scholarly journals Asymptotic efficiency of the OLS estimator with singular limiting sample moment matrices

2016 ◽  
Vol 114 ◽  
pp. 104-110
Author(s):  
Yoshimasa Uematsu
Keyword(s):  
Asymptotic Efficiency ◽  
Sample Moment

Semiparametric IV Estimation with Parameter Dependent Instruments

1992 ◽  
Vol 8 (3) ◽  
pp. 403-406
Author(s):  
Paul Rilstone
Keyword(s):  
Nonparametric Estimation ◽  
Method Of Moments ◽  
Conditional Expectation ◽  
Asymptotic Efficiency ◽  
Functional Form ◽  
Moment Equations ◽  
Unknown Parameters ◽  
Iv Estimation ◽  
Sample Moment ◽  
Parameter Dependent

A well-known result in the method of moments literature is that the efficient instruments for the estimation of a model are functions of the conditional expectation of its gradient. Some recent studies have suggested the nonparametric estimation of these instruments when they are of unknown functional form. When these instruments in turn depend on the unknown parameters it has been suggested that these be replaced by preliminary consistent estimates. It is shown here that solving the sample moment equations simultaneously over the instruments and the residuals of the model will generally produce the same asymptotic efficiency and avoid the disadvantages inherent with the use of preliminary estimates.

scholarly journals On Asymptotic Efficiency of the M2M4 Signal-to-Noise Estimator for Deterministic Complex Sinusoids

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 4950
Author(s):  
Gianmarco Romano
Keyword(s):  
Covariance Matrix ◽  
Gaussian Noise ◽  
Asymptotic Efficiency ◽  
Noise Power ◽  
Finite Sample ◽  
Signal To Noise ◽  
Numerical Examples ◽  
Unknown Phase ◽  
The Moment ◽  
Asymptotically Efficient

The moment-based M2M4 signal-to-noise (SNR) estimator was proposed for a complex sinusoidal signal with a deterministic but unknown phase corrupted by additive Gaussian noise by Sekhar and Sreenivas. The authors studied its performances only through numerical examples and concluded that the proposed estimator is asymptotically efficient and exhibits finite sample super-efficiency for some combinations of signal and noise power. In this paper, we derive the analytical asymptotic performances of the proposed M2M4 SNR estimator, and we show that, contrary to what it has been concluded by Sekhar and Sreenivas, the proposed estimator is neither (asymptotically) efficient nor super-efficient. We also show that when dealing with deterministic signals, the covariance matrix needed to derive asymptotic performances must be explicitly derived as its known general form for random signals cannot be extended to deterministic signals. Numerical examples are provided whose results confirm the analytical findings.

REDUNDANCY OF MOMENT CONDITIONS AND THE EFFICIENCY OF OLS IN SUR MODELS

2008 ◽  
Vol 24 (5) ◽  
pp. 1456-1460 ◽  
Author(s):  
Hailong Qian
Keyword(s):  
Least Squares ◽  
Asymptotic Efficiency ◽  
Generalized Method Of Moments ◽  
Sufficient Conditions ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
American Statistical Association ◽  
Orthogonality Condition ◽  
Moment Conditions ◽  
Necessary And Sufficient

In this note, based on the generalized method of moments (GMM) interpretation of the usual ordinary least squares (OLS) and feasible generalized least squares (FGLS) estimators of seemingly unrelated regressions (SUR) models, we show that the OLS estimator is asymptotically as efficient as the FGLS estimator if and only if the cross-equation orthogonality condition is redundant given the within-equation orthogonality condition. Using the condition for redundancy of moment conditions of Breusch, Qian, Schmidt, and Wyhowski (1999, Journal of Econometrics 99, 89–111), we then derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of SUR models. We also provide several useful sufficient conditions for the equal asymptotic efficiency of OLS and FGLS estimators that can be interpreted as various mixings of the two famous sufficient conditions of Zellner (1962, Journal of the American Statistical Association 57, 348–368).

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