upper and lower bounds on loess

I am trying to smooth my x, y data via loess and rloess, however I am unable to create upper and lower bounds. In "computational Statistics handbok with MATLAB" they use the function "csloess" to create the upper/lower boundaries. I have not been able to find this function anywhere, so if anyone has suggestions I would love to hear them!

I can smooth my data easily using loess, but I can't create a fit type, as that requires x,y,z data.

Answer 1

[Shishir Reddy]

Hi Kristian

Creating upper and lower bounds for a LOESS (Locally Estimated Scatterplot Smoothing) fit involves estimating the variability of the fit at each point, which can be done using bootstrapping or other resampling methods.

Here's a general approach using MATLAB:

1. Fit LOESS to Your Data: Use MATLAB's fit function with the loess method to fit your data.

x = your_x_data;
y = your_y_data;
span = 0.3;
loessFit = fit(x, y, 'loess', 'Span', span);

2. Bootstrap Resampling: Perform bootstrap resampling to estimate the variability of the LOESS fit. This involves repeatedly sampling your data with replacement and fitting LOESS to each sample.

numBootstraps = 1000;
bootstrapFits = zeros(length(x), numBootstraps);

for i = 1:numBootstraps
    indices = randi(length(x), length(x), 1);
    xSample = x(indices);
    ySample = y(indices);
    bootFit = fit(xSample, ySample, 'loess', 'Span', span);
    bootstrapFits(:, i) = feval(bootFit, x);
end

3. Calculate Confidence Intervals: Compute the upper and lower bounds for the confidence intervals from the bootstrap results.

alpha = 0.05;  % 95% confidence interval
lowerBound = quantile(bootstrapFits, alpha/2, 2);
upperBound = quantile(bootstrapFits, 1 - alpha/2, 2);

The span parameter in LOESS controls the amount of smoothing. So, you may need to adjust it based on the data.

For more information regarding fit, quantile kindly refer the following documentation links -

https://www.mathworks.com/help/curvefit/fit.html

https://www.mathworks.com/help/matlab/ref/quantile.html

I hope this helps.