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Journal articles on the topic 'Nadaraya-Watson estimator'

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Published: 4 June 2021

Last updated: 19 February 2022

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1

Lamusu, Febriolah, Tedy Machmud, and Resmawan Resmawan. "Estimator Nadaraya-Watson dengan Pendekatan Cross Validation dan Generalized Cross Validation untuk Mengestimasi Produksi Jagung." Indonesian Journal of Applied Statistics 3, no. 2 (January 23, 2021): 85. http://dx.doi.org/10.13057/ijas.v3i2.42125.

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<p>Nadaraya-Watson Estimator with kernel approach depends on two-parameter, those are kernel function and bandwidth choice. However, between the two of them, bandwidth choice gave a huge impact on the result of the estimation. By minimizing the value of Mean Square Error (MSE), Cross-Validation (CV) and Generalized Cross-Validation (GCV) gave the optimal bandwidth value. In this research, corn production was considered as the dependent variable, while the planted area, harvested area, and the fertilizer as the independent variable. The result of this research showed that Nadaraya-Watson Estimator with Generalized Cross-Validation gives a better corn production estimation with optimal bandwidth value 742392,2, with and with MSE 202583,9.</p><p><strong>Keywords</strong>: kernel, estimator Nadaraya-Watson, cross validation, generalized cross validation.</p>

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2

Rao, Nageswara S. V. "Nadaraya-Watson estimator for sensor fusion." Optical Engineering 36, no. 3 (March 1, 1997): 642. http://dx.doi.org/10.1117/1.601136.

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3

Chan, Nigel, and Qiying Wang. "UNIFORM CONVERGENCE FOR NONPARAMETRIC ESTIMATORS WITH NONSTATIONARY DATA." Econometric Theory 30, no. 5 (April 25, 2014): 1110–33. http://dx.doi.org/10.1017/s026646661400005x.

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Sharp upper and lower uniform bounds are established for a general class of functionals of integrated and fractionally integrated time series. The main result is used to develop optimal uniform convergence for the Nadaraya-Watson estimator and the local linear nonparametric estimator in a nonlinear cointegrating regression model. Unlike the point-wise situation, it is shown that the performance of the local linear nonparametric estimator is superior to that of the Nadaraya-Watson estimator in uniform asymptotics.

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4

A. Hamad, Sarwar, and Kawa S. Mohamed Ali. "A Comparative Study of Nearest Neighbor Regression and Nadaraya Watson Regression." Academic Journal of Nawroz University 10, no. 2 (May 24, 2021): 180–88. http://dx.doi.org/10.25007/ajnu.v10n2a505.

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Two non-parametric statistical methods are studied in this work. These are the nearest neighbor regression and the Nadaraya Watson kernel smoothing technique. We have proven that under a precise circumstance, the nearest neighborhood estimator and the Nadaraya Watson smoothing produce a smoothed data with a same error level, which means they have the same performance. Another result of the paper is that nearest neighborhood estimator performs better locally, but it graphically shows a weakness point when a large data set is considered on a global scale.

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5

Poměnková, Jitka. "Nonparametric estimate remarks." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 54, no. 3 (2006): 93–100. http://dx.doi.org/10.11118/actaun200654030093.

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Kernel smoothers belong to the most popular nonparametric functional estimates. They provide a simple way of finding structure in data. The idea of the kernel smoothing can be applied to a simple fixed design regression model. This article is focused on kernel smoothing for fixed design regresion model with three types of estimators, the Gasser-Müller estimator, the Nadaraya-Watson estimator and the local linear estimator. At the end of this article figures for ilustration of desribed estimators on simulated and real data sets are shown.

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6

Li, Jiexiang. "On asymptotic behavior of Nadaraya–Watson regression estimator." Communications in Statistics - Theory and Methods 45, no. 19 (July 19, 2016): 5751–61. http://dx.doi.org/10.1080/03610926.2014.948209.

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7

Hussein, Saja Mohammad. "Comparison of Some Suggested Estimators Based on Differencing Technique in the Partial Linear Model Using Simulation." Baghdad Science Journal 16, no. 4 (December 1, 2019): 0918. http://dx.doi.org/10.21123/bsj.2019.16.4.0918.

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In this paper new methods were presented based on technique of differences which is the difference- based modified jackknifed generalized ridge regression estimator(DMJGR) and difference-based generalized jackknifed ridge regression estimator(DGJR), in estimating the parameters of linear part of the partially linear model. As for the nonlinear part represented by the nonparametric function, it was estimated using Nadaraya Watson smoother. The partially linear model was compared using these proposed methods with other estimators based on differencing technique through the MSE comparison criterion in simulation study.

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8

Park, Cheolyong, and Tae Yoon Kim. "Bootstrapping stationary sequences by the Nadaraya-Watson regression estimator." Journal of Nonparametric Statistics 14, no. 4 (January 2002): 399–407. http://dx.doi.org/10.1080/10485250213116.

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9

Khulood, Hamed Aljuhani, and Ismail Al turk Lutfiah. "Modification of the adaptive Nadaraya-Watson kernel regression estimator." Scientific Research and Essays 9, no. 22 (November 30, 2014): 966–71. http://dx.doi.org/10.5897/sre2014.6121.

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10

Kim, Tae Yoon, Myung Sang Moon, and Sangyeol Lee. "Large bandwidth asymptotics for Nadaraya–Watson auto-regression estimator." Journal of the Korean Statistical Society 37, no. 4 (December 2008): 313–22. http://dx.doi.org/10.1016/j.jkss.2008.02.003.

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11

Fajardo, Jesús A. "A Criterion for the Fuzzy Set Estimation of the Regression Function." Journal of Probability and Statistics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/593036.

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We propose a criterion to estimate the regression function by means of a nonparametric and fuzzy set estimator of the Nadaraya-Watson type, for independent pairs of data, obtaining a reduction of the integrated mean square error of the fuzzy set estimator regarding the integrated mean square error of the classic kernel estimators. This reduction shows that the fuzzy set estimator has better performance than the kernel estimations. Also, the convergence rate of the optimal scaling factor is computed, which coincides with the convergence rate in classic kernel estimation. Finally, these theoretical findings are illustrated using a numerical example.

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12

ARFI, Mounir. "On the Convergence Rate for a Kernel Estimate of the Regression Function." International Journal of Statistics and Probability 5, no. 2 (February 10, 2016): 29. http://dx.doi.org/10.5539/ijsp.v5n2p29.

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We give the rate of the uniform convergence for the kernel estimate of the regression function over a sequence of compact sets which increases to $\mathbb{R}^{d}$ when $n$ approaches the infinity and when the observed process is $\varphi$-mixing. The used estimator for the regression function is the kernel estimator proposed by Nadaraya, Watson (1964).

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13

Wan, Zailong, and Takeru Igusa. "Statistics of Nadaraya-Watson estimator errors in surrogate-based optimization." Optimization and Engineering 7, no. 3 (September 2006): 385–97. http://dx.doi.org/10.1007/s11081-006-9980-9.

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14

Romanchak, V. M. "APPROXIMATELY SINGULAR WAVELET." «System analysis and applied information science», no. 2 (August 7, 2018): 23–28. http://dx.doi.org/10.21122/2309-4923-2018-2-23-28.

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The problem of approximation is relevant for most engineering applications. In this connection, the universal methods of approximation are of interest. The method of nonparametric approximation is developing in the paper – the method of singular wavelets. The method includes an effective numerical algorithm based on the summation of a recursive sequence of functions. The universal algorithm of approximation makes it possible to apply it to approximate one-dimensional and multidimensional functions, in decision support systems, in the processing of stochastic information, pattern recognition, and solution of boundary-value problems.The introduction explain the idea of the method of singular wavelets – to combine the theory of wavelets with the Nadaraya-Watson kernel regression estimator. Usually, Nadaraya-Watson kernel regression are considered as an example of non- parametric estimation. However, one parameter, the smoothing parameter, is still present in the traditional kernel regression algorithm. The choice of the optimal value of this parameter is a complex mathematical problem, and numerous studies have been devoted to this question. In the approximation by the method of singular wavelets, summation of Nadaraya-Watson kernel regression estimates with the smoothing parameter takes place, which solves the problem of the optimal choice of this parameter.In the main part of the paper theorems are formulated that determine the properties of the regularized wavelet transform. Sufficient conditions for uniform convergence of the wavelet series are obtained for the first time. To illustrate the effectiveness of the numerical approximation algorithm, we consider an example of the quasi-interpolation of the Runge function by wavelets with a uniform distribution of interpolation nodes.

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15

Ziegler, Klaus. "On approximations to the bias of the nadaraya-watson regression estimator." Journal of Nonparametric Statistics 13, no. 4 (January 2001): 583–89. http://dx.doi.org/10.1080/10485250108832866.

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16

Long, Hongwei, and Lianfen Qian. "Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions." Electronic Journal of Statistics 7 (2013): 1387–418. http://dx.doi.org/10.1214/13-ejs811.

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17

Joshi, Venkatesh B., and Bhargavi Deshpande. "A NEW MODIFICATION TO THE ADAPTIVE NADARAYA-WATSON KERNEL REGRESSION ESTIMATOR." Advances and Applications in Statistics 49, no. 4 (October 26, 2016): 245–56. http://dx.doi.org/10.17654/as049040245.

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18

Dychko, H. M., and R. E. Maĭboroda. "A generalized Nadaraya–Watson estimator for observations obtained from a mixture." Theory of Probability and Mathematical Statistics 100 (August 4, 2020): 61–76. http://dx.doi.org/10.1090/tpms/1098.

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19

Geenens, Gery. "Explicit Formula for Asymptotic Higher Moments of the Nadaraya-Watson Estimator." Sankhya A 76, no. 1 (September 17, 2013): 77–100. http://dx.doi.org/10.1007/s13171-013-0035-y.

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20

Nakarmi, Janet, Hailin Sang, and Lin Ge. "Variable bandwidth kernel regression estimation." ESAIM: Probability and Statistics 25 (2021): 55–86. http://dx.doi.org/10.1051/ps/2021003.

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In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in ℝ2 to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of O(hn4) under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.

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21

Xu, Ke-Li. "REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS." Econometric Theory 26, no. 2 (September 30, 2009): 541–63. http://dx.doi.org/10.1017/s0266466609100087.

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The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

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22

Wang, Qiying, and Peter C. B. Phillips. "ASYMPTOTIC THEORY FOR ZERO ENERGY FUNCTIONALS WITH NONPARAMETRIC REGRESSION APPLICATIONS." Econometric Theory 27, no. 2 (August 27, 2010): 235–59. http://dx.doi.org/10.1017/s0266466610000277.

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A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya–Watson estimator has the same limit distribution (to the second order including bias) as the local linear nonparametric estimator.

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23

Njeri Ngure, Josephine, and Anthony Gichuhi Waititu. "Consistency of an Estimator for Change Point in Volatility of Financial Returns." Journal of Mathematics Research 13, no. 1 (January 27, 2021): 56. http://dx.doi.org/10.5539/jmr.v13n1p56.

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A non parametric Auto-Regressive Conditional Heteroscedastic model for financial returns series is considered in which the conditional mean and volatility functions are estimated non-parametrically using Nadaraya Watson kernel. A test statistic for unknown abrupt change point in volatility which takes into consideration conditional heteroskedasticity, dependence, heterogeneity and the fourth moment of financial returns, since kurtosis is a function of the fourth moment is considered. The test is based on L2norm of the conditional variance functions of the squared residuals. A non-parametric change point estimator in volatility of financial returns is further obtained. The consistency of the estimator is shown theoretically and through simulation. An application of the estimator in change point estimation in volatility of United States Dollar/Kenya Shilling exchange rate returns data set is made. Through binary segmentation procedure, three change points in volatility of the exchange rate returns are estimated and further accounted for.

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24

Nishida, Kiheiji, and Yuichiro Kanazawa. "INTRODUCTION TO THE VARIANCE-STABILIZING BANDWIDTH FOR THE NADARAYA-WATSON REGRESSION ESTIMATOR." Bulletin of informatics and cybernetics 43 (December 2011): 53–66. http://dx.doi.org/10.5109/1434311.

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25

Glad, Ingrid K. "A note on unconditional properties of a parametrically guided Nadaraya-Watson estimator." Statistics & Probability Letters 37, no. 1 (January 1998): 101–8. http://dx.doi.org/10.1016/s0167-7152(97)00106-5.

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26

El Machkouri, M., X. Fan, and L. Reding. "On the Nadaraya–Watson kernel regression estimator for irregularly spaced spatial data." Journal of Statistical Planning and Inference 205 (March 2020): 92–114. http://dx.doi.org/10.1016/j.jspi.2019.06.006.

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27

Cai, Zongwu. "REGRESSION QUANTILES FOR TIME SERIES." Econometric Theory 18, no. 1 (February 2002): 169–92. http://dx.doi.org/10.1017/s0266466602181096.

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In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology.

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28

Cheruiyot, Langat Reuben, Odhiambo Romanus Otieno, and George O. Orwa. "A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total." International Journal of Statistics and Probability 8, no. 3 (April 27, 2019): 83. http://dx.doi.org/10.5539/ijsp.v8n3p83.

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This study explores the estimation of finite population total. For many years design-based approach dominated the scene in statistical inference in sample surveys. The scenario has since changed with emergence of the other approaches (Model-Based, Model-Assisted and the Randomization-Assisted), which have proved to rival the conventional approach. This paper focuses on a model based approach. Within this framework a nonparametric regression estimator for finite population total is developed. The nonparametric technique has been found from previous studies to be advantageous than its parametric counterpart in terms of robustness and flexibility.  Kernel smoother has been used in construction of the estimator. The challenge of the boundary problem encountered with the Nadaraya-Watson estimator has been addressed by modifying it using reflection technique. The performance of the proposed estimator has been compared to the design-based Horvitz Thompson estimator and the model –based nonparametric regression estimator proposed by (Dorfman, 1992) and the ratio estimator using simulated data.

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29

Luo, Zhi-Ming, Gyu Moon Song, and Tae Yoon Kim. "Central limit theorem for quadratic errors of Nadaraya–Watson regression estimator under dependence." Journal of the Korean Statistical Society 40, no. 4 (December 2011): 425–35. http://dx.doi.org/10.1016/j.jkss.2011.01.003.

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30

Bii, Nelson Kiprono, Christopher Ouma Onyango, and John Odhiambo. "Estimation of a Finite Population Mean under Random Nonresponse Using Kernel Weights." Journal of Probability and Statistics 2020 (April 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/8090381.

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Nonresponse is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random nonresponse using auxiliary data. In this study, it is assumed that random nonresponse occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random nonresponse. In particular, auxiliary information is used via an improved Nadaraya–Watson kernel regression technique to compensate for random nonresponse. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of a finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at 95% coverage rate. The results obtained in this study are useful for instance in choosing efficient estimators of a finite population mean in demographic sample surveys.

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31

Zinde-Walsh, Victoria. "KERNEL ESTIMATION WHEN DENSITY MAY NOT EXIST." Econometric Theory 24, no. 3 (February 26, 2008): 696–725. http://dx.doi.org/10.1017/s0266466608080298.

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Nonparametric kernel estimation of density and conditional mean is widely used, but many of the pointwise and global asymptotic results for the estimators are not available unless the density is continuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Nonsmooth density and mass points in distributions arise in various situations that are examined in empirical studies; some examples and explanations are discussed in the paper. Generally, any distribution function consists of absolutely continuous, discrete, and singular components, but only a few special cases of nonparametric estimation involving singularity have been examined in the literature, and asymptotic theory under the general setup has not been developed. In this paper the asymptotic process for the kernel estimator is examined by means of the generalized functions and generalized random processes approach; it provides a unified theory because density and its derivatives can be defined as generalized functions for any distribution, including cases with singular components. The limit process for the kernel estimator of density is fully characterized in terms of a generalized Gaussian process. Asymptotic results for the Nadaraya–Watson conditional mean estimator are also provided.

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32

Conn, Daniel, and Gang Li. "An oracle property of the Nadaraya–Watson kernel estimator for high‐dimensional nonparametric regression." Scandinavian Journal of Statistics 46, no. 3 (December 26, 2018): 735–64. http://dx.doi.org/10.1111/sjos.12370.

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33

Hanafusa, Ryo, and Takeshi Okadome. "Bayesian Kernel Regression for Noisy Inputs Based on Nadaraya–Watson Estimator Constructed from Noiseless Training Data." Advances in Data Science and Adaptive Analysis 12, no. 01 (January 2020): 2050004. http://dx.doi.org/10.1142/s2424922x20500047.

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In regression for noisy inputs, noise is typically removed from a given noisy input if possible, and then the resulting noise-free input is provided to the regression function. In some cases, however, there is no available time or method for removing noise. The regression method proposed in this paper determines a regression function for noisy inputs using the estimated posterior of their noise-free constituents with a nonparametric estimator for noiseless explanatory values, which is constructed from noiseless training data. In addition, a probabilistic generative model is presented for estimating the noise distribution. This enables us to determine the noise distribution parametrically from a single noisy input, using the distribution of the noise-free constituent of noisy input estimated from the training data set as a prior. Experiments conducted using artificial and real data sets show that the proposed method suppresses the overfitting of the regression function for noisy inputs and the root mean squared errors (RMSEs) of the predictions are smaller compared with those of an existing method.

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34

Aspirot, Laura, Karine Bertin, and Gonzalo Perera. "Asymptotic normality of the Nadaraya–Watson estimator for nonstationary functional data and applications to telecommunications." Journal of Nonparametric Statistics 21, no. 5 (July 2009): 535–51. http://dx.doi.org/10.1080/10485250902878655.

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35

Tosatto, Samuele, Riad Akrour, and Jan Peters. "An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions." Stats 4, no. 1 (December 30, 2020): 1–17. http://dx.doi.org/10.3390/stats4010001.

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The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in several related literature. However, given its asymptotic nature, it gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making surges the need for hard (non-probabilistic) guarantees. To alleviate this issue, we propose an upper bound of the bias which holds for finite bandwidths using Lipschitz assumptions and mitigating some of the prerequisites of Rosenblatt’s analysis. Our bound has potential applications in fields like surgical robots or self-driving cars, where some hard guarantees on the prediction-error are needed.

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36

Pratiwi, Deni, Lalu Abd Azis Mursy, Muhammad Rizaldi, and Nurul Fitriyani. "Regresi Nonparametrik Kernel Gaussian pada Pemodelan Angka Kelahiran Kasar di Provinsi Nusa Tenggara Barat." EIGEN MATHEMATICS JOURNAL 3, no. 2 (December 30, 2020): 100. http://dx.doi.org/10.29303/emj.v3i2.78.

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This study aims to model Crude Birth Rates (CBR) in West Nusa Tenggara Province. The nonparametric regression method was used in this research by considering data distribution patterns that do not show a linear relationship between variables. In this case, the kernel nonparametric regression using the Gaussian function and the Nadaraya-Watson estimator. The results showed optimal bandwidths of 0.55542837, 1.29042927, 0.94706041, and 0.92278896 with a value of minimum Generalized Cross-Validation (GCV) of 0.000000000432613511, which was minimized by the simulated annealing algorithm. The resulting model's accuracy can be seen from the coefficient of determination (R2) of 99.23% and the Mean Absolute Percentage Error (MAPE) of 0.007049%.

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HANIF, Muhammad, Shabnam SHAHZADI, Usman SHAHZAD, and Nursel KOYUNCU. "On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size." Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 2 (June 12, 2018): 511. http://dx.doi.org/10.19113/sdufbed.70996.

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38

Bercu, Bernard, Thi Mong Ngoc Nguyen, and Jerome Saracco. "On the asymptotic behaviour of the recursive Nadaraya–Watson estimator associated with the recursive sliced inverse regression method." Statistics 49, no. 3 (February 5, 2014): 660–79. http://dx.doi.org/10.1080/02331888.2014.884097.

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39

Orzeszko, Witold. "Several Aspects of Nonparametric Prediction of Nonlinear Time Series." Przegląd Statystyczny 65, no. 1 (January 30, 2019): 7–24. http://dx.doi.org/10.5604/01.3001.0014.0522.

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Nonparametric regression is an alternative to the parametric approach, which consists of applying parametric models, i.e. models of the certain functional form with a fixed number of parameters. As opposed to the parametric approach, nonparametric models have a general form, which can be approximated increasingly precisely when the sample size grows. Hereby they do not impose such restricted assumptions about the form of the modelling dependencies and in consequence, they are more flexible and let the data speak for themselves. That is why they are a promising tool for forecasting, especially in case of nonlinear time series. One of the most popular nonparametric regression method is the Nadaraya- Watson kernel smoothing. Nowadays, there are a number of variations of this method, like the local-linear kernel estimator, which combines the local linear approximation and the kernel estimator. In the paper a Monte Carlo study is conducted in order to assess the usefulness of the kernel smoothers to nonlinear time series forecasting and to compare them with the other techniques of forecasting.

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40

Rahayu, Putri Indi, and Pardomuan Robinson Sihombing. "PENERAPAN REGRESI NONPARAMETRIK KERNEL DAN SPLINE DALAM MEMODELKAN RETURN ON ASSET (ROA) BANK SYARIAH DI INDONESIA." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 14, no. 2 (March 2, 2021): 115. http://dx.doi.org/10.20527/epsilon.v14i2.2968.

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Sharia Bank Return On Assets (ROA) modeling in Indonesia in 2018 aims to analyze the relationship pattern of Retturn On Assets (ROA) with interest rates. The analysis that is often used for modeling is regression analysis. Regression analysis is divided into two, namely parametric and nonparametric. The most commonly used nonparametric regression methods are kernel and spline regression. In this study, the nonparametric regression used was kernel regression with the Nadaraya-Watson (NWE) estimator and Local Polynomial (LPE) estimator, while the spline regression was smoothing spline and B-splines. The fitting curve results show that the best model is the B-splines regression model with a degree of 3 and the number of knots 5. This is because the B-splines regression model has a smooth curve and more closely follows the distribution of data compared to other regression curves. The B-splines regression model has a determination coefficient of R ^ 2 of 74.92%,%, meaning that the amount of variation in the ROA variable described by the B-splines regression model is 74.92%, while the remaining 25.8% is explained by other variables not included in the model.

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41

Cai, Zongwu. "Weighted Nadaraya–Watson regression estimation." Statistics & Probability Letters 51, no. 3 (February 2001): 307–18. http://dx.doi.org/10.1016/s0167-7152(00)00172-3.

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42

García-Soidán, Pilar. "Asymptotic normality of the Nadaraya–Watson semivariogram estimators." TEST 16, no. 3 (March 6, 2007): 479–503. http://dx.doi.org/10.1007/s11749-006-0016-8.

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43

Kato, K. "Weighted Nadaraya-Watson Estimation of Conditional Expected Shortfall." Journal of Financial Econometrics 10, no. 2 (February 15, 2012): 265–91. http://dx.doi.org/10.1093/jjfinec/nbs002.

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Hanif, Muhammad, HanChao Wang, and ZhengYan Lin. "Reweighted Nadaraya-Watson estimation of jump-diffusion models." Science China Mathematics 55, no. 5 (December 29, 2011): 1005–16. http://dx.doi.org/10.1007/s11425-011-4340-4.

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Bandi, Federico M., and Guillermo Moloche. "ON THE FUNCTIONAL ESTIMATION OF MULTIVARIATE DIFFUSION PROCESSES." Econometric Theory 34, no. 4 (September 18, 2017): 896–946. http://dx.doi.org/10.1017/s0266466617000305.

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Abstract:

We propose a nonparametric estimation theory for the occupation density, the drift vector, and the diffusion matrix of multivariate diffusion processes. The estimators are sample analogues to infinitesimal conditional expectations constructed as Nadaraya-Watson kernel averages. Mild assumptions are imposed on the statistical properties of the multivariate system to obtain limiting results. Harris recurrence is all that we require to show consistency and asymptotic (mixed) normality of the proposed functional estimators. The identification method and asymptotic theory apply to both stationary and nonstationary multivariate diffusion processes of the recurrent type.

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Song, Yuping, Zhengyan Lin, and Hanchao Wang. "Re-weighted Nadaraya–Watson estimation of second-order jump-diffusion model." Journal of Statistical Planning and Inference 143, no. 4 (April 2013): 730–44. http://dx.doi.org/10.1016/j.jspi.2012.09.010.

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El Shekh Ahmed, Hazem I., Raid B. Salha, and Hossam O. EL-Sayed. "Adaptive weighted Nadaraya–Watson estimation of the conditional quantiles by varying bandwidth." Communications in Statistics - Simulation and Computation 49, no. 5 (April 21, 2020): 1105–17. http://dx.doi.org/10.1080/03610918.2015.1048880.

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Xiong, Xianzhu, Meijuan Ou, and Ailian Chen. "Reweighted Nadaraya–Watson estimation of conditional density function in the right-censored model." Statistics & Probability Letters 168 (January 2021): 108933. http://dx.doi.org/10.1016/j.spl.2020.108933.

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Orang’o Herbert, Imboga. "Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing." International Journal of Theoretical and Applied Mathematics 3, no. 3 (2017): 122. http://dx.doi.org/10.11648/j.ijtam.20170303.14.

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Kanaya, Shin. "UNIFORM CONVERGENCE RATES OF KERNEL-BASED NONPARAMETRIC ESTIMATORS FOR CONTINUOUS TIME DIFFUSION PROCESSES: A DAMPING FUNCTION APPROACH." Econometric Theory 33, no. 4 (July 14, 2016): 874–914. http://dx.doi.org/10.1017/s0266466616000219.

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Abstract:

In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya–Watson type, introducing a new technical device called adamping function. This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant functions can be significantly relaxed. Restrictions on kernel functions are also minimal: We allow for kernels with discontinuity, unbounded support, and slowly decaying tails. Our proofs proceed by using the covering-number technique from empirical process theory and exploiting the mixing and martingale properties of the processes. We also present new results on the path-continuity property of Brownian motions and diffusion processes over an infinite time horizon. These path-continuity results, which should also be of some independent interest, are used to control discretization biases of the nonparametric estimators. The obtained convergence results are useful for non/semiparametric estimation and testing problems of diffusion processes.

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