scholarly journals Robust Estimation for a Generalised Ratio Model

2021 ◽  
Vol 50 (1) ◽  
pp. 74-87
Author(s):  
Kazumi Wada ◽  
Keiichiro Sakashita ◽  
Hiroe Tsubaki
Keyword(s):  
Weighted Least Squares ◽  
Robust Estimator ◽  
Ratio Model ◽  
Absolute Deviation ◽  
Regression Estimate ◽  
Data Transformations ◽  
Scale Parameters ◽  
Economic Census ◽  
Error Terms ◽  
M Estimation

It is known that data such as business sales and household income need data transformation prior to regression estimate as the data has a homoscedastic error. However, data transformations make the estimation of mean and total unstable. Therefore, the ratio model is often used for imputation in the field of official statistics to avoid the problem. Our study aims to robustify the estimator following the ratio model by means of M-estimation. Reformulation of the conventional ratio model with homoscedastic quasi-error term provides quasi-residuals which can be used as a measure of outlyingness as same as a linear regression model. A generalisation of the model, which accommodates varied error terms with different heteroscedasticity, is also proposed. Functions for robustified estimators of the generalised ratio model are implemented by the iterative re-weighted least squares algorithm in R environment and illustrated using random datasets. Monte Carlo simulation confirms accuracy of the proposed estimators, as well as their computational efficiency. A comparison of the scale parameters between the average absolute deviation (AAD) and median absolute deviation (MAD) is made regarding Tukey's biweight function. The results with Huber's weight function are also provided for reference. The proposed robust estimator of the generalised ratio model is used for imputation of major corporate accounting items of the 2016 Economic Census for Business Activity in Japan.

POWER SYSTEM STATE ESTIMATION USING A ROBUST ESTIMATOR

2019 ◽  
Vol XVI (4) ◽  
pp. 53-65
Author(s):  
Zahid Khan ◽  
Katrina Lane Krebs ◽  
Sarfaraz Ahmad ◽  
Misbah Munawar
Keyword(s):  
Power Systems ◽  
State Estimation ◽  
Loss Function ◽  
Weighted Least Squares ◽  
Primary Data ◽  
Robust Estimator ◽  
System State ◽  
State Estimator ◽  
Suggested Approach ◽  
Power System State Estimation

State estimation (SE) is a primary data processing algorithm which is utilised by the control centres of advanced power systems. The most generally utilised state estimator is based on the weighted least squares (WLS) approach which is ineffective in addressing gross errors of input data of state estimator. This paper presents an innovative robust estimator for SE environments to overcome the non-robustness of the WLS estimator. The suggested approach not only includes the similar functioning of the customary loss function of WLS but also reflects loss function built on the modified WLS (MWLS) estimator. The performance of the proposed estimator was assessed based on its ability to decrease the impacts of gross errors on the estimation results. The properties of the suggested state estimator were investigated and robustness of the estimator was studied considering the influence function. The effectiveness of the proposed estimator was demonstrated with the help of examples which also indicated non-robustness of MWLS estimator in SE algorithm.

Robust Weighted Least Squares Estimation of Regression Parameter in the Presence of Outliers and Heteroscedastic Errors

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Bello Abdulkadir Rasheed ◽  
Robiah Adnan ◽  
Seyed Ehsan Saffari ◽  
Kafi Dano Pati
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Robust Regression ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Model Parameters ◽  
Constant Variance ◽  
Regression Parameters ◽  
M Estimation

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

An Adaptive Overload Detection Policy Based on the Estimator Sn in Cloud Environment

2017 ◽  
Vol 8 (3) ◽  
pp. 93-107 ◽  
Author(s):  
Minu Bala ◽  
Devanand Padha
Keyword(s):  
Service Providers ◽  
Cloud Service ◽  
Energy Performance ◽  
Median Absolute Deviation ◽  
Robust Estimator ◽  
Virtual Machine Migration ◽  
Absolute Deviation ◽  
Cloud Datacenter ◽  
Migration Technique ◽  
Better Than

Efficient use of cloud resources and providing QoS to its clients is quite challenging for cloud service providers. On one hand, deployment of excessive active resources leads to increase in operational cost and on the other hand, shortage of resources may affect the QoS and SLA violations. In order to optimize the resource utilization of datacenter keeping SLA intact, the issues like over-loaded and under-loaded servers in a cloud datacenter are very important to deal with. Virtual machine migration technique is quite effective in handling such issues. The present work focuses on the adaptive threshold based overload detection policy which uses the robust estimator Sn for statistically analyzing the historical CPU usage of hosts, periodically and accordingly adjusts the upper CPU utilization threshold. The results obtained from proposed policy are compared with Median Absolute Deviation policy for overload detection and it has been found that energy performance efficiency of proposed policy is better than the median absolute deviation policy.

scholarly journals MAD saccade: statistically robust saccade threshold estimation

2019 ◽  
Author(s):  
Benjamin Voloh ◽  
Marcus Watson ◽  
Seth König ◽  
Thilo Womelsdorf
Keyword(s):  
Standard Deviation ◽  
Marked Improvement ◽  
Common Method ◽  
Robust Estimator ◽  
Classification Algorithms ◽  
Threshold Estimation ◽  
False Negatives ◽  
Absolute Deviation ◽  
The Mean ◽  
Modified Algorithm

Saccade detection is a critical step in the analysis of gaze data. A common method for saccade detection is to use a simple threshold for velocity or acceleration values, which is typically estimated from the data using the mean and standard deviation. However, this method has the downside of being influenced by the very signal it is trying to detect, the outlying velocities or accelerations that occur during saccades. We propose instead to use the median absolute deviation (MAD), a robust estimator of the standard deviation that is not influenced by outliers. We modify an algorithm proposed by Nyström and colleagues, and quantify saccade detection performance in both simulated and human data. Our modified algorithm shows a significant and marked improvement in saccade detection, showing both more true positives and less false negatives. We conclude that robust estimators can be widely adopted in other common, automatic gaze classification algorithms due to their ease of implementation.

scholarly journals Empirical tests of performance of some M – estimators

2014 ◽  
Vol 63 (2) ◽  
pp. 127-146 ◽  
Author(s):  
Marek Banaś ◽  
Marcin Ligas
Keyword(s):  
Covariance Matrices ◽  
Standard Normal Distribution ◽  
Residual Variance ◽  
Iteratively Reweighted Least Squares ◽  
Empirical Comparison ◽  
Absolute Deviation ◽  
Standard Normal ◽  
Empirical Tests ◽  
M Estimation ◽  
Robust Measures

Abstract The paper presents an empirical comparison of performance of three well known M - estimators (i.e. Huber, Tukey and Hampel’s M - estimators) and also some new ones. The new M - estimators were motivated by weighting functions applied in orthogonal polynomials theory, kernel density estimation as well as one derived from Wigner semicircle probability distribution. M - estimators were used to detect outlying observations in contaminated datasets. Calculations were performed using iteratively reweighted least-squares (IRLS). Since the residual variance (used in covariance matrices construction) is not a robust measure of scale the tests employed also robust measures i.e. interquartile range and normalized median absolute deviation. The methods were tested on a simple leveling network in a large number of variants showing bad and good sides of M - estimation. The new M - estimators have been equipped with theoretical tuning constants to obtain 95% efficiency with respect to the standard normal distribution. The need for data - dependent tuning constants rather than those established theoretically is also pointed out.

Reliability Assessment of the Small Sample Aero-Engine Bearings

2014 ◽  
Vol 986-987 ◽  
pp. 858-861
Author(s):  
Feng Ding ◽  
Jiu Cheng Yin ◽  
Jun Qiang Dang
Keyword(s):  
Weibull Distribution ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Small Sample ◽  
Point Estimation ◽  
Scale Parameters ◽  
Weighted Least Squares Method ◽  
Bearing Life ◽  
Aero Engine ◽  
Engine Bearing

Aiming at the test of Aero-engine bearing is expensive, small sample without failure, and bearing life obeys Weibull distribution, small sample data is introduced in order to estimate the reliability of bearing with the method of Bayesian point estimation. The weighted least squares method is utilized to estimate the shape and scale parameters of Weibull distribution in the case of no failure. The bearing cumulative failure function, failure rate and average life can be gotten. Finally, the bearing experiment data is used to verify the validity of the small sample evaluation. It is proved that the method has an important value for the replacement and maintenance of Aero-engine bearing.

scholarly journals Time-of-arrival source localization based on weighted least squares estimator in line-of-sight/non-line-of-sight mixture environments

2016 ◽  
Vol 12 (12) ◽  
pp. 155014771668382 ◽  
Author(s):  
Chee-Hyun Park ◽  
Joon-Hyuk Chang
Keyword(s):  
Least Squares ◽  
Source Localization ◽  
Weighted Least Squares ◽  
Line Of Sight ◽  
Time Of Arrival ◽  
Mean Square ◽  
Localization Algorithm ◽  
Absolute Deviation ◽  
Weighted Least Squares Estimator ◽  
Non Line Of Sight

In this article, we propose a line-of-sight/non-line-of-sight time-of-arrival source localization algorithm that utilizes the weighted least squares. The proposed estimator combines multiple sorted measurements using the spatial sign concept, Mahalanobis distance, and Stahel–Donoho estimator, that is, assigning less weight to the samples as they are far from the center of inlier distribution. Also, the eigendecomposition Kendall’s [Formula: see text] covariance matrix is utilized as the scatter measure instead of the conventional median absolute deviation. Thus, the adverse effects by outliers can be attenuated effectively. To validate the superiority of the proposed methods, the root mean square error performances are compared with that of the existing algorithms via extensive simulation.

scholarly journals FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE

2021 ◽  
Vol 2 ◽  
pp. 181-186
Author(s):  
Oleg Uzhga Rebrov ◽  
Galina Kuleshova
Keyword(s):  
Extreme Values ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Arithmetic Mean ◽  
Data Uncertainty ◽  
Absolute Deviation ◽  
Scale Parameters ◽  
Robust Estimates ◽  
Fuzzy Random

A random variable is a variable whose components are random values. To characterise a random variable, the arithmetic mean is widely used as an estimate of the location parameter, and variation as an estimate of the scale parameter. The disadvantage of the arithmetic mean is that it is sensitive to extreme values, outliers in the data. Due to that, to characterise random variables, robust estimates of the location and scale parameters are widely used: the median and median absolute deviation from the median. In real situations, the components of a random variable cannot always be estimated in a deterministic way. One way to model the initial data uncertainty is to use fuzzy estimates of the components of a random variable. Such variables are called fuzzy random variables. In this paper, we examine fuzzy robust estimates of location and scale parameters of a fuzzy random variable: fuzzy median and fuzzy median of the deviations of fuzzy component values from the fuzzy median. 

scholarly journals M-ESTIMATION IN GARCH MODELS

2008 ◽  
Vol 24 (6) ◽  
pp. 1530-1553 ◽  
Author(s):  
Kanchan Mukherjee
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Score Function ◽  
Error Distribution ◽  
Garch Models ◽  
Likelihood Estimator ◽  
Absolute Deviation ◽  
Class Of Estimators ◽  
M Estimation ◽  
Quasi Maximum Likelihood

This paper derives asymptotic normality of a class of M-estimators in the generalized autoregressive conditional heteroskedastic (GARCH) model. The class of estimators includes least absolute deviation and Huber's estimator in addition to the well-known quasi maximum likelihood estimator. For some estimators, the asymptotic normality results are obtained only under the existence of fractional unconditional moment assumption on the error distribution and some mild smoothness and moment assumptions on the score function.

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