Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation
The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in m...
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| Format: | Article |
| Language: | English |
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Springer
2020-10-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125945410/view |
| _version_ | 1818231325631447040 |
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| author | Langat Reuben Cheruiyot |
| author_facet | Langat Reuben Cheruiyot |
| author_sort | Langat Reuben Cheruiyot |
| collection | DOAJ |
| description | The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind getting a model that fits the data well can be a challenge. There are many situations where parametric estimation is disadvantageous because of the possible misspecification of the model. Under such circumstance, many researchers normally allow the data to suggest a model for itself in the technique that has become so popular in recent years called the nonparametric regression estimation. In this technique the use of kernel estimators is common. This paper explores the famous Nadaraya–Watson estimator and local linear regression estimator on the boundary bias. A global measure of error criterion-asymptotic mean integrated square error (AMISE) has been computed from simulated data at the empirical stage to assess the performance of the two estimators in regression estimation. This study shows that local linear regression estimator has a sterling performance over the standard Nadaraya–Watson estimator. |
| first_indexed | 2024-12-12T10:48:36Z |
| format | Article |
| id | doaj.art-cac56c5ed9a846e3bd28b4a880d45d9a |
| institution | Directory Open Access Journal |
| issn | 2214-1766 |
| language | English |
| last_indexed | 2024-12-12T10:48:36Z |
| publishDate | 2020-10-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-cac56c5ed9a846e3bd28b4a880d45d9a2022-12-22T00:26:50ZengSpringerJournal of Statistical Theory and Applications (JSTA)2214-17662020-10-0119310.2991/jsta.d.201016.001Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression EstimationLangat Reuben CheruiyotThe precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind getting a model that fits the data well can be a challenge. There are many situations where parametric estimation is disadvantageous because of the possible misspecification of the model. Under such circumstance, many researchers normally allow the data to suggest a model for itself in the technique that has become so popular in recent years called the nonparametric regression estimation. In this technique the use of kernel estimators is common. This paper explores the famous Nadaraya–Watson estimator and local linear regression estimator on the boundary bias. A global measure of error criterion-asymptotic mean integrated square error (AMISE) has been computed from simulated data at the empirical stage to assess the performance of the two estimators in regression estimation. This study shows that local linear regression estimator has a sterling performance over the standard Nadaraya–Watson estimator.https://www.atlantis-press.com/article/125945410/viewKernel estimatorsNonparametric regression estimationLocal linear regressionBiasVarianceAsymptotic mean integrated square error (AMISE) |
| spellingShingle | Langat Reuben Cheruiyot Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation Journal of Statistical Theory and Applications (JSTA) Kernel estimators Nonparametric regression estimation Local linear regression Bias Variance Asymptotic mean integrated square error (AMISE) |
| title | Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation |
| title_full | Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation |
| title_fullStr | Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation |
| title_full_unstemmed | Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation |
| title_short | Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation |
| title_sort | local linear regression estimator on the boundary correction in nonparametric regression estimation |
| topic | Kernel estimators Nonparametric regression estimation Local linear regression Bias Variance Asymptotic mean integrated square error (AMISE) |
| url | https://www.atlantis-press.com/article/125945410/view |
| work_keys_str_mv | AT langatreubencheruiyot locallinearregressionestimatorontheboundarycorrectioninnonparametricregressionestimation |