TY - JOUR
T1 - Reweighting approximate GM estimators
T2 - Asymptotics and residual-based graphics
AU - Simpson, Douglas G.
AU - Chang, Yuan Chin Ivan
N1 - Funding Information:
"~ This research was supported by NSF contract DMS 92-07730, NSA contract MDA 904-92-H-3058 and travel funds from Academia Sinica, Taiwan, ROC. * Corresponding author. Tel.: +1 217 333 2167; fax: +1 217 244 7190; e-mail: [email protected].
PY - 1997/2/1
Y1 - 1997/2/1
N2 - The iterative weighted least squares algorithm is handy for solving generalized estimating equations. In some situations it may be desirable to limit the number of iterations to a fixed finite number, for instance, to keep the breakdown point under control. Such a scheme is called reweighting. Usually reweighting leads to a different large sample theory than full iteration, and the reweighted estimator may inherit deficiencies of the starting value. When might the reweighting scheme work? To answer this question we define a broad class of estimators, namely, approximate GM estimators, and we show that reweighting leads to the same large sample theory as full iteration within this class. As an example, we provide conditions under which one-step Newton-Raphson estimators are approximate GM estimators. We then use the reweighting to construct residual-based graphics for approximate GM estimates, adapting weighted residual plots that have been proposed previously, and developing new plots to provide complementary views of the data.
AB - The iterative weighted least squares algorithm is handy for solving generalized estimating equations. In some situations it may be desirable to limit the number of iterations to a fixed finite number, for instance, to keep the breakdown point under control. Such a scheme is called reweighting. Usually reweighting leads to a different large sample theory than full iteration, and the reweighted estimator may inherit deficiencies of the starting value. When might the reweighting scheme work? To answer this question we define a broad class of estimators, namely, approximate GM estimators, and we show that reweighting leads to the same large sample theory as full iteration within this class. As an example, we provide conditions under which one-step Newton-Raphson estimators are approximate GM estimators. We then use the reweighting to construct residual-based graphics for approximate GM estimates, adapting weighted residual plots that have been proposed previously, and developing new plots to provide complementary views of the data.
KW - Added variable plot
KW - Generalized estimating equation
KW - One-step estimator
KW - Regression diagnostics
KW - Robust methods
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U2 - 10.1016/s0378-3758(96)00049-3
DO - 10.1016/s0378-3758(96)00049-3
M3 - Article
AN - SCOPUS:0031068514
SN - 0378-3758
VL - 57
SP - 273
EP - 293
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 2
ER -