scholarly journals Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

2014 ◽  
Author(s):  
Manuel Gil
Keyword(s):  
Maximum Likelihood ◽  
Markov Models ◽  
Mean Squared Error ◽  
Covariance Structure ◽  
Accurate Estimation ◽  
Summary Statistic ◽  
Substitution Model ◽  
Squared Error ◽  
The Mean ◽  
Path Lengths

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account in any process that compares or combines distances to increase precision. In this paper, we present a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei and Jin, 1989) which links the covariance to path lengths. We prove it here under a simple symmetric substitution model. In a simulation, we show that our estimator outperforms previously published ones in terms of the mean squared error.

scholarly journals Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

2014 ◽  
Author(s):  
Manuel Gil
Keyword(s):  
Maximum Likelihood ◽  
Markov Models ◽  
Mean Squared Error ◽  
Covariance Structure ◽  
Accurate Estimation ◽  
Summary Statistic ◽  
Substitution Model ◽  
Squared Error ◽  
The Mean ◽  
Path Lengths

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account in any process that compares or combines distances to increase precision. In this paper, we present a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei and Jin, 1989) which links the covariance to path lengths. We prove it here under a simple symmetric substitution model. In a simulation, we show that our estimator outperforms previously published ones in terms of the mean squared error.

scholarly journals Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

2014 ◽  
Author(s):  
Manuel Gil
Keyword(s):  
Markov Models ◽  
Mean Squared Error ◽  
Covariance Structure ◽  
Pairwise Distance ◽  
Accurate Estimation ◽  
Summary Statistic ◽  
Substitution Model ◽  
Squared Error ◽  
The Mean ◽  
Path Lengths

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates from pairwise distances with overlapping paths covary because of shared mutation events. In any process that compares or combines distances, it is desirable to take these covariance structure into account to increase precision. In this paper, we present fast estimator for the covariance of two pairwise distance estimates under general Markov models. The estimator is based on a conjecture (going back to Nei and Jin, 1989) which links the covariance to path lengths. We prove it here under a simple symmetric substitution model. In a simulation, we show that our estimator outperforms previously published ones in terms of the mean squared error.

scholarly journals A new family of polyno-expo-trigonometric distributions with applications

2019 ◽  
Vol 22 (04) ◽  
pp. 1950027
Author(s):  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Mean Squared Error ◽  
Real Life ◽  
Likelihood Method ◽  
Lifetime Data ◽  
New Family ◽  
Squared Error ◽  
The Mean ◽  
Special Case

In this paper, a new family of polyno-expo-trigonometric distributions is presented and investigated. A special case using the Weibull distribution, with three parameters, is considered as statistical model for lifetime data. The estimation of the parameters is performed with the maximum likelihood method. A numerical simulation study verifies that the bias and the mean squared error of the maximum likelihood estimators tend to zero as the sample size is increased. Three real life datasets are then analyzed. We show that our model has a good fit in comparison to the other well-known powerful models in the literature.

scholarly journals On Estimation of P(Y_1

2020 ◽  
pp. 845-853 ◽  
Author(s):  
Bsma Abdul Hameed ◽  
Abbas N. Salman ◽  
Bayda Atiya Kalaf
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Estimation Methods ◽  
Simulation Experiments ◽  
Kumaraswamy Distribution ◽  
Shrinkage Methods ◽  
Squared Error ◽  
The Mean

This paper deals with the estimation of the stress strength reliability for a component which has a strength that is independent on opposite lower and upper bound stresses, when the stresses and strength follow Inverse Kumaraswamy Distribution. D estimation approaches were applied, namely the maximum likelihood, moment, and shrinkage methods. Monte Carlo simulation experiments were performed to compare the estimation methods based on the mean squared error criteria.

scholarly journals Multicomponent Inverse Lomax Stress-Strength Reliability

2020 ◽  
pp. 72-80
Author(s):  
Nada S. Karam ◽  
Shahbaa M. Yousif ◽  
Bushra J. Tawfeeq
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Model Systems ◽  
Estimation Methods ◽  
Squared Error ◽  
Mathematical Expressions ◽  
Distribution Parameters ◽  
The Mean ◽  
Inverse Lomax Distribution

In this article we derive two reliability mathematical expressions of two kinds of s-out of -k stress-strength model systems; and . Both stress and strength are assumed to have an Inverse Lomax distribution with unknown shape parameters and a common known scale parameter. The increase and decrease in the real values of the two reliabilities are studied according to the increase and decrease in the distribution parameters. Two estimation methods are used to estimate the distribution parameters and the reliabilities, which are Maximum Likelihood and Regression. A comparison is made between the estimators based on a simulation study by the mean squared error criteria, which revealed that the maximum likelihood estimator works the best.

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.

The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution

2006 ◽  
Vol 25 (1) ◽  
pp. 117-138 ◽  
Author(s):  
Fernanda P. M. Peixe ◽  
Alastair R. Hall ◽  
Kostas Kyriakoulis
Keyword(s):  
Instrumental Variables ◽  
Mean Squared Error ◽  
Elliptical Distribution ◽  
Squared Error ◽  
The Mean

Computing trade-offs in robust design: Perspectives of the mean squared error

2011 ◽  
Vol 60 (2) ◽  
pp. 248-255 ◽  
Author(s):  
Sangmun Shin ◽  
Funda Samanlioglu ◽  
Byung Rae Cho ◽  
Margaret M. Wiecek
Keyword(s):  
Robust Design ◽  
Mean Squared Error ◽  
Squared Error ◽  
Trade Offs ◽  
The Mean

scholarly journals Day-Ahead Forecasting of Hourly Photovoltaic Power Based on Robust Multilayer Perception

2018 ◽  
Vol 10 (12) ◽  
pp. 4863 ◽  
Author(s):  
Chao Huang ◽  
Longpeng Cao ◽  
Nanxin Peng ◽  
Sijia Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Power Plants ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Multilayer Perception ◽  
Squared Error ◽  
The Mean ◽  
Effectiveness And Efficiency ◽  
Mlp Network ◽  
Grid Operation ◽  
Better Than

Photovoltaic (PV) modules convert renewable and sustainable solar energy into electricity. However, the uncertainty of PV power production brings challenges for the grid operation. To facilitate the management and scheduling of PV power plants, forecasting is an essential technique. In this paper, a robust multilayer perception (MLP) neural network was developed for day-ahead forecasting of hourly PV power. A generic MLP is usually trained by minimizing the mean squared loss. The mean squared error is sensitive to a few particularly large errors that can lead to a poor estimator. To tackle the problem, the pseudo-Huber loss function, which combines the best properties of squared loss and absolute loss, was adopted in this paper. The effectiveness and efficiency of the proposed method was verified by benchmarking against a generic MLP network with real PV data. Numerical experiments illustrated that the proposed method performed better than the generic MLP network in terms of root mean squared error (RMSE) and mean absolute error (MAE).

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

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