• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.575-583
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• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• 한국지능시스템학회논문지
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• 제25권5호
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• pp.477-482
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• 2015

단기풍속 예측을 위한 진화적 선형 및 비선형 회귀분석 기반의 보정 기법을 비교한다. 모델의 체계적 오류를 교정하기 위한 효율적인 MOS(Model Output Statistics)의 개발이 필요하나, 기존의 선형회귀분석 기반의 보정기법은 다양한 기상요소의 복잡한 비선형 특성을 반영하기 힘들다. 이를 개선하기 위해서 유전 프로그래밍을 사용하여 풍속 예측에 대한 비선형 보정 수식을 생성하는 기법을 제안하고 기본 다중선형회귀분석법 및 Ridge, Lasso 회귀분석법과 비교한다. 더불어, 선형회귀분석법과 진화적 비선형회귀분석 기법의 인자 선택의 차이와 유사성을 비교하고 분석한다. 2007년~2013년의 KLAPS(Korea Local Analysis and Prediction System) 재분석자료를 사용하여 제주도와 부산지역의 격자점에 대한 실험을 수행한다.

• 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.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.155-178
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• 2024

Regression discontinuity (RD) design is one of the most widely used methods in causal inference for estimation of treatment effect when the treatment is created by a cutpoint from the covariate of interest. There has been little attention to RD design, although it provides a very useful tool for analysis of treatment effect for censored data. In this paper, we define the causal effect for survival function in RD design when the treatment is assigned deterministically by the covariate of interest. We propose estimators of this causal effect for survival data by using transformation, which leads unbiased estimator of the survival function with local linear regression. Simulation studies show the validity of our approach. We also illustrate our proposed method using the prostate, lung, colorectal and ovarian (PLCO) dataset.

• Communications for Statistical Applications and Methods
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• 제30권6호
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• pp.605-629
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• 2023

This paper proposes some diagnostics procedures for the skew-t linear regression model with censored response. The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and student's-t distributions as special cases. Inspired by the power and wide applicability of the EM-type algorithm, local and global influence analysis, based on the conditional expectation of the complete-data log-likelihood function are developed, following Zhu and Lee's approach. For the local influence analysis, four specific perturbation schemes are discussed. Two real data sets, from education and economics, which are right and left censoring, respectively, are analyzed in order to illustrate the usefulness of the proposed methodology.

• Journal of the Korean Statistical Society
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• 제27권4호
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• pp.515-529
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• 1998

Burman (1987) and Hall and Titterington (1987) studied kernel smoothing for sparse multinomial data in detail. Both of their estimators for cell probabilities are sparse asymptotic consistent under some restrictive conditions on the true cell probabilities. Dong and Simonoff (1994) adopted boundary kernels to relieve the restrictive conditions. We propose a local linear kernel estimator which is popular in nonparametric regression to estimate cell probabilities. No boundary adjustment is necessary for this estimator since it adapts automatically to estimation at the boundaries. It is shown that our estimator attains the optimal rate of convergence in mean sum of squared error under sparseness. Some simulation results and a real data application are presented to see the performance of the estimator.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.273-283
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• 2006

In bioassay, the response curve is usually assumed monotone increasing, but its exact form is unknown, so it is very difficult to select the proper functional form for the parametric model. Therefore, we should probably use the nonparametric regression model rather than the parametric model unless we have at least the partial information about the true response curve. However, it is well known that the nonparametric regression estimate is not necessarily monotone. Therefore the monotonizing transformation technique is of course required. In this paper, we compare the finite sample properties of the monotone transformation methods which can be applied to the local linear quasi-likelihood response curve estimate.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.401-411
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• 2007

In this paper we propose an influence measure for detecting potentially influential observations using the infinitesimal perturbation and the local influence in the log-linear regression model. Also, we propose a goodness-of-fit measure for variable selection. A real data set are used for illustration.

• Communications for Statistical Applications and Methods
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• 제4권2호
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• pp.445-452
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• 1997

In this paper, twicing technique for the improvement of asymptotic boundary bias in nonparametric regression is considered. Asymptotic mean squared errors of the nonparametric regression estimators are derived at the boundary region by twicing the Nadaraya-Waston and local linear smoothing. Asymptotic biases of the resulting estimators are of order$h^2$and$h^4$ respectively.

• Journal of the Korean Statistical Society
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• 제25권2호
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• pp.217-233
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• 1996

This paper gives a rigorous proof of an asymptotic result about bias and variance for a transformation-based nonparametric regression estimator proposed by Park et al (1995).