Questions tagged [total-least-squares]
A technique to estimate parameters $\beta$ of the linear model $Y=X\beta$ when both $Y$ and $X$ are subject to measurement error. Includes Orthogonal and Deming regression as special cases.
95 questions
13 votes
2 answers
694 views
How can I estimate the rotation between two cooordinate frames?
I have measurements of N points, p, in 3D in two coordinate frames (xyz and XYZ): $$ p_i: \vec{xm_i}, \vec{Xm_i} $$ I model the measurement process as: $$ \vec{xm_i} = \vec{x_i} + \vec{\epsilon_i} $$ ...
- 743
3 votes
1 answer
103 views
Deming regression and Numerical Recipes
I'm trying to sort through Deming regression, meaning that I want to fit a function (a straight line) through data that have "errors" in both the x and y coordinates. I'm looking at ...
- 33
1 vote
0 answers
99 views
Calculate variance of a prediction for TLS
Definitions I have a set of data. Let's assume the true underlying model to be $\eta_i=\beta_0+\beta_1\zeta_i$. Where $\beta_i$ are the true coefficients of the model, $\eta_i$ are the true ...
- 155
2 votes
1 answer
92 views
Derivative of Linear Model with respect to Residual
I am looking at two sections on the wikipedia page for total least squares, specifically: #Allowing_observation_errors_in_all_variables and #Example I have two questions, the first is how does one ...
- 425
1 vote
0 answers
39 views
How to estimate a feasible Generalized Error-in-Variable Model (combine deming regression/TLS and f-generalized least squares)
I have observational data with spatial structure. A hypothetical dataset could be brain mass for 100 species of birds and body mass for those same species. The data has spatial structure because ...
- 425
2 votes
0 answers
132 views
Is reduced major axis regression a special case of total least squares?
Edit: It seems the answer to my first question is that the website has a typo. $\lambda = V_{y}/V_{x}$, NOT $\lambda = V_{x}/V_{y}$. But I'm still stumped on the second question about why it cannot be ...
- 425
1 vote
0 answers
29 views
Has the generalized Deming model been developed?
I am familiar with Deming regression and wonder if anyone has generalized it to other error families and links beyond Gaussian and identity.
- 1,541
1 vote
1 answer
161 views
Comparing Deming/Orthogonal Regression to Null Hypothesis
I have some data of with the relationship Y=commonFactor+error1 and X=Alpha+Beta*commonFactor+error2 I want to test the hypothesis that Beta is non-zero, or that there is a significant relationship ...
- 425
2 votes
1 answer
273 views
Applications of total least squares and related pitfalls (in biology/ecology)
I recently discovered TLS for a bio-statistical (ecological) problem I am working on. However, I was not able to find a lot of (ecological) literature that uses TLS in their analysis. From other ...
- 175
1 vote
0 answers
144 views
Mixed-level Deming regression?
Is there an implementation of Deming regression that also handles random intercepts and slopes in the sample? We have a situation where we have compelling theoretical reason to believe that one ...
- 1,541
4 votes
1 answer
220 views
What does Deming regression estimate?
Least squares regression estimates conditional means. Least absolute regression estimates conditional medians. Quantile regressions estimate conditional quantiles (a special case of which is the ...
- 72.9k
3 votes
1 answer
162 views
What is the name of this regression model?
I am wondering how I can map this problem to something known. Let us start with a standard linear regression framework, and suppose we want to reconstruct an observed signal $y$ from single known ...
- 455
2 votes
0 answers
152 views
Total least squares estimator
In the paper Ivan Markovsky, Sabine Van Huffel - Overview of Total Least Squares Methods, at the top of the sixth page, it is claimed that the estimate of $\beta$ in the total least squares model $y \...
- 20.7k
1 vote
1 answer
82 views
Reorder dataset to achive LSE between two data sets
Assume I have two datasets, each one containing 5000 samples, and each sample has three dimensions. I am looking for a way to "reorder" the samples in one (or probably both) dataset such ...
- 43
0 votes
0 answers
211 views
Orthogonal regression that minimizes absolute error instead of squared error
Fitting a line through 3D points is usually done by orthogonal least squares (aka "total least squares"), i.e., by minimizing the mean squared orthogonal distance between the points and the ...
- 6,255