scholarly journals Robust estimation and inference for general varying coefficient models with missing observations

Test ◽  
2019 ◽  
Vol 29 (4) ◽  
pp. 966-988
Author(s):  
Francesco Bravo
Keyword(s):  
Nonlinear Least Squares ◽  
Missing At Random ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Varying Coefficient ◽  
Finite Sample Properties ◽  
Local Linear Estimation ◽  
Nonlinear Least Squares Estimation

AbstractThis paper considers estimation and inference for a class of varying coefficient models in which some of the responses and some of the covariates are missing at random and outliers are present. The paper proposes two general estimators—and a computationally attractive and asymptotically equivalent one-step version of them—that combine inverse probability weighting and robust local linear estimation. The paper also considers inference for the unknown infinite-dimensional parameter and proposes two Wald statistics that are shown to have power under a sequence of local Pitman drifts and are consistent as the drifts diverge. The results of the paper are illustrated with three examples: robust local generalized estimating equations, robust local quasi-likelihood and robust local nonlinear least squares estimation. A simulation study shows that the proposed estimators and test statistics have competitive finite sample properties, whereas two empirical examples illustrate the applicability of the proposed estimation and testing methods.

scholarly journals Inference in nonparametric/semiparametric moment equality models with shape restrictions

2020 ◽  
Vol 11 (2) ◽  
pp. 609-636
Author(s):  
Yu Zhu
Keyword(s):  
Finite Sample ◽  
Confidence Sets ◽  
Dimensional Parameter ◽  
Inference Problem ◽  
Infinite Dimensional ◽  
Ascending Auctions ◽  
Shape Restrictions ◽  
Finite Sample Properties ◽  
Us Forest Service ◽  
Shape Restriction

This paper studies the inference problem of an infinite‐dimensional parameter with a shape restriction. This parameter is identified by arbitrarily many unconditional moment equalities. The shape restriction leads to a convex restriction set. I propose a test of the shape restriction, which controls size uniformly and applies to both point‐identified and partially identified models. The test can be inverted to construct confidence sets after imposing the shape restriction. Monte Carlo experiments show the finite‐sample properties of this method. In an empirical illustration, I apply the method to ascending auctions held by the US Forest Service and show that imposing shape restrictions can significantly improve inference.

Imputed Estimation For Varying Coefficient Models with Missing Covariates

2013 ◽  
Vol 787 ◽  
pp. 1089-1092
Author(s):  
Pei Xin Zhao
Keyword(s):  
Missing Data ◽  
Estimation Procedure ◽  
Estimating Equation ◽  
Equation Method ◽  
Missing Covariates ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Varying Coefficient

By using the imputation-based estimating equation method, an imputed estimation procedure for the coefficient functions is proposed. The proposed procedure can attenuate the effect of the missing data, and performs well for the finite sample.

scholarly journals Composite Quantile Regression for Varying Coefficient Models with Response Data Missing at Random

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1065 ◽  
Author(s):  
Shuanghua Luo ◽  
Cheng-yi Zhang ◽  
Meihua Wang
Keyword(s):  
Quantile Regression ◽  
Real Life ◽  
Missing At Random ◽  
Unknown Coefficient ◽  
Varying Coefficient Models ◽  
Test Procedures ◽  
Composite Quantile Regression ◽  
Varying Coefficient ◽  
Response Data ◽  
Data Missing

Composite quantile regression (CQR) estimation and inference are studied for varying coefficient models with response data missing at random. Three estimators including the weighted local linear CQR (WLLCQR) estimator, the nonparametric WLLCQR (NWLLCQR) estimator, and the imputed WLLCQR (IWLLCQR) estimator are proposed for unknown coefficient functions. Under some mild conditions, the proposed estimators are asymptotic normal. Simulation studies demonstrate that the unknown coefficient estimators with IWLLCQR are superior to the other two with WLLCQR and NWLLCQR. Moreover, bootstrap test procedures based on the IWLLCQR fittings is developed to test whether the coefficient functions are actually varying. Finally, a type of investigated real-life data is analyzed to illustrated the applications of the proposed method.

SMOOTH VARYING-COEFFICIENT ESTIMATION AND INFERENCE FOR QUALITATIVE AND QUANTITATIVE DATA

2010 ◽  
Vol 26 (6) ◽  
pp. 1607-1637 ◽  
Author(s):  
Qi Li ◽  
Jeffrey S. Racine
Keyword(s):  
Bandwidth Selection ◽  
Rates Of Convergence ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Qualitative And Quantitative ◽  
Varying Coefficient ◽  
Coefficient Estimation ◽  
Wide Range ◽  
Potential Applications ◽  
Frequency Estimator

We propose a semiparametric varying-coefficient estimator that admits both qualitative and quantitative covariates along with a test for correct specification of parametric varying-coefficient models. The proposed estimator is exceedingly flexible and has a wide range of potential applications including hierarchical (mixed) settings, small area estimation, etc. A data-driven cross-validatory bandwidth selection method is proposed that can handle both the qualitative and quantitative covariates and that can also handle the presence of potentially irrelevant covariates, each of which can result in finite-sample efficiency gains relative to the conventional frequency (sample-splitting) estimator that is often found in such settings. Theoretical underpinnings including rates of convergence and asymptotic normality are provided. Monte Carlo simulations are undertaken to assess the proposed estimator’s finite-sample performance relative to the conventional semiparametric frequency estimator and to assess the finite-sample performance of the proposed test for correct parametric specification.

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

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