When BLUE is not best: non-normal errors and the linear model

2018 ◽  
Vol 8 (1) ◽  
pp. 136-148 ◽  
Author(s):  
Daniel K. Baissa ◽  
Carlisle Rainey
Keyword(s):  
Monte Carlo ◽  
Statistical Theory ◽  
Monte Carlo Simulations ◽  
Least Squares ◽  
Political Science ◽  
Linear Model ◽  
Linear Models ◽  
Least Squares Estimators ◽  
Data Points ◽  
Least Squares Estimates

AbstractResearchers in political science often estimate linear models of continuous outcomes using least squares. While it is well known that least-squares estimates are sensitive to single, unusual data points, this knowledge has not led to careful practices when using least-squares estimators. Using statistical theory and Monte Carlo simulations, we highlight the importance of using more robust estimators along with variable transformations. We also discuss several approaches to detect, summarize, and communicate the influence of particular data points.

scholarly journals Sensitivity analysis in linear models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Shuangzhe Liu ◽  
Tiefeng Ma ◽  
Yonghui Liu
Keyword(s):  
Sensitivity Analysis ◽  
Least Squares ◽  
Linear Model ◽  
Linear Models ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
The Other ◽  
Regression Coefficients ◽  
General Linear ◽  
Least Squares Estimators

AbstractIn this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

scholarly journals Nonstationary INAR(1) Process with th-Order Autocorrelation Innovation

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Kaizhi Yu ◽  
Hong Zou ◽  
Daimin Shi
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Monte Carlo Simulations ◽  
Least Squares ◽  
Limit Distribution ◽  
Nonstationary Process ◽  
Random Walk Process ◽  
Autoregressive Coefficient ◽  
Least Squares Estimators ◽  
Conditional Least Squares

This paper is concerned with an integer-valued random walk process withqth-order autocorrelation. Some limit distributions of sums about the nonstationary process are obtained. The limit distribution of conditional least squares estimators of the autoregressive coefficient in an auxiliary regression process is derived. The performance of the autoregressive coefficient estimators is assessed through the Monte Carlo simulations.

Autoregressive processes with infinite variance

1977 ◽  
Vol 14 (02) ◽  
pp. 411-415 ◽  
Author(s):  
E. J. Hannan ◽  
Marek Kanter
Keyword(s):  
Least Squares ◽  
Autoregressive Model ◽  
Infinite Variance ◽  
Autoregressive Processes ◽  
Stable Law ◽  
Least Squares Estimators ◽  
Data Points

The least squares estimators β i(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(β i(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi (N).

INFLUENCE OF MATRIX ERRORS ON PARAMETER ESTIMATES BY THE LEAST SQUARES METHOD

2021 ◽  
Author(s):  
V. A. Galanina ◽  
◽  
L. A. Reshetov ◽  
M. V. Sokolovskay ◽  
A. E. Farafonova ◽  
...  
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
Statistical Characteristics ◽  
Parameter Estimates ◽  
Model Matrix ◽  
Least Squares Estimates

The paper investigates the effect of distorsions of the linear model matrix on the statistical characteristics of the least squares estimates.

Machine Learning Techniques on Multidimensional Curve Fitting Data Based on R- Square and Chi-Square Methods

2016 ◽  
Vol 6 (3) ◽  
pp. 974 ◽  
Author(s):  
Vidyullatha P ◽  
D. Rajeswara Rao
Keyword(s):  
Machine Learning ◽  
Linear Model ◽  
Curve Fitting ◽  
Linear Models ◽  
Machine Learning Techniques ◽  
Chi Square ◽  
Curve Fit ◽  
Learning Techniques ◽  
Non Linear ◽  
Data Points

<p>Curve fitting is one of the procedures in data analysis and is helpful for prediction analysis showing graphically how the data points are related to one another whether it is in linear or non-linear model. Usually, the curve fit will find the concentrates along the curve or it will just use to smooth the data and upgrade the presence of the plot. Curve fitting checks the relationship between independent variables and dependent variables with the objective of characterizing a good fit model. Curve fitting finds mathematical equation that best fits given information. In this paper, 150 unorganized data points of environmental variables are used to develop Linear and non-linear data modelling which are evaluated by utilizing 3 dimensional ‘Sftool’ and ‘Labfit’ machine learning techniques. In Linear model, the best estimations of the coefficients are realized by the estimation of R- square turns in to one and in Non-Linear models with least Chi-square are the criteria. </p>

Performance of Msplit estimates in the context of vertical displacement analysis

2020 ◽  
Vol 14 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Patrycja Wyszkowska ◽  
Robert Duchnowski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Least Squares ◽  
Vertical Displacement ◽  
Least Squares Estimation ◽  
Small Magnitude ◽  
Displacement Analysis ◽  
Better Than

AbstractThis paper concerns two types of Msplit estimation: squared Msplit estimation (SMS), which assumes normality of observation errors and absolute Msplit estimation (AMS), which applies {\text{L}_{1}} norm criterion. The main objective of the paper is to assess the accuracy of such estimators in vertical displacement analysis by applying Monte Carlo simulations. Another issue is to compare the accuracy of both estimators with the accuracy of the least squares estimation (LS). The paper shows that the accuracy of both Msplit estimates is like the accuracy of LS estimates. However, if some nonrandom errors occur, then accuracy of AMS estimates might be better than the accuracy of the rest of the estimates considered here. It stems from the fact that AMS estimates are robust against disturbances which have a small magnitude. It is also worth noting that the accuracy of both Msplit estimates might depend on the magnitude of the displacement.

A simulation study of impacts of error structure on modeling stock–recruitment data using generalized linear models

2004 ◽  
Vol 61 (1) ◽  
pp. 122-133 ◽  
Author(s):  
Yan Jiao ◽  
Yong Chen ◽  
David Schneider ◽  
Joe Wroblewski
Keyword(s):  
Linear Model ◽  
Generalized Linear Model ◽  
Linear Models ◽  
Least Squares Method ◽  
Estimation Of Parameters ◽  
Estimation Errors ◽  
Error Structure ◽  
Stock Recruitment ◽  
Data Points ◽  
The Impact

Stock–recruitment (S–R) models are commonly fitted to S–R data with a least-squares method. Errors in modeling are usually assumed to be normal or lognormal, regardless of whether such an assumption is realistic. A Monte Carlo simulation approach was used to evaluate the impact of the assumption of error structure on S–R modeling. The generalized linear model, which can readily deal with different error structures, was used in estimating parameters. This study suggests that the quality of S–R parameter estimation, measured by estimation errors, can be influenced by the realism of error structure assumed in an estimation, the number of S–R data points, and the number of outliers in modeling. A small number of S–R data points and the presence of outliers in S–R data could increase the difficulty in identifying an appropriate error structure in modeling, which might lead to large biases in the S–R param eter estimation. This study shows that generalized linear model methods can help identify an appropriate error distribution in S–R modeling, leading to an improved estimation of parameters even when there are outliers and the number of S–R data points is small. We recommend the generalized linear model be used for quantifying stock–recruitment relationships.

A Comment on Diagnostic Tools for Counterfactual Inference

2009 ◽  
Vol 17 (1) ◽  
pp. 89-106 ◽  
Author(s):  
Nicholas Sambanis ◽  
Alexander Michaelides
Keyword(s):  
Monte Carlo ◽  
Political Science ◽  
Diagnostic Tools ◽  
Counterfactual Analysis ◽  
Data Sets ◽  
Explanatory Variables ◽  
Monte Carlo Experiments ◽  
Data Points

We evaluate two diagnostic tools used to determine if counterfactual analysis requires extrapolation. Counterfactuals based on extrapolation are model dependent and might not support empirically valid inferences. The diagnostics help researchers identify those counterfactual “what if” questions that are empirically plausible. We show, through simple Monte Carlo experiments, that these diagnostics will often detect extrapolation, suggesting that there is a risk of biased counterfactual inference when there is no such risk of extrapolation bias in the data. This is because the diagnostics are affected by what we call the n/k problem: as the number of data points relative to the number of explanatory variables decreases, the diagnostics are more likely to detect the risk of extrapolation bias even when such risk does not exist. We conclude that the diagnostics provide too severe a test for many data sets used in political science.

Sign in / Sign up

Export Citation Format

Share Document