• Communications for Statistical Applications and Methods
• /
• 제22권5호
• /
• pp.463-473
• /
• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.

• 대한수학회지
• /
• 제44권4호
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• 제19권5호
• /
• pp.721-729
• /
• 2012

Various methods control the influence of a covariate on a response variable. These methods are analysis of covariance(ANCOVA), RANK ANCOVA, ANOVA of (covariate-adjusted) residuals, and Kruskal-Wallis tests on residuals. Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set that ignore the treatment levels or factors. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and covariate means are equal for all treatments. In this paper, we proposed the new nonparametric method on the ANCOVA model, as applying joint placement in a one-way layout on residuals as described in Chung and Kim (2007). A Monte Carlo simulation study is adapted to compare the power of the proposed procedure with those of the previous procedure.

• Journal of the Korean Statistical Society
• /
• 제30권4호
• /
• pp.645-660
• /
• 2001

In this paper we propose a goodness-of-fit test statistic for testing the (null) parametric model versus the (alternative) nonparametric model. Most of existing nonparametric test statistics are based on the residuals which are obtained by regressing the data to a parametric model. Our test is based on the bootstrap estimator of the probability that the smoothing parameter estimator is infinite when fitting residuals to cubic smoothing spline. Power performance of this test is investigated and is compared with many other tests. Illustrative examples based on real data sets are given.

• Journal of the Korean Data and Information Science Society
• /
• 제9권2호
• /
• pp.357-363
• /
• 1998

In this paper we propose a nonparametric lack of fit test based on the bootstrap method for testing the null parametric linear model by using linear smoothers. Most of existing nonparametric test statistics are based on the residuals. Our test is based on the centered bootstrap residuals. Power performance of proposed bootstrap lack of fit test is investigated via Monte carlo simulation.

• 응용통계연구
• /
• 제30권3호
• /
• pp.427-439
• /
• 2017

공변량(covariate)이 존재하는 경우, 각 처리군 간 효과의 차이를 검정하기 위한 대표적인 비모수적 방법에는 Quade (1967)가 제안한 검정법이 있다. 또한 반응변수에 대해 공변량으로 단순선형회귀분석을 실시하여 얻은 잔차에 대해 일원배치분산분석과 Kruskal Wallis가 제안한 방법을 적용하는 방법, 그리고 Hwang과 Kim (2012)이 제안한 비모수적 도구인 위치(placement)를 이용한 방법이 있다. 본 논문에서는 공분산분석 모형에서 Hwang과 Kim (2012)이 제안한 방법을 확장하여 공분산분석에서의 새로운 방법을 제안하였다. 또한 모의실험(Monte Carlo simulation study)을 통하여 기존의 검정법들과 제안한 방법의 검정력을 비교하였다.

• 품질경영학회지
• /
• 제23권4호
• /
• pp.58-63
• /
• 1995

To access the quality of a fit to a set of data it is always useful to conduct a posteriori analysis involving the examination of residuals, detection of influential data values, etc. Smoothing splines are a type of nonparametric regression estimators for the diagnostic problem. And leverage value, Cook's distance, and DFFITS are used for detecting influential data. Since high leverage points will always have small residuals, the new diagnostic measures including of properties of leverage and residuals are needed. In this paper, we propose FVARATIO version as diagnostic measure in nonparametric regression. Also we consider the rough bound as analogy with linear regression case.

• Communications for Statistical Applications and Methods
• /
• 제5권2호
• /
• pp.411-416
• /
• 1998

A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.

• Communications for Statistical Applications and Methods
• /
• 제3권3호
• /
• pp.39-46
• /
• 1996

Most of existing nonparametric test statistics are based on the residuals which are obtained by regressing the data to a parametric model. In this paper we compare power of goodness-of-fit test statistics for testing the (null)parametric model versus the (alternative) nonparametric model.

• Journal of applied mathematics & informatics
• /
• 제8권2호
• /
• pp.669-682
• /
• 2001

In this paper a nonparametric test for the parallelism of k regression lines against ordered alternatives, when the independent variables are positive and all regression lines have a common intercept is proposed. The proposed test is based on a Jonckheere-type statistic applied to residuals. Under some conditions the proposed test statistic is asymptotically distribution-free. The small-sample powers of our test are compared with other tests by a Monte Carlo study. The simulation results show that the proposed test has significantly higher empirical powers than the other tests considered in this paper.