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12 views

The weights estimates for Weighted Deming regression

I'm currently trying to build an algorithm to perform a Weighted Deming regression for medical devises comparison and I've having some hard time doing it. I'm having trouble understanding how to ...
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0answers
78 views

Bayesian estimates for Deming regression coinciding with least-squares estimates

Consider the following Deming model with independent replicates : $$x_{i,j} \mid \theta_{i} \sim {\cal N}(\theta_{i}, \gamma_X^2), \quad y_{i,j} \mid \theta_{i} \sim {\cal N}(\alpha+\beta\theta_{i}, ...
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1answer
96 views

Nonlinear total least squares / Deming regression in R

I've been using nls() to fit a custom model to my data, but I don't like how the model is fitting and I would like to use an approach that minimizes residuals in ...
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35 views

Deming Regression/Errors-in-Variables with replicates

I have a question about a model related to Deming regression and would appreciate some help and/or publications to further study this model. Statistical Model: \begin{align} ...
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38 views

Estimating variances in orthogonal regression

In orthogonal regression it is assumed that both variables have noise. I'm interested in the simplest possible case. That is, I have a very large number of data points $(X_1,Y_1), ..., (X_n,Y_n)$. ...
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1answer
53 views

Slope estimate dependent on covariance?

I am trying to perform a linear regression with equal errors on x and y (ex =1 and ey=1) in a Bayesian framework (using WinBugs). Using Winbugs (solid line in the Figure), I managed to reproduce the ...
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0answers
47 views

How do I get from the eigenvectors of the covariance matrix to the regression parameters? [duplicate]

I have a linear regression problem $$ y = a x + b$$ with errors on $x$ and $y$ that are uncorrelated and unitary and I have to find $a$ and $b$. To do this, I want to use principal component ...
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1answer
144 views

Estimated critical value for hypothesis testing

For the classical simple linear regression model I have derived an hypothesis test for $H_0\colon \left\{\frac{y^*(x^*)-x^*}{\sigma}>1 \right\}$ where $x^*$ is a given value of the covariate $x$ ...
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1answer
321 views

Tolerance interval for Deming regression

I am trying to derive (one-sided) tolerance intervals related to the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are ...
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0answers
166 views

Two-stage least squares approach to Deming regression

I am interested in statistical inference for the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are nonrandom fixed numbers, ...
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0answers
375 views

What are good references for Deming's regression?

Do you know some good references (papers or books) for the theoretical inference in Deming's regression model ? EDIT: I was a little disconcerted about a point in Ripley and Thompson's paper ...
12
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1answer
658 views

Errors-in-variables regression: is it valid to pool data from three sites?

I recently had a client come to me to do a bootstrap analysis because an FDA reviewer said that their errors-in-variables regression was invalid because when pooling data from sites the analysis ...
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3answers
2k views

How to perform orthogonal regression (total least squares) via PCA?

I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$ Today I learned about ...
3
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1answer
2k views

What is the prediction error while using deming regression (weighted total least squares)

Deming Regression is a regression technique taking into account uncertainty in both the explanatory and dependent variable. Although I have found some interesting references on the calculation of ...