• Journal for History of Mathematics
• /
• v.16 no.3
• /
• pp.95-100
• /
• 2003

The recent surge of interest in the more technical aspects of nonparametric density estimation and nonparametric regression estimation has brought the subject into public view. In this paper, we investigate the general concept of the nonparametric density estimation, the nonparametric regression estimation and its performance criteria.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.11a
• /
• pp.103-108
• /
• 2002

We consider an estimation of discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of a change point and jump size in variance function and then construct an estimator of entire variance function. We examine the rates of convergence of these estimators and give results on their asymptotics. Numerical work reveals that the effectiveness of change point analysis in variance function estimation is quite significant.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.15-27
• /
• 2001

One proposal is made for constructing nonparametric estimator of slope parameters in a regression model under symmetric error distributions. This estimator is based on the use of idea of Johns for estimating the center of the symmetric distribution together with the idea of regression quantiles and regression trimmed mean. This nonparametric estimator and some other L-estimators are studied by Monte Carlo.

• Journal of the Korean Statistical Society
• /
• v.35 no.1
• /
• pp.1-23
• /
• 2006

In this paper we consider an estimation of the discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of the change point in the variance function and then construct an estimator of the entire variance function. We examine the rates of convergence of these estimators and give results for their asymptotics. Numerical work reveals that using the proposed change point analysis in the variance function estimation is quite effective.

• Communications for Statistical Applications and Methods
• /
• v.15 no.6
• /
• pp.899-908
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.2 no.2
• /
• pp.243-248
• /
• 1995

The problem of optimal design for a nonparametric regression with binary data is considered. The aim of the statistical analysis is the estimation of a quantal response surface in two dimensions. Bias, variance and IMSE of kernel estimates are derived. The optimal design density with respect to asymptotic IMSE is constructed.

• Communications for Statistical Applications and Methods
• /
• v.19 no.1
• /
• pp.193-211
• /
• 2012

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider $Z_i=(X_i,Y_i)$, $i{\in}\mathbb{N}^N$ be a $\mathcal{F}{\times}\mathbb{R}$-valued measurable strictly stationary spatial process, where $\mathcal{F}$ is a semi-metric space and we study the spatial interaction of $X_i$ and $Y_i$ via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.

• The Korean Journal of Applied Statistics
• /
• v.25 no.5
• /
• pp.793-802
• /
• 2012

One proposal is made to construct a nonparametric estimator of slope parameters in a regression model under symmetric error distributions. This estimator is based on the use of the idea of minimizing approximate variance of a proposed estimator using regression quantiles. This nonparametric estimator and some other L-estimators are studied and compared with well known M-estimators through a simulation study.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.835-844
• /
• 2007

This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.

• International Journal of Advanced Culture Technology
• /
• v.10 no.1
• /
• pp.236-241
• /
• 2022

We consider methods of estimating a binary regression function using a nonparametric kernel estimation when there is only one covariate. For this, the Nadaraya-Watson estimation method using single and double bandwidths are used. For choosing a proper smoothing amount, the cross-validation and plug-in methods are compared. In the real data analysis for case study, German credit data and heart disease data are used. We examine whether the nonparametric estimation for binary regression function is successful with the smoothing parameter using the above two approaches, and the performance is compared.