scholarly journals Adaptive Kernel Estimation of the Conditional Quantiles

2015 ◽  
Vol 5 (1) ◽  
pp. 79
Author(s):  
Raid B. Salha ◽  
Hazem I. El Shekh Ahmed ◽  
Hossam O. EL-Sayed
Keyword(s):  
Distribution Function ◽  
Conditional Distribution ◽  
Mean Squared Error ◽  
Kernel Estimation ◽  
Conditional Quantiles ◽  
Squared Error ◽  
Adaptive Kernel ◽  
The Mean ◽  
Bias Variance ◽  
Kernel Estimations

In this paper, we define the adaptive kernel estimation of the conditional distribution function (cdf) for independent and identically distributed (iid) data using varying bandwidth. The bias, variance and the mean squared error of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated.<br /><br />The results of the simulation study show that the adaptive kernel estimation of the conditional quantiles with varying bandwidth have better performance than the kernel estimations with fixed bandwidth.

scholarly journals Information in Missing Patterns: Enhancing Prediction Accuracy in Weighted Linear Regression with Missing Data Using Soft Clustering

2020 ◽  
Author(s):  
Ashkan Esmaeili ◽  
Mohammadamin Fakharian ◽  
Yasaman Amiri Abyaneh
Keyword(s):  
Prediction Accuracy ◽  
Mean Squared Error ◽  
State Of The Art ◽  
Missing Information ◽  
Learning Capability ◽  
Constraint Matrix ◽  
New Methods ◽  
Squared Error ◽  
The Mean ◽  
Bias Variance

The linear system with missing information is <div>investigated in this paper. New methods are </div><div>introduced to improve the Mean Squared Error (MSE) </div><div>on the test set in comparison to state-of-the-art method</div><div>s, through appropriate tuning of Bias-Variance </div><div>trade-off. The concept is to cluster the data and </div><div>adapt the learning model to each cluster. Hence, </div><div>we set forth a controlled bias into the problem and </div><div>positively utilize it to enhance learning capability on </div><div>the instances considered in some specific </div><div>neighborhood. To deal with missing infrormation, </div><div>we propose a novel algorithm "Missing-SCOP" based </div><div>on SCOP-KMEANS algorithm introduced by Wagstaff,</div><div> et al., utilizing the missing pattern of the dataset for </div><div>construction of a soft-constraint matrix and clustering </div><div>in missing scenario. It is shown that controlled </div><div>over-fitting suggested by our algorithm improves </div><div>prediction accuracy in various cases. </div><div>Numerical experiments approve the efficacy of our</div><div> proposed algorithm in enhancing the prediction</div><div> accuracy.</div>

scholarly journals Information in Missing Patterns: Enhancing Prediction Accuracy in Weighted Linear Regression with Missing Data Using Soft Clustering

2020 ◽  
Author(s):  
Ashkan Esmaeili ◽  
Mohammadamin Fakharian ◽  
Yasaman Amiri Abyaneh
Keyword(s):  
Prediction Accuracy ◽  
Mean Squared Error ◽  
State Of The Art ◽  
Missing Information ◽  
Learning Capability ◽  
Constraint Matrix ◽  
New Methods ◽  
Squared Error ◽  
The Mean ◽  
Bias Variance

The linear system with missing information is <div>investigated in this paper. New methods are </div><div>introduced to improve the Mean Squared Error (MSE) </div><div>on the test set in comparison to state-of-the-art method</div><div>s, through appropriate tuning of Bias-Variance </div><div>trade-off. The concept is to cluster the data and </div><div>adapt the learning model to each cluster. Hence, </div><div>we set forth a controlled bias into the problem and </div><div>positively utilize it to enhance learning capability on </div><div>the instances considered in some specific </div><div>neighborhood. To deal with missing infrormation, </div><div>we propose a novel algorithm "Missing-SCOP" based </div><div>on SCOP-KMEANS algorithm introduced by Wagstaff,</div><div> et al., utilizing the missing pattern of the dataset for </div><div>construction of a soft-constraint matrix and clustering </div><div>in missing scenario. It is shown that controlled </div><div>over-fitting suggested by our algorithm improves </div><div>prediction accuracy in various cases. </div><div>Numerical experiments approve the efficacy of our</div><div> proposed algorithm in enhancing the prediction</div><div> accuracy.</div>

scholarly journals ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS

2005 ◽  
Vol 4 (1) ◽  
pp. 51
Author(s):  
I W. MANGKU ◽  
I. WIDIYASTUTI ◽  
I G. P. PURNABA
Keyword(s):  
Asymptotic Normality ◽  
Poisson Process ◽  
Power Function ◽  
Mean Squared Error ◽  
Asymptotic Bias ◽  
Inhomogeneous Poisson Process ◽  
Squared Error ◽  
Single Realization ◽  
The Mean ◽  
Bias Variance

<p>An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.</p>

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

On the Use of a Modified Intersection of Confidence Intervals (MICIH) Kernel Density Estimation Approach

2021 ◽  
Vol 8 (4) ◽  
pp. 309-332
Author(s):  
Efosa Michael Ogbeide ◽  
Joseph Erunmwosa Osemwenkhae
Keyword(s):  
Confidence Intervals ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Mean Squared Error ◽  
Kernel Density ◽  
Window Size ◽  
National Bureau ◽  
Squared Error ◽  
Data Density ◽  
Adaptive Kernel

Density estimation is an important aspect of statistics. Statistical inference often requires the knowledge of observed data density. A common method of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a window size (smoothing parameter H). It aids density estimation and pattern recognition. So, this work focuses on the use of a modified intersection of confidence intervals (MICIH) approach in estimating density. The Nigerian crime rate data reported to the Police as reported by the National Bureau of Statistics was used to demonstrate this new approach. This approach in the multivariate kernel density estimation is based on the data. The main way to improve density estimation is to obtain a reduced mean squared error (MSE), the errors for this approach was evaluated. Some improvements were seen. The aim is to achieve adaptive kernel density estimation. This was achieved under a sufficiently smoothing technique. This adaptive approach was based on the bandwidths selection. The quality of the estimates obtained of the MICIH approach when applied, showed some improvements over the existing methods. The MICIH approach has reduced mean squared error and relative faster rate of convergence compared to some other approaches. The approach of MICIH has reduced points of discontinuities in the graphical densities the datasets. This will help to correct points of discontinuities and display adaptive density. Keywords: approach, bandwidth, estimate, error, kernel density

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.

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