• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.77-84
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• 2012

반복이 있는 랜덤화 블록 계획법을 검정하는 비모수 검정방법에는 Mack과 Skillings (1980)가 제안한 검정법이 있다. 이 방법은 각 블록의 처리에서 반복된 각 관측값 대신에 반복된 관측값들의 평균을 이용하여 순위를 매기기 때문에 정보의 손실이 있을 수 있다. 본 논문에서는 Hodges와 Lehmann (1962)이 제안한 정렬방법을 이용하여 새로운 비모수 검정법을 제안한다. 또한 모의실험을 통하여 여러 비모수 검정방법들의 검정력을 비교하였다.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.193-211
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• 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.

• Communications for Statistical Applications and Methods
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• 제14권3호
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• pp.609-621
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• 2007

Diagnostic test results, which are approximately normal with a few number of outliers, but non-normal probability distribution, are frequently observed in practice. In the evaluation of two diagnostic tests, Greenhouse and Mantel (1950) proposed a parametric test under the assumption of normality but this test is inappropriate for the above non-normal case. In this paper, we propose a computationally simple nonparametric test that is based on quantile estimators of mean and standard deviation, instead of the moment-based mean and standard deviation as in some parametric tests. Parametric and nonparametric tests are compared with simulations under the assumption of, respectively, normality and non-normality, and under various combinations of the probability distributions for the normal and diseased groups.

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

• Communications for Statistical Applications and Methods
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• 제30권3호
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• pp.227-244
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• 2023

In this paper, a depth-based nonparametric test for a multivariate two-sample scale problem is proposed. The proposed test statistic is based on the depth-induced ranks and is thus distribution-free. In this article, the depth values of data points of one sample are calculated with respect to the other sample or distribution and vice versa. A comprehensive simulation study is used to examine the performance of the proposed test for symmetric as well as skewed distributions. Comparison of the proposed test with the existing depth-based nonparametric tests is accomplished through empirical powers over different depth functions. The simulation study admits that the proposed test outperforms existing nonparametric depth-based tests for symmetric and skewed distributions. Finally, an actual life data set is used to demonstrate the applicability of the proposed test.

• Communications for Statistical Applications and Methods
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• 제26권6호
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• pp.611-622
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• 2019

This paper considers the estimation of the long memory parameter in nonparametric regression with strongly correlated errors. The key idea is to minimize a unified mean squared error of long memory parameter to select both kernel bandwidth and the number of frequencies used in exact local Whittle estimation. A unified mean squared error framework is more natural because it provides both goodness of fit and measure of strong dependence. The block bootstrap is applied to evaluate the mean squared error. Finite sample performance using Monte Carlo simulations shows the closest performance to the oracle. The proposed method outperforms existing methods especially when dependency and sample size increase. The proposed method is also illustreated to the volatility of exchange rate between Korean Won for US dollar.

• 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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• 제27권5호
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• pp.547-568
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• 2020

Modeling the statistical autocorrelations in spatial data is often achieved through the estimation of the variograms, where the selection of the appropriate valid variogram model, especially for small samples, is crucial for achieving precise spatial prediction results from kriging interpolations. To estimate such a variogram, we traditionally start by computing the empirical variogram (traditional Matheron or robust Cressie-Hawkins or kernel-based nonparametric approaches). In this article, we conduct numerical studies comparing the performance of these empirical variograms. In most situations, the nonparametric empirical variable nearest-neighbor (VNN) showed better performance than its competitors (Matheron, Cressie-Hawkins, and Nadaraya-Watson). The analysis of the spatial groundwater dataset used in this article suggests that the wave variogram model, with hole effect structure, fitted to the empirical VNN variogram is the most appropriate choice. This selected variogram is used with the ordinary kriging model to produce the predicted pollution map of the nitrate concentrations in groundwater dataset.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.743-752
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• 2002

The estimation of the response curve is the important problem in the quantal bioassay. When we estimate the response curve, we determine the design points in advance of the experiment. Then naturally we have a question of which design would be optimal. As a response curve estimator, locally weighted quasi-likelihood estimator has several more appealing features than the traditional nonparametric estimators. The optimal design density for the locally weighted quasi-likelihood estimator is derived and its ability both in theoretical and in empirical point of view are investigated.

• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.187-194
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• 1996

We treat the problem of estimating reliability R = P[Y < X] in the stress-strength model in which a unit of strength X is subfected to enviromental stress Y./ In this paper several nonparametric approaches to estimation of R are analyzed and compared by simulations.