Limit distributions and comparative asymptotic efficiency of the Smirnov — Kolmogorov statistics with a random index

1981 ◽  
Vol 16 (2) ◽  
pp. 1042-1049 ◽  
Author(s):  
Ya. Yu. Nikitin
Keyword(s):  
Asymptotic Efficiency ◽  
Limit Distributions ◽  
Random Index

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.

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (2) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

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).

scholarly journals Principal Functions for Bi-free Central Limit Distributions

2016 ◽  
Vol 85 (1) ◽  
pp. 91-108
Author(s):  
Kenneth J. Dykema ◽  
Wonhee Na
Keyword(s):  
Central Limit ◽  
Limit Distributions
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