scholarly journals Average Derivative Estimation from Biased Data

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Christophe Chesneau ◽  
Maher Kachour ◽  
Fabien Navarro
Keyword(s):  
Rate Of Convergence ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Derivative Estimation ◽  
Squared Error ◽  
The Mean ◽  
Average Derivative Estimation ◽  
Average Derivative

We investigate the estimation of the density-weighted average derivative from biased data. An estimator integrating a plug-in approach and wavelet projections is constructed. We prove that it attains the parametric rate of convergence 1/n under the mean squared error.

scholarly journals Complete subset averaging with many instruments

2020 ◽  
Author(s):  
Seojeong Lee ◽  
Youngki Shin
Keyword(s):  
Demand Function ◽  
Simulation Experiment ◽  
Mean Squared Error ◽  
Asymptotic Optimality ◽  
Weighted Average ◽  
Subset Size ◽  
Extensive Simulation ◽  
Squared Error ◽  
Many Instruments ◽  
Class Of Estimators

Summary We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weighted average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The subset size is chosen by minimising the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalise the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated. As an empirical illustration, we estimate the logistic demand function in Berry et al. (1995) and find that the CSA-2SLS estimate is better supported by economic theory than are the alternative estimates.

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>

scholarly journals Performance Analysis of AOA-Based Localization Using the LS Approach: Explicit Expression of Mean-Squared Error

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Byung-Kwon Son ◽  
Do-Jin An ◽  
Joon-Ho Lee
Keyword(s):  
Explicit Expression ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Localization Algorithm ◽  
Angle Of Arrival ◽  
Squared Error ◽  
Distance Weighted ◽  
The Mean ◽  
Passive Localization ◽  
Location Estimate

In this paper, a passive localization of the emitter using noisy angle-of-arrival (AOA) measurements, called Brown DWLS (Distance Weighted Least Squares) algorithm, is considered. The accuracy of AOA-based localization is quantified by the mean-squared error. Various estimates of the AOA-localization algorithm have been derived (Doğançay and Hmam, 2008). Explicit expression of the location estimate of the previous study is used to get an analytic expression of the mean-squared error (MSE) of one of the various estimates. To validate the derived expression, we compare the MSE from the Monte Carlo simulation with the analytically derived MSE.

Estimation of critical torque using intermittent isometric maximal voluntary contractions of the quadriceps in humans

2009 ◽  
Vol 106 (3) ◽  
pp. 975-983 ◽  
Author(s):  
Mark Burnley
Keyword(s):  
Laboratory Tests ◽  
Mean Squared Error ◽  
Voluntary Activation ◽  
Peripheral Fatigue ◽  
Contraction Time ◽  
Twitch Interpolation ◽  
Squared Error ◽  
The Mean ◽  
Duration Relationship ◽  
Voluntary Contractions

To determine whether the asymptote of the torque-duration relationship (critical torque) could be estimated from the torque measured at the end of a series of maximal voluntary contractions (MVCs) of the quadriceps, eight healthy men performed eight laboratory tests. Following familiarization, subjects performed two tests in which they were required to perform 60 isometric MVCs over a period of 5 min (3 s contraction, 2 s rest), and five tests involving intermittent isometric contractions at ∼35–60% MVC, each performed to task failure. Critical torque was determined using linear regression of the torque impulse and contraction time during the submaximal tests, and the end-test torque during the MVCs was calculated from the mean of the last six contractions of the test. During the MVCs voluntary torque declined from 263.9 ± 44.6 to 77.8 ± 17.8 N·m. The end-test torque was not different from the critical torque (77.9 ± 15.9 N·m; 95% paired-sample confidence interval, −6.5 to 6.2 N·m). The root mean squared error of the estimation of critical torque from the end-test torque was 7.1 N·m. Twitch interpolation showed that voluntary activation declined from 90.9 ± 6.5% to 66.9 ± 13.1% ( P < 0.001), and the potentiated doublet response declined from 97.7 ± 23.0 to 46.9 ± 6.7 N·m ( P < 0.001) during the MVCs, indicating the development of both central and peripheral fatigue. These data indicate that fatigue during 5 min of intermittent isometric MVCs of the quadriceps leads to an end-test torque that closely approximates the critical torque.

ENHANCEMENT OF MAMMOGRAPHIC PHANTOM FEATURES BY NOISE REDUCTION

2007 ◽  
Vol 21 (06) ◽  
pp. 1047-1057
Author(s):  
MOULOUD ADEL ◽  
DANIEL ZUWALA ◽  
MONIQUE RASIGNI ◽  
SALAH BOURENNANE
Keyword(s):  
Noise Reduction ◽  
Mean Squared Error ◽  
Point Of View ◽  
Reduction Scheme ◽  
Squared Error ◽  
Modification Method ◽  
Optimal Function ◽  
Direct Contrast ◽  
The Mean ◽  
Simulated Images

A noise reduction scheme on digitized mammographic phantom images is presented. This algorithm is based on a direct contrast modification method with an optimal function, obtained by using the mean squared error as a criterion. Computer simulated images containing objects similar to those observed in the phantom are built to evaluate the performance of the algorithm. Noise reduction results obtained on both simulated and real phantom images show that the developed method may be considered as a good preprocessing step from the point of view of automating phantom film evaluation by means of image processing.

A Theoretical Framework for Estimating Swarm Success Probability Using Scouts

2010 ◽  
Vol 1 (4) ◽  
pp. 17-45
Author(s):  
Antons Rebguns ◽  
Diana F. Spears ◽  
Richard Anderson-Sprecher ◽  
Aleksey Kletsov
Keyword(s):  
Mean Squared Error ◽  
Success Probability ◽  
Ground Truth ◽  
Theoretical Framework ◽  
Bernoulli Trials ◽  
Lennard Jones ◽  
Squared Error ◽  
The Mean ◽  
The Bayesian Approach ◽  
Bayesian Formula

This paper presents a novel theoretical framework for swarms of agents. Before deploying a swarm for a task, it is advantageous to predict whether a desired percentage of the swarm will succeed. The authors present a framework that uses a small group of expendable “scout” agents to predict the success probability of the entire swarm, thereby preventing many agent losses. The scouts apply one of two formulas to predict – the standard Bernoulli trials formula or the new Bayesian formula. For experimental evaluation, the framework is applied to simulated agents navigating around obstacles to reach a goal location. Extensive experimental results compare the mean-squared error of the predictions of both formulas with ground truth, under varying circumstances. Results indicate the accuracy and robustness of the Bayesian approach. The framework also yields an intriguing result, namely, that both formulas usually predict better in the presence of (Lennard-Jones) inter-agent forces than when their independence assumptions hold.

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