I seek to estimate $b_1$ and $b_0$ from data of the form:

$$y_i = b_1x_i + b_0 + e_i, \quad i\in\{0,1,...,N-1\}$$

given $\{y_i\}$ and $\{\tilde{x}_i\}$ where $\tilde{x}_i=x_i + n_i$ (i.e., error-in-variables or measurement error).

In my problem, $e_i$ has lower standard deviation than $n_i$. Also, $N$ is small (i.e., less than 10). I found (via Monte Carlo simulation) that standard techniques like Deming regression or maximum likelihood (assuming zero mean Gaussian errors of known variances) don't perform much better in an RMSE sense than ordinary least squares for small samples.

Are there any other approaches worth trying?


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