alt Hacker NewsHad a QuantSci Prof who was fond of asking "Who can name a data collection scenario where the x data has no error?" and then taught Deming regression as a generally preferred analysis [1]
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From that wikipedia article, delta is the ratio of y variance to x variance. If x variance is tiny compared to y variance (often the case in practice) then will we not get an ill-conditioned model due to the large delta?
In my field, the X data error (measurement jitter) is generally <10ns, which might as well be no error.
For most time series, noise in time measurement is negligible. However, this does not prevent complex coupling phenomena from occurring for other parameters, such as GPS coordinates.
The issue in that case is that OLS is BLUE, the best linear unbiased estimator (best in the sense of minimum variance). This property is what makes OLS exceptional.
Most of the time, if you have a sensor that you sample at, say 1 KHz and you’re using a reliable MCU and clock, the noise terms in the sensor will vastly dominate the jitter of sampling.
So for a lot of sensor data, the error in the Y coordinate is orders of magnitude higher than the error in the X coordinate and you can essentially neglect X errors.