NONPARAMETRIC REGRESSION WITH ERROR-IN-VARIABLES MODEL BASED ON DIFFERENT KERNEL FUNCTIONS

Yıl 2021, Cilt: 9 Sayı: Iconat Special Issue 2021, 94 - 102, 24.12.2021

Dursun Aydın , Ersin Yılmaz

https://doi.org/10.20290/estubtdb.1015940

Öz

Estimation of error-invariable models is a specific problem in different fields such as medicine, economics, industry, and biostatistics. The main different between classical regression and error-in-variable models is that explanatory variables involve random error terms. Therefore, classical estimation methods that do not include the necessary adjustments for the contaminated explanatory variables give biased results. Regarding the error-in variables, there are important studied in the literature such as [1], [2], [3], [4], [5] and [6]. In this paper, nonparametric regression with measurement error is considered and estimated by kernel smoothing estimator which is studied detailed by [6]. This paper differs from their study with the idea of using two different kernel functions to compared them on quality of estimations. These functions are suitable for different error behaviors (see [7]). The goal of the paper is encouraged by a Monte Carlo simulation study and results are presented.

Anahtar Kelimeler

Error in variables, kernel smoothing, nonparametric regression, kernel functions

Kaynakça

• [1] Fan J & Truong YK. Nonparametric regression with errors in variables. The Annals of Statistics, 1993; 1900-1925.
• [2] Stefanski LA & Cook JR. Simulation-extrapolation: the measurement error jackknife. Journal of the American Statistical Association, 1995; 90(432): 1247-1256.
• [3] Carroll R J Maca, JD & Ruppert D. Nonparametric regression in the presence of measurement error. Biometrika, 1999; 86(3): 541-554.
• [4] Carroll RJ & Hall P. Low order approximations in deconvolution and regression with errors in variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2004; 66(1): 31-46.
• [5] Delaigle A & Meister A. Nonparametric regression estimation in the heteroscedastic errors-in-variables problem. Journal of the American Statistical Association, 2007; 102(480): 1416-1426.
• [6] Wang XF & Wang B. Deconvolution estimation in measurement error models: the R package decon. Journal of statistical software, 2011; 39(10): i10.
• [7] Fan J. On the optimal rates of convergence for nonparametric deconvolution problems. The Annals of Statistics, 1991; 1257-1272.
• [8] Berry SM Carroll RJ & Ruppert D. Bayesian smoothing and regression splines for measurement error problems. Journal of the American Statistical Association, 2002; 97(457): 160-169.
• [9] Liang H & Wang N. Partially linear single-index measurement error models. Statistica Sinica, 2005; 99-116.
• [10] Stefanski LA & Carroll RJ. Deconvolving kernel density estimators. Statistics, 1990; 21(2): 169-184.
• [11] Nadaraya EA. On estimating regression. Theory of Probability & Its Applications, 1964; 9(1): 141-142.
• [12] Watson GS. Smooth regression analysis. Sankhyā: The Indian Journal of Statistics, Series A, 1964; 26(4): 359-372.
• [13] Li T & Vuong Q. Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis, 1998; 65(2): 139-165.
• [14] Craven P & Wahba G. Smoothing noisy data with spline functions. Numerische Mathematik, 1979; 31(4): 377-403.