scholarly journals One-step estimation for the fractional Gaussian noise at high-frequency

2020 ◽  
Vol 24 ◽  
pp. 827-841
Author(s):  
Alexandre Brouste ◽  
Marius Soltane ◽  
Irene Votsi
Keyword(s):  
Maximum Likelihood ◽  
Gaussian Noise ◽  
High Frequency ◽  
Finite Size ◽  
Maximum Likelihood Estimators ◽  
Parametric Estimation ◽  
Fractional Gaussian Noise ◽  
One Step ◽  
Asymptotically Efficient ◽  
Frequency Observation

The present paper concerns the parametric estimation for the fractional Gaussian noise in a high-frequency observation scheme. The sequence of Le Cam’s one-step maximum likelihood estimators (OSMLE) is studied. This sequence is defined by an initial sequence of quadratic generalized variations-based estimators (QGV) and a single Fisher scoring step. The sequence of OSMLE is proved to be asymptotically efficient as the sequence of maximum likelihood estimators but is much less computationally demanding. It is also advantageous with respect to the QGV which is not variance efficient. Performances of the estimators on finite size observation samples are illustrated by means of Monte-Carlo simulations.

scholarly journals Maximum Likelihood Estimation of Clock Skew in IEEE 1588 with Fractional Gaussian Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-24 ◽  
Author(s):  
Chagai Levy ◽  
Monika Pinchas
Keyword(s):  
Maximum Likelihood ◽  
Gaussian Noise ◽  
Likelihood Estimation ◽  
Packet Delay ◽  
Fractional Gaussian Noise ◽  
Clock Skew ◽  
Ieee 1588 ◽  
Accuracy And Precision ◽  
Ethernet Network ◽  
Synchronization Accuracy

To support system-wide synchronization accuracy and precision in the sub-microsecond range without using GPS technique, the precise time protocol (PTP) standard IEEE-1588 v2 is chosen. Recently, a new clock skew estimation technique was proposed for the slave based on a dual slave clock method that assumes that the packet delay variation (PDV) in the Ethernet network is a constant delay. However, papers dealing with the Ethernet network have shown that this PDV is a long range dependency (LRD) process which may be modeled as a fractional Gaussian noise (fGn) with Hurst exponent (H) in the range of0.5<H<1. In this paper, we propose a new clock skew estimator based on the maximum likelihood (ML) technique and derive an approximated expression for the Cramer-Rao lower bound (CRLB) both valid for the case where the PDV is modeled as fGn (0.5<H<1). Simulation results indicate that our new clock skew method outperforms the dual slave clock approach and that the simulated mean square error (MSE) obtained by our new proposed clock skew estimator approaches asymptotically the developed CRLB.

Parametric estimation and inference

2019 ◽  
pp. 165-185
Author(s):  
M. D. Edge
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Wald Test ◽  
Parametric Model ◽  
Parametric Estimation ◽  
Ratio Test ◽  
Sampling Variance ◽  
Squared Error Loss Function ◽  
Squared Error

If it is reasonable to assume that the data are generated by a fully parametric model, then maximum-likelihood approaches to estimation and inference have many appealing properties. Maximum-likelihood estimators are obtained by identifying parameters that maximize the likelihood function, which can be done using calculus or using numerical approaches. Such estimators are consistent, and if the costs of errors in estimation are described by a squared-error loss function, then they are also efficient compared with their consistent competitors. The sampling variance of a maximum-likelihood estimate can be estimated in various ways. As always, one possibility is the bootstrap. In many models, the variance of the maximum-likelihood estimator can be derived directly once its form is known. A third approach is to rely on general properties of maximum-likelihood estimators and use the Fisher information. Similarly, there are many ways to test hypotheses about parameters estimated by maximum likelihood. This chapter discusses the Wald test, which relies on the fact that the sampling distribution of maximum-likelihood estimators is normal in large samples, and the likelihood-ratio test, which is a general approach for testing hypotheses relating nested pairs of models.

scholarly journals Asymptotic Enumeration of Orientations of a Graph as a Function of the Out-Degree Sequence

10.37236/8929 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Mikhail Isaev ◽  
Tejas Iyer ◽  
Brendan D McKay
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Formula ◽  
Degree Sequence ◽  
Maximum Likelihood Estimators ◽  
Strong Mixing ◽  
Paired Comparisons ◽  
Asymptotic Enumeration ◽  
Mixing Properties ◽  
One Step

We prove an asymptotic formula for the number of orientations with given out-degree (score) sequence for a graph $G$. The graph $G$ is assumed to have average degrees at least $n^{1/3 + \epsilon}$ for some $\epsilon > 0$, and to have strong mixing properties, while the maximum imbalance (out-degree minus in-degree) of the orientation should be not too large. Our enumeration results have applications to the study of subdigraph occurrences in random orientations with given imbalance sequence. As one step of our calculation, we obtain new bounds for the maximum likelihood estimators for the Bradley-Terry model of paired comparisons.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

Sign in / Sign up

Export Citation Format

Share Document