computing_GMM_estimator

Computes Generalized Method of Moments (GMM) estimators by combining
moment-corrected estimating equations and phase-function estimating
equations. The GMM weighting matrix is estimated via a cluster bootstrap
that accounts for uncertainty in estimating the measurement error
covariance.

internal

Estimation and inference for coefficients of linear EIV models with symmetric measurement errors.
The measurement errors can be homoscedastic or heteroscedastic, for the latter, replication for at least some observations needs to be available. The estimation method and asymptotic inference are
based on a generalised method of moments framework, where the estimating equations are formed from (1) minimising the distance between the empirical phase function (normalised characteristic function) of the response and that of the linear combination of all the covariates at the estimates,
and (2) minimising a corrected least-square discrepancy function. Specifically, for a linear EIV model with p error-prone and q error-free covariates, if replicates are available, the GMM approach is based on a 2(p+q) estimating equations if some replicates are available and based on p+2q estimating equations if no replicate is available.
The details of the method are described in Nghiem and Potgieter (2020) <doi:10.1093/biomet/asaa025> and Nghiem and Potgieter (2025) <doi:10.5705/ss.202022.0331>.

Chang Liu

PhaseGMM

Phase-Function Based Estimation and Inference for Linear
Errors-in-Variables (EIV) Models

Linh Nghiem

computing_GMM_estimator function

<dl><dt>W</dt>
<dd>Numeric array of dimension <code>n x p x J</code> containing replicate
measurements of contaminated covariates.</dd>
<dt>y</dt>
<dd>Numeric vector of length <code>n</code> containing the response.</dd>
<dt>Zmat</dt>
<dd>Numeric matrix of dimension <code>n x q</code> containing error-free
covariates.</dd>
<dt>B</dt>
<dd>Integer specifying the number of bootstrap replicates.</dd>
<dt>t_grid_length</dt>
<dd>Integer specifying the length of optimal t for
computational intergration.</dd></dl>

Arguments

GMM estimator combining moment-corrected and phase-function equations — computing_GMM_estimator

<dl>

<dt>W</dt>
<dd>Numeric array of dimension <code>n x p x J</code> containing replicate
measurements of contaminated covariates.</dd>


<dt>y</dt>
<dd>Numeric vector of length <code>n</code> containing the response.</dd>


<dt>Zmat</dt>
<dd>Numeric matrix of dimension <code>n x q</code> containing error-free
covariates.</dd>


<dt>B</dt>
<dd>Integer specifying the number of bootstrap replicates.</dd>


<dt>t_grid_length</dt>
<dd>Integer specifying the length of optimal t for
computational intergration.</dd>

</dl>

computing_GMM_estimator: GMM estimator combining moment-corrected and phase-function equations

Description

Usage

Value

Arguments