A paradox concerning nuisance parameters and projected estimating functions

Henmi, Masayuki

doi:10.1093/biomet/91.4.929

Cited by 67 publications

(55 citation statements)

References 12 publications

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“…In other words, in terms of the augmented model described above, we get a better estimator of θ 1 when we use the estimated θ 2 in the second step than if we used the true θ 2 . This phenomenon has been discussed by Wooldridge (1999Wooldridge ( , 2001Wooldridge ( , 2002bWooldridge ( , 2007, and it has also been noted in a number of previous works, including Pierce (1982), Rosenbaum (1987), Imbens (1992), Robins et al (1992), Robins and Rotnitzky (1995), Hirano et al (2003), Henmi and Eguchi (2004) and Hitomi et al (2008). This is puzzling because knowledge of θ 2 , if properly exploited, cannot be harmful.…”

Section: Introductionmentioning

confidence: 77%

“…Earlier papers that have ''explained'' the paradox that the twostep estimator dominates the know-θ 2 estimator include Pierce (1982), Henmi and Eguchi (2004) and Hirano et al (2003). Basically their explanation is that two-step dominates know-θ 2 whenθ 1,two-step andθ 2,two-step are asymptotically independent.…”

Section: Theorem 22 For the Estimators Defined In Definitions 21-2mentioning

confidence: 99%

“…Our Statement 10 is a generalization of their results because it includes more estimators in its comparisons, but also because our condition (D 12 = C 12 C −1 22 D 22 ) does not imply thatθ 1,two-step andθ 2,two-step are asymptotically independent. However, the information equalities that arise in the selectivity model (D 12 = −C 12 and D 22 = −C 22 ) do imply thatθ 1,two-step andθ 2,two-step are asymptotically independent, so that the explanation of Pierce (1982) and Henmi and Eguchi (2004) does apply in this model.…”

Section: Theorem 22 For the Estimators Defined In Definitions 21-2mentioning

confidence: 99%

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GMM redundancy results for general missing data problems

Prokhorov¹,

Schmidt²

2009

Journal of Econometrics

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Section: Introductionmentioning

confidence: 77%

Section: Theorem 22 For the Estimators Defined In Definitions 21-2mentioning

confidence: 99%

Section: Theorem 22 For the Estimators Defined In Definitions 21-2mentioning

confidence: 99%

See 1 more Smart Citation

GMM redundancy results for general missing data problems

Prokhorov¹,

Schmidt²

2009

Journal of Econometrics

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“…WL estimating equations with known sampling weights only involve data for subjects sampled at phase 2; estimation of the weights allows incorporation of phase 1 data available for all subjects. Provided the weights are estimated efficiently, this increases the efficiency of the WL estimators of the Euclidean parameters of interest (Henmi & Eguchi, 2004). When fitting logistic regression models by WL to phase 2 case-control samples, for example, use of the empirical (estimated) weights leads to fully efficient estimates of odds ratio parameters whereas use of the a priori sampling weights may be seriously inefficient (Scott & Wild, 1986).…”

Section: Notation Assumptions and Problem Statementmentioning

confidence: 99%

“…See Henmi & Eguchi (2004) for a recent discussion and interpretation. This suggests the following estimation procedure:…”

Section: Bernoulli Sampling With Estimated Weightsmentioning

confidence: 99%

Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression

Breslow

Wellner

2006

Scandinavian J Statistics

129

196

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ABSTRACT. We consider semiparametric models for which solution of Horvitz-Thompson or inverse probability weighted (IPW) likelihood equations with two-phase stratified samples leads to √ N consistent and asymptotically Gaussian estimators of both Euclidean and nonparametric parameters. For Bernoulli (independent and identically distributed) sampling, standard theory shows that the Euclidean parameter estimator is asymptotically linear in the IPW influence function. By proving weak convergence of the IPW empirical process, and borrowing results on weighted bootstrap empirical processes, we derive a parallel asymptotic expansion for finite population stratified sampling. Several of our key results have been derived already for Cox regression with stratified case-cohort and more general survey designs. This paper is intended to help interpret this previous work and to pave the way towards a general Horvitz-Thompson approach to semiparametric inference with data from complex probability samples.

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Semiparametric median residual life model and inference

Yin

2010

Can J Statistics

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For randomly censored data, the authors propose a general class of semiparametric median residual life models. They incorporate covariates in a generalized linear form while leaving the baseline median residual life function completely unspecified. Despite the non‐identifiability of the survival function for a given median residual life function, a simple and natural procedure is proposed to estimate the regression parameters and the baseline median residual life function. The authors derive the asymptotic properties for the estimators, and demonstrate the numerical performance of the proposed method through simulation studies. The median residual life model can be easily generalized to model other quantiles, and the estimation method can also be applied to the mean residual life model. The Canadian Journal of Statistics 38: 665–679; 2010 © 2010 Statistical Society of Canada

show abstract

A paradox concerning nuisance parameters and projected estimating functions

Cited by 67 publications

References 12 publications

GMM redundancy results for general missing data problems

GMM redundancy results for general missing data problems

Weighted Likelihood for Semiparametric Models and Two‐phase Stratified Samples, with Application to Cox Regression

Semiparametric median residual life model and inference

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