regression estimator
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Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2387
Author(s):  
Xiaoshuang Zhou ◽  
Xiulian Gao ◽  
Yukun Zhang ◽  
Xiuling Yin ◽  
Yanfeng Shen

In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the optimal estimator is obtained. Furthermore, we conduct some simulations to evaluate the performance of our proposed estimators under different symmetric error distributions. Simulation studies further illustrate that both estimators work better than the local linear least square estimator for all the symmetric errors considered except the normal error, and the weighted quantile average estimator performs better than the weighted composite quantile regression estimator in most situations.


2021 ◽  
Vol 19 (1) ◽  
pp. 1-7
Author(s):  
F. S. APANTAKU ◽  
O. M. OLAYIWOLA ◽  
A. O. AJAYI ◽  
O. S. JAIYEOLA

Generalized Chain ratio in regression type estimator is efficient for estimating the population mean. Many authors have derived a Generalized Chain ratio in regression type estimator. However, the computation of its Mean Square Error (MSE) is cumbersome based on the fact that several iterations have to be done, hence the need for a modified generalized chain ratio in regression estimator with lower MSE. This study proposed a modified generalized chain ratio in regression estimator which is less cumbersome in its computation. Two data sets were used in this study. The first data were on tobacco production by tobacco producing countries with yield of tobacco (variable of interest), area of land and production in metric tonnes as the auxiliary variables. The second data were the number of graduating pupils (variable of interest) in Ado-Odo/Ota local government, Ogun state with the number of enrolled pupils in primaries one and five as the auxiliary variables. The mean square errors in the existing and proposed estimators for various values of alpha were derived and relative efficiency was determined. The MSE for the existing estimator of tobacco production gave six values 0.0080, 0.0079, 0.0080, 0.0082, 0.0087 and 0.0093 with 0.0079 as the minimum while the proposed estimator gave 0.0054. The MSEs for the existing estimator for the graduating pupils were 20.73, 11.08, 7.49, 9.96, 18.50 and 33.10 with 7.49 as the minimum while the proposed was 6.52. The results of this study showed that the proposed estimator gave lower MSE for the two data sets, hence it is more efficient.      


Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3057
Author(s):  
Mohammad Arashi ◽  
Mina Norouzirad ◽  
Mahdi Roozbeh ◽  
Naushad Mamode Mamode Khan

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the growing dimension, i.e., p→∞ when n is fixed. Under some mild regularity conditions, we prove the proposed estimator’s consistency and derive its asymptotic properties. Some Monte Carlo simulation experiments are executed in their performance, and the implementation is considered to analyze a high-dimensional genetic dataset.


Author(s):  
Ceren Ünal ◽  
Cem Kadilar

In this article, we propose an estimator using the exponential function for the population mean in the case of non-response on both the study and the auxiliary variables. The equations for the Bias and Mean Square Error (MSE) are derived to the first order of approximation and theoretical comparisons are made with existing estimators in literature. Besides, we examine the efficiency of the proposed estimator according to the classical ratio and regression estimator, Hansen-Hurwitz unbiased estimator, and the estimator of Singh et al. (2009). Following theoretical comparisons, we infer that the proposed estimator is more efficient than compared estimators under the obtained conditions in theory. Moreover, these theoretical results are supported numerically by providing an empirical study on five different data sets.


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