, 15, 18, 21, 24, and 27 months of age. For the multiple trait method estimates of genetic and residual variance for total sperm cells were heterogeneous among age classifications. When comparing multiple trait method to random regression, heritability estimates were similar except for total sperm cells at 24 months of age. The multiple trait method also resulted in higher estimates of heritability of total sperm cells at every age when compared to random regression results. Random regression analysis provided more detail with regard to changes of variance components with age. Random regression methods are the most appropriate to analyze semen traits as they are longitudinal data measured over the lifetime of boars.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.185-193
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• 2002

The purpose of this paper is to suggest a method for detecting the linear regression change-points or variance change-points in regression model by the combination of Schwarz information criteria. The advantage of the suggested method is to detect change-points more detailed when one compares the suggest method with Chen (1998)'s method.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.949-954
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• 2009

The autoregressive process is applied in this paper to kernel regression in order to infer nonlinear models for predicting responses. We propose a kernel method for the autoregressive data which estimates the mean function by kernel machines. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which affect the performance of kernel regression. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of mean function in the presence of autocorrelation between data.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.519-524
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• 2003

We suggest a method of identifying outliers, using local influence, in regression when linear constraints are imposed on the regression coefficients. An example is given for illustration.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.1-10
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• 1999

When the component proportions in mixture experiments are restricted by lower and upper bounds multicollinearity appears all too frequently. The ridge regression can be used to stabilize the coefficient estimates in the fitted model. I propose a graphical method for evaluating the mixture component effects of ridge regression estimator with respect to the prediction variance and the prediction bias.