Phase‐smoothed robust M-estimation of magnetotelluric impedance functions

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 1999-2007 ◽  
Author(s):  
D. Sutarno ◽  
K. Vozoff
Keyword(s):  
Least Squares ◽  
Reference Data ◽  
Accurate Estimation ◽  
Robust Estimates ◽  
Gaussian Statistics ◽  
M Estimation ◽  
Columbia River Plateau ◽  
The Hilbert Transform ◽  
Noise Contamination ◽  
Impedance Functions

Accurate estimation of impedance functions is essential for the correct interpretation of magnetotelluric (MT) measurements. Noise is inevitably encountered when MT observations are conducted and, consequently, impedance estimates are usually based on least‐squares (LS) regression. Least squares ultimately assumes simple Gaussian statistics. However, estimation procedures based on LS would not be statistically optimal, as outliers (abnormal data) are frequently superimposed on a normal ambient MT noise field which is approximately Gaussian. In this situation, the estimation can be seriously misleading. An alternative method for making unbiased robust estimates of MT impedance functions is based on regression M-estimation and the Hilbert Transform, operating on minimum‐phase MT impedance functions. In the resulting regression estimates, outlier contamination is removed and other departures from Gauss‐Markov optimality are not critical. Using MT data from the Columbia River Plateau and the EMSLAB Lincoln line, it is shown that the method can produce usable MT impedance functions even under conditions of severe noise contamination and in the absence of remote reference data.

scholarly journals Constrained robust estimation of magnetotelluric impedance functions based on a bounded-influence regression M-estimator and the Hilbert transform

2008 ◽  
Vol 15 (2) ◽  
pp. 287-293 ◽  
Author(s):  
D. Sutarno
Keyword(s):  
Robust Estimation ◽  
Hilbert Transform ◽  
Least Square ◽  
The Real ◽  
Estimation Procedures ◽  
Input Variables ◽  
Bounded Influence ◽  
The Hilbert Transform ◽  
Noise Contamination ◽  
Impedance Functions

Abstract. Robust impedance estimation procedures are now in standard use in magnetotelluric (MT) measurements and research. These always yield impedance estimates which are better than the conventional least square (LS) estimation because the 'real' MT data almost never satisfy the statistical assumptions of Gaussian distribution upon which normal spectral analysis is based. The robust estimation procedures are commonly based on M-estimators that have the ability to reduce the influence of unusual data (outliers) in the response (electric field) variables, but are often not sensitive to exceptional predictors (magnetic field) data, which are termed leverage points. This paper proposes an alternative procedure for making reliably robust estimates of MT impedance functions, which simultaneously provide protection from the influence of outliers in both response and input variables. The means for accomplishing this is based on the bounded-influence regression M-estimation and the Hilbert Transform operating on the causal MT impedance functions. In the resulting regression estimates, outlier contamination is removed and the self consistency between the real and imaginary parts of the impedance estimates is guaranteed. Using synthetic and real MT data, it is shown that the method can produce improved MT impedance functions even under conditions of severe noise contamination.

scholarly journals Estimation of Soil Nutrient Content Using Hyperspectral Data

Agriculture ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1129
Author(s):  
Yiping Peng ◽  
Lu Wang ◽  
Li Zhao ◽  
Zhenhua Liu ◽  
Chenjie Lin ◽  
...  
Keyword(s):  
Least Squares ◽  
Soil Nutrients ◽  
Cross Validation ◽  
Regional Scale ◽  
Soil Nutrient ◽  
Nutrient Content ◽  
New Method ◽  
Accurate Estimation ◽  
Support Vector ◽  
Soil Nutrient Content

Soil nutrients play a vital role in plant growth and thus the rapid acquisition of soil nutrient content is of great significance for agricultural sustainable development. Hyperspectral remote-sensing techniques allow for the quick monitoring of soil nutrients. However, at present, obtaining accurate estimates proves to be difficult due to the weak spectral features of soil nutrients and the low accuracy of soil nutrient estimation models. This study proposed a new method to improve soil nutrient estimation. Firstly, for obtaining characteristic variables, we employed partial least squares regression (PLSR) fit degree to select an optimal screening algorithm from three algorithms (Pearson correlation coefficient, PCC; least absolute shrinkage and selection operator, LASSO; and gradient boosting decision tree, GBDT). Secondly, linear (multi-linear regression, MLR; ridge regression, RR) and nonlinear (support vector machine, SVM; and back propagation neural network with genetic algorithm optimization, GABP) algorithms with 10-fold cross-validation were implemented to determine the most accurate model for estimating soil total nitrogen (TN), total phosphorus (TP), and total potassium (TK) contents. Finally, the new method was used to map the soil TK content at a regional scale using the soil component spectral variables retrieved by the fully constrained least squares (FCLS) method based on an image from the HuanJing-1A Hyperspectral Imager (HJ-1A HSI) of the Conghua District of Guangzhou, China. The results identified the GBDT-GABP was observed as the most accurate estimation method of soil TN ( of 0.69, the root mean square error of cross-validation (RMSECV) of 0.35 g kg−1 and ratio of performance to interquartile range (RPIQ) of 2.03) and TP ( of 0.73, RMSECV of 0.30 g kg−1 and RPIQ = 2.10), and the LASSO-GABP proved to be optimal for soil TK estimations ( of 0.82, RMSECV of 3.39 g kg−1 and RPIQ = 3.57). Additionally, the highly accurate LASSO-GABP-estimated soil TK (R2 = 0.79) reveals the feasibility of the LASSO-GABP method to retrieve soil TK content at the regional scale.

scholarly journals A Robust Regression by Using Huber Estimator and Tukey Bisquare Estimator for Predicting Availability of Corn in Karanganyar Regency, Indonesia

2018 ◽  
Vol 1 (1) ◽  
pp. 37
Author(s):  
Hasih Pratiwi ◽  
Yuliana Susanti ◽  
Sri Sulistijowati Handajani
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Likelihood Estimation ◽  
Corn Production ◽  
Least Squares Fit ◽  
Class Of Estimators ◽  
M Estimation ◽  
Heavy Tailed ◽  
Least Squares Estimates ◽  
Huber Estimator

Linear least-squares estimates can behave badly when the error distribution is not normal, particularly when the errors are heavy-tailed. One remedy is to remove influential observations from the least-squares fit. Another approach, robust regression, is to use a fitting criterion that is not as vulnerable as least squares to unusual data. The most common general method of robust regression is M-estimation. This class of estimators can be regarded as a generalization of maximum-likelihood estimation. In this paper we discuss robust regression model for corn production by using two popular estimators; i.e. Huber estimator and Tukey bisquare estimator.<br />Keywords : robust regression, M-estimation, Huber estimator, Tukey bisquare estimator

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.

scholarly journals Bayesian modelling of a hepatitis A outbreak in men who have sex with men in Sydney, Australia, 1991/1992

2019 ◽  
Vol 147 ◽  
Author(s):  
X.-S. Zhang ◽  
A. Charlett
Keyword(s):  
Least Squares ◽  
Hepatitis A ◽  
Hepatitis A Virus ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Bayesian Modelling ◽  
Distributed Parameters ◽  
Sex With Men ◽  
Sydney Australia

Abstract To control hepatitis A spread by vaccination, accurate estimation of transmissibility is vital. Regan et al. (2016) proposed a model of hepatitis A virus (HAV) transmission and used least squares to calibrate model to the 1991/1992 HAV outbreak in men who have sex with men (MSM) in Sydney, Australia. Based on the estimate of R0, they obtained the critical immunity of 70% and showed that when the proportion immune <70%, there is a definite chance for outbreaks to take place. The immunity level from previous surveys ranges from 32% to 64% after 1996 while no outbreaks in Australian MSMs have been reported since 1996. Further noticing the ill-distributed parameters, we argue that their estimate of R0 is not accurate. In this study, we revisited their model by Bayesian inference, which has privilege over least squares. We obtained the appropriate posterior distributions of parameters and the estimate of R0 ranges from 1.38 to 2.89, indicating a critical immunity of 65%. The reduction in critical immunity and outbreak probabilities predicts the absence of outbreaks in Australian MSMs since 1996. Our study shows the importance of using appropriate methods to provide reliable and accurate estimates of the model parameters especially the transmissibility.

Regression Analysis and Determination of Activity Coefficients of Cd-Pb Alloy

2011 ◽  
Vol 311-313 ◽  
pp. 736-741
Author(s):  
Shun Zhong Yao ◽  
Yong Nian Dai ◽  
Hao Huang ◽  
Xiao Hong Wan
Keyword(s):  
Regression Analysis ◽  
Least Squares ◽  
Activity Coefficients ◽  
Reference Data ◽  
Generalized Least Squares ◽  
Chemical Compositions ◽  
Cadmium And Lead ◽  
Determination Of Activity

Chemical compositions of Cadmium and lead were measured with conditions that the temperature between 400-700°C and remaining pressure of 10-60 Pa as in which Materials containing Cadmium and lead evaporate. Activity coefficients of cadmium and lead were calculated using the generalized least squares（GLS）, three relations were deduced in Cd-Pb system，namely relation between activity coefficients and temperatures, relation between activity coefficients and chemical compositions, and that of activity coefficients and temperatures together with chemical compositions. This article provides a theoretical reference data for separation of alloys in cadmium systems.

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