The Numerical Effect of Measurement Error in the Explanatory Variables on the Observed Least Squares Estimate

1993 ◽  
Vol 14 (3) ◽  
pp. 677-687 ◽  
Author(s):  
Samprit Chatterjee ◽  
Glenn Heller
Keyword(s):  
Measurement Error ◽  
Least Squares ◽  
Explanatory Variables ◽  
Least Squares Estimate ◽  
Numerical Effect

A Least Squares Estimate of Satellite Attitude (Grace Wahba)

SIAM Review ◽  
1966 ◽  
Vol 8 (3) ◽  
pp. 384-386 ◽  
Author(s):  
J. L. Farrell ◽  
J. C. Stuelpnagel ◽  
R. H. Wessner ◽  
J. R. Velman ◽  
J. E. Brook
Keyword(s):  
Least Squares ◽  
Least Squares Estimate ◽  
Satellite Attitude

scholarly journals The Nexus between Financial Development and Economic Growth: Panel Data Evidence from Developing Countries

2021 ◽  
Vol 14 (10) ◽  
pp. 489
Author(s):  
E. M. Ekanayake ◽  
Ranjini Thaver
Keyword(s):  
Economic Growth ◽  
Developing Countries ◽  
Panel Data ◽  
Least Squares ◽  
Financial Development ◽  
Panel Cointegration ◽  
Sub Saharan Africa ◽  
Explanatory Variables ◽  
Cointegration Tests ◽  
Sub Saharan

The objective of this study is to investigate the nexus between financial development (FD) in economic growth (GROWTH) in developing countries. The study uses panel data from 138 developing countries during the period 1980–2018. The relationship between financial development and economic growth is investigated using four explanatory variables that are commonly used to measure the level of financial development and several other control variables, including a dummy variable representing the financial and banking crises. The sample of 138 developing countries is also classified into six geographic regions. We have carried out panel unit-root tests and panel cointegration tests before estimating the specified models using both Panel Least Squares (Panel LS) and Panel Fully Modified Least Squares (FMOLS) methods. In addition, panel Granger causality tests have been conducted to identify the direction of causality between FD and GROWTH for each of the regions. The results of the study provide evidence of a direct relationship between FD and GROWTH in developing countries. Furthermore, there is evidence of bi-directional causality running from FD to GROWTH and from GROWTH to FD in samples of Europe and Central Asia, South Asia, and all countries, but not in East Asia and Pacific, Latin America and the Caribbean, Middle East and North Africa, and Sub-Saharan Africa.

scholarly journals Tracking—A

2021 ◽  
pp. 163-192
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Least Squares ◽  
Recursive Algorithm ◽  
Nonlinear Function ◽  
Random Variables ◽  
Random Variable ◽  
Linear Least Squares ◽  
Least Squares Estimate ◽  
Related Notion

AbstractThis chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

scholarly journals 4D Flow MRI Pressure Estimation Using Velocity Measurement-Error-Based Weighted Least-Squares

2020 ◽  
Vol 39 (5) ◽  
pp. 1668-1680 ◽  
Author(s):  
Jiacheng Zhang ◽  
Melissa C. Brindise ◽  
Sean Rothenberger ◽  
Susanne Schnell ◽  
Michael Markl ◽  
...  
Keyword(s):  
Measurement Error ◽  
Least Squares ◽  
Velocity Measurement ◽  
Weighted Least Squares ◽  
4D Flow Mri ◽  
4D Flow ◽  
Flow Mri ◽  
Pressure Estimation

Least-squares estimation of diet composition from n-alkanes in herbage and faeces using matrix mathematics

1995 ◽  
Vol 46 (4) ◽  
pp. 793 ◽  
Author(s):  
JA Newman ◽  
WA Thompson ◽  
PD Penning ◽  
RW Mayes
Keyword(s):  
Least Squares ◽  
Diet Composition ◽  
Least Squares Estimation ◽  
Simultaneous Equations ◽  
Desirable Property ◽  
Least Squares Estimate ◽  
Ruminant Animals

It is possible to estimate diet composition from an analysis of n-alkanes in the faeces of ruminant animals. For instance, to estimate the proportion of two species in a diet, two equations are constructed using the known concentrations of two different n-alkanes in the herbage and in the animal's faeces. These two equations are solved for the two unknown quantities of the diet components. Two problems exist with this method. First, it is often the case that we have estimated concentrations of more than two different n-alkanes. This can lead to a problem in deciding which two n-alkanes to use to construct the simultaneous equations. The choice of this pair of n-alkanes is arbitrary in its selection and wasteful of other useful information. The second problem is that sometimes the solution to the simultaneous equations yields nonsensical answers, such as a negative proportion of one species in the diet. In addition to making it difficult to estimate dietary proportions, estimating digestibility becomes impossible. In this paper, we present a technique which provides an estimate of the dietary proportions. This estimate uses information on all the n-alkanes available, and it has a very desirable property of being a least squares estimate. We also present a method for determining the least squares estimate subject to the constraint that all proportions must be non-negative. We provide examples for estimating the proportions of grass and clover in the diet of sheep and the digestibility of those diets.

scholarly journals Testing for the presence of measurement error in Stata

2020 ◽  
Vol 20 (2) ◽  
pp. 382-404
Author(s):  
Young Jun Lee ◽  
Daniel Wilhelm
Keyword(s):  
Monte Carlo ◽  
Measurement Error ◽  
Monte Carlo Simulations ◽  
Nonparametric Test ◽  
Parametric Models ◽  
Empirical Application ◽  
Explanatory Variables ◽  
Working Paper ◽  
Linear Regressions

In this article, we describe how to test for the presence of measurement error in explanatory variables. First, we discuss the test of such hypotheses in parametric models such as linear regressions and then introduce a new command, dgmtest, for a nonparametric test proposed in Wilhelm (2018, Working Paper CWP45/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies). To illustrate the new command, we provide Monte Carlo simulations and an empirical application to testing for measurement error in administrative earnings data.

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