• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.373-381
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• 2009

Evidence of linkage is expressed as a decreasing trend of the squared trait difference of two siblings with increasing identical by descent scores. In contrast to successes in the application of a parametric approach of Haseman-Elston regression, notably low powers are demonstrated in the nonparametric linkage analysis methods for complex traits and diseases with sib-pairs data. We report that the Genehunter nonparametric linkage statistic is biased and furthermore the variance formula that they used is an inflated one, and this is one reason for a low performance. Thus, we propose bias-corrected nonparametric linkage statistics. Simulation studies comparing our proposed nonparametric test statistics versus the existing test statistics suggest that the bias-corrected new nonparametric test statistics are more powerful and attains efficiencies close to that of Haseman-Elston regression.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.453-463
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• 1997

Nonparametric kernel regression has recently gained widespread acceptance as an attractive method for the nonparametric estimation of the mean function from noisy regression data. Also, the practical implementation of kernel method is enhanced by the availability of reliable rule for automatic selection of the bandwidth. In this article, we propose a method for automatic selection of the bandwidth that minimizes the asymptotic mean square error. Then, the estimated bandwidth by the proposed method is compared with the theoretical optimal bandwidth and a bandwidth by plug-in method. Simulation study is performed and shows satisfactory behavior of the proposed method.

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

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.575-587
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• 2011

We investigate some statistical properties of several dierence-based error variance estimators in nonparametric regression model. Most of existing dierence-based methods are developed under asymptotical properties. Our focus is on the exact form of mean and variance for the lag-k dierence-based estimator and the second-order dierence-based estimator in a nite sample size. Our approach can be extended to Tong's estimator (2005) and be helpful to obtain optimal k.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.327-349
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• 2021

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.157-169
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• 2016

We compare four methods to estimate a regression coefficient under linear regression models with serially correlated errors. We assume that regression errors are generated with nonlinear autoregressive models. The four methods are: ordinary least square estimator, general least square estimator, parametric regression error correction method, and nonparametric regression error correction method. We also discuss some properties of nonlinear autoregressive models by presenting numerical studies with typical examples. Our numerical study suggests that no method dominates; however, the nonparametric regression error correction method works quite well.

• Journal of Korea Water Resources Association
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• v.33 no.1
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• pp.31-38
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• 2000

Relationships between hydrologic variables are often nonlinear. Usually the functional form of such a relationship is not known a priori. A multivariate, nonparametric regression methodology is provided here for approximating the underlying regression function using locally weighted polynomials. Locally weighted polynomials consider the approximation of the target function through a Taylor series expansion of the function in the neighborhood of the point of estimate. The utility of this nonparametric regression approach is demonstrated through an application to nonparametric short term forecasts of the biweekly Great Salt Lake volume.volume.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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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.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.574-574
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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.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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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.