scholarly journals UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

2010 ◽  
Vol 26 (5) ◽  
pp. 1529-1564 ◽  
Author(s):  
Efang Kong ◽  
Oliver Linton ◽  
Yingcun Xia
Keyword(s):  
Additive Model ◽  
Regression Function ◽  
Stationary Processes ◽  
Local Polynomial Fitting ◽  
Bahadur Representation ◽  
Local Polynomial ◽  
Strongly Mixing ◽  
Higher Order Terms ◽  
Strong Uniform Consistency ◽  
Consistency Rate

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi,Xi)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model.

Local Modeling Algorithm Based on Similarity of Vector

2012 ◽  
Vol 182-183 ◽  
pp. 1060-1064
Author(s):  
Jing Zeng ◽  
Jun Wang ◽  
Jin Yu Guo
Keyword(s):  
Local Model ◽  
Local Models ◽  
Local Polynomial Fitting ◽  
Local Polynomial ◽  
Data Matching ◽  
Local Modeling ◽  
Fitting Algorithm ◽  
System Input ◽  
Simulation Results ◽  
Historical System

A mutli-model modeling method based on local model is given. The modeling idea is firstly to find some data matching with the current working point from vast historical system input-output datasets, and in this paper, we give a new method of choose data information based on similarity of vector which improve the accuracy of data greatly. Secondly to choose the weight and optimum bandwidth then develop a local model using local polynomial fitting algorithm. With the change of working points, multiple local models are built. The effectiveness of the proposed method is demonstrated by simulation results.

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (4) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

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