Strong uniform consistency rate of an M-estimator of regression function for incomplete data under α-mixing condition

2020 ◽  
pp. 1-34
Author(s):  
Hassiba Benseradj ◽  
Zohra Guessoum
Keyword(s):  
Incomplete Data ◽  
Regression Function ◽  
Mixing Condition ◽  
Uniform Consistency ◽  
M Estimator ◽  
Strong Uniform Consistency ◽  
Consistency Rate ◽  
Strong Uniform Consistency Rate

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.

scholarly journals LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE: UNIFORM CONSISTENCY WITH CONVERGENCE RATES

2012 ◽  
Vol 28 (5) ◽  
pp. 935-958 ◽  
Author(s):  
Degui Li ◽  
Zudi Lu ◽  
Oliver Linton
Keyword(s):  
Convergence Rates ◽  
Regression Function ◽  
Linear Estimator ◽  
Uniform Consistency ◽  
Linear Fitting ◽  
Semiparametric Modeling ◽  
Local Linear Fitting ◽  
Local Linear ◽  
Local Linear Estimator ◽  
Nonparametric Kernel

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

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