scholarly journals LIKELIHOOD INFERENCE ON SEMIPARAMETRIC MODELS WITH GENERATED REGRESSORS

2019 ◽  
Vol 36 (4) ◽  
pp. 626-657 ◽  
Author(s):  
Yukitoshi Matsushita ◽  
Taisuke Otsu
Keyword(s):  
Likelihood Ratio Statistic ◽  
Likelihood Inference ◽  
Second Step ◽  
Inference Method ◽  
Nonparametric Likelihood ◽  
Estimation Problems ◽  
Moment Functions ◽  
Class Of Estimators ◽  
Nonparametric Estimates ◽  
Generated Regressors

Hahn and Ridder (2013, Econometrica 81, 315–340) formulated influence functions of semiparametric three-step estimators where generated regressors are computed in the first step. This class of estimators covers several important examples for empirical analysis, such as production function estimators by Olley and Pakes (1996, Econometrica 64, 1263–1297) and propensity score matching estimators for treatment effects by Heckman, Ichimura, and Todd (1998, Review of Economic Studies 65, 261–294). The present article studies a nonparametric likelihood-based inference method for the parameters in such three-step estimation problems. In particular, we apply the general empirical likelihood theory of Bravo, Escanciano, and van Keilegom (2018, Annals of Statistics, forthcoming) to modify semiparametric moment functions to account for influences from plug-in estimates into the above important setup, and show that the resulting likelihood ratio statistic becomes asymptotically pivotal without undersmoothing in the first and second step nonparametric estimates.

scholarly journals Empirical Likelihood Inference for First-Order Random Coefficient Integer-Valued Autoregressive Processes

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Zhiwen Zhao ◽  
Wei Yu
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Simulation Study ◽  
Asymptotic Theory ◽  
Likelihood Ratio Statistic ◽  
Random Coefficient ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Autoregressive Processes ◽  
First Order

We apply the empirical likelihood method to estimate the variance of random coefficient in the first-order random coefficient integer-valued autoregressive (RCINAR(1)) processes. The empirical likelihood ratio statistic is derived and some asymptotic theory for it is presented. Furthermore, a simulation study is presented to demonstrate the performance of the proposed method.

Two-sample nonparametric likelihood inference based on incomplete data with an application to a pneumonia study

2010 ◽  
Vol 52 (3) ◽  
pp. 348-361 ◽  
Author(s):  
Albert Vexler ◽  
Jihnhee Yu ◽  
Lili Tian ◽  
Shuling Liu
Keyword(s):  
Incomplete Data ◽  
Likelihood Inference ◽  
Nonparametric Likelihood

Testing and Estimation in the Block Compound Symmetry Problem

1982 ◽  
Vol 7 (1) ◽  
pp. 3-18 ◽  
Author(s):  
Ted H. Szatrowski
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Null Distribution ◽  
Covariance Matrices ◽  
Maximum Likelihood Estimates ◽  
Testing Problem ◽  
Compound Symmetry ◽  
Estimation Problems ◽  
Symmetry Problem

Known results for testing and estimation problems for patterned means and covariance matrices with explicit linear maximum likelihood estimates are applied to the block compound symmetry problem. New results given include the constants for G.P.E. Box’s approximate null distribution of the likelihood ratio statistic. These techniques are applied to the analysis of an educational testing problem.

scholarly journals Block Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Errors-in-Variables Models with Longitudinal Data

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yafeng Xia ◽  
Hu Da
Keyword(s):  
Longitudinal Data ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Likelihood Ratio Statistic ◽  
Likelihood Inference ◽  
Errors In Variables ◽  
Varying Coefficient ◽  
Mild Conditions ◽  
Partially Linear ◽  
Log Likelihood

Block empirical likelihood inference for semiparametric varying-coeffcient partially linear errors-in-variables models with longitudinal data is investigated. We apply the block empirical likelihood procedure to accommodate the within-group correlation of the longitudinal data. The block empirical log-likelihood ratio statistic for the parametric component is suggested. And the nonparametric version of Wilk’s theorem is derived under mild conditions. Simulations are carried out to access the performance of the proposed procedure.

Series Estimation of Regression Functionals

1994 ◽  
Vol 10 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Whitney K. Newey
Keyword(s):  
Instrumental Variables ◽  
Correction Term ◽  
Asymptotic Variance ◽  
Semiparametric Regression ◽  
Second Step ◽  
Residual Variance ◽  
Variance Estimator ◽  
Series Estimation ◽  
Consistency And Asymptotic Normality ◽  
Generated Regressors

Two-step estimators, where the first step is the predicted value from a nonparametric regression, are useful in many contexts. Examples include a non-parametric residual variance, probit with nonparametric generated regressors, efficient GMM estimation with randomly missing data, heteroskedasticity corrected least squares, semiparametric regression, and efficient nonlinear instrumental variables estimators. The purpose of this paper is the development of consistency and asymptotic normality results when the first step is a series estimator. The paper presents the form of a correction term for the first step on the second-step asymptotic variance and gives a consistent variance estimator. Data-dependent numbers of terms are allowed for, and the regressor distribution can be discrete, continuous, or a mixture of the two. Results for several new estimators are given.

NONPARAMETRIC TWO-STEP SIEVE M ESTIMATION AND INFERENCE

2018 ◽  
Vol 34 (6) ◽  
pp. 1281-1324 ◽  
Author(s):  
Jinyong Hahn ◽  
Zhipeng Liao ◽  
Geert Ridder
Keyword(s):  
Gaussian Approximation ◽  
Asymptotic Variance ◽  
Closed Form Expression ◽  
Second Step ◽  
Consistent Estimate ◽  
Finite Sample ◽  
Inference Procedure ◽  
Nonparametric Models ◽  
M Estimation ◽  
Nonparametric Estimates

This article studies two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. The asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.

scholarly journals First steps towards the reconstruction of the squark flavour structure

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Jordan Bernigaud ◽  
Björn Herrmann
Keyword(s):  
Multivariate Analysis ◽  
Large Hadron Collider ◽  
Standard Model ◽  
Supersymmetric Standard Model ◽  
Minimal Supersymmetric Standard Model ◽  
Hadron Collider ◽  
Likelihood Inference ◽  
Simplified Model ◽  
Inference Method

Assuming the observation of a squark at the Large Hadron Collider, we investigate methods to access its flavour content and thus gain information on the underlying flavour structure of the theory. Based on simple observables, we apply a likelihood inference method to determine the top-flavour content of the observed particle. In addition, we employ a multivariate analysis in order to classify different flavour hypotheses. Both methods are discussed within a simplified model and the more general Minimal Supersymmetric Standard Model including most general squark mixing. We conclude that the likelihood inference may provide an estimation of the top-flavour content if additional knowledge, especially on the gaugino sector is available, while the multivariate analysis identifies different flavour patterns and can accommodate a more minimalistic set of observables.

Nonparametric-likelihood inference based on cost-effectively-sampled-data

2011 ◽  
Vol 38 (4) ◽  
pp. 769-783 ◽  
Author(s):  
Albert Vexler ◽  
Shuling Liu ◽  
Enrique F. Schisterman
Keyword(s):  
Likelihood Inference ◽  
Sampled Data ◽  
Nonparametric Likelihood
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