Related Experiment Video
Updated: May 18, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in
Liyun Su1, Yanyong Zhao, Tianshun Yan
1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China. cloudhopping@163.com
Abstract:
Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.
Related Concept Videos
Multiple Regression
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Application of Linearization and Approximation
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Linearization and Approximation
Microsoft Excel: Regression Analysis
To perform regression...