Linear regression by functional least squares

1982 ◽  
Vol 19 (A) ◽  
pp. 225-239 ◽  
Author(s):  
C. R. Heathcote
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Natural Extension ◽  
Real Variable ◽  
Ordinary Least Squares ◽  
Scalar Function ◽  
Error Distribution ◽  
Variance Function ◽  
Standard Linear ◽  
Asymptotic Normal

The standard linear regression model is analysed using a method called functional least squares which yields a family of estimators for the slope parameter indexed by a real variable t, |t| ≦ T. The choice t = 0 corresponds to ordinary least squares, non-zero values being appropriate if the error distribution is long-tailed, and it is argued that the approach is a natural extension of least squares methodology. It emerges that the asymptotic normal distribution of these estimators has a covariance matrix characterised by a scalar function of t, called the variance function, which is determined by the error distribution. Properties of this variance function suggest graphical criteria for detecting departures from normality.

Linear regression by functional least squares

1982 ◽  
Vol 19 (A) ◽  
pp. 225-239 ◽  
Author(s):  
C. R. Heathcote
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Natural Extension ◽  
Real Variable ◽  
Ordinary Least Squares ◽  
Scalar Function ◽  
Error Distribution ◽  
Variance Function ◽  
Standard Linear ◽  
Asymptotic Normal

The standard linear regression model is analysed using a method called functional least squares which yields a family of estimators for the slope parameter indexed by a real variable t, |t| ≦ T. The choice t = 0 corresponds to ordinary least squares, non-zero values being appropriate if the error distribution is long-tailed, and it is argued that the approach is a natural extension of least squares methodology. It emerges that the asymptotic normal distribution of these estimators has a covariance matrix characterised by a scalar function of t, called the variance function, which is determined by the error distribution. Properties of this variance function suggest graphical criteria for detecting departures from normality.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

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 Modelling the Influences of Economic, Demographic, and Institutional Factors on Fiscal Pressure Using OLS, PCSE, and FD-GMM Approaches

2020 ◽  
Vol 12 (4) ◽  
pp. 1681
Author(s):  
Alina-Cristina Nuță ◽  
Florian-Marcel Nuță
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Institutional Factors ◽  
Standard Errors ◽  
Panel Analysis ◽  
Fiscal Pressure ◽  
Robust Standard Errors

The purpose of our article is to assess the effect of diverse factors, such as economic, demographic, and institutional factors, on global and social fiscal pressure. The study is based on a panel analysis of 38 states during 2000–2017. We used ordinary least squares (OLS) as a base model for our estimations, and a linear regression with panel-corrected standard errors and a first difference generalized method of moments (GMM) with robust standard errors and orthogonal deviations. The results of our study indicate that the demographic and institutional factors involved in the analysis contribute to the identification of some variables that affect the global or social fiscal pressure.

scholarly journals A Comparison of Ordinary Least Squares and Least Absolute Error Estimation

1988 ◽  
Vol 4 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Andrew A. Weiss
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Error Estimation ◽  
Method Of Moments ◽  
Linear Regression Model ◽  
Generalized Method Of Moments ◽  
Absolute Error ◽  
Ordinary Least Squares ◽  
Hausman Test ◽  
Heteroscedastic Errors

In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

The description and analysis of wool growth

1977 ◽  
Vol 28 (4) ◽  
pp. 737 ◽  
Author(s):  
BN Nagorcka
Keyword(s):  
Growth Rate ◽  
Body Weight ◽  
Linear Regression ◽  
Least Squares ◽  
Ordinary Least Squares ◽  
Time Dependent ◽  
Recursive Least Squares ◽  
Growth Time ◽  
Body Weight Change ◽  
Wool Growth

Analyses of experimental estimates of the wool growth rate as a function of intake have previously been based on time-independent equations and linear regression with ordinary least squares. Some of these results are reanalysed with the assumption that the sheep is a dynamic system; hence a time-dependent description of wool growth is proposed. A recursive least squares technique has been used, and the results demonstrate that there is a 3½ week lag between intake and wool growth. Time-independent descriptions have not taken account of this and have led to the misconception that efficiency is a function of body weight change.

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