How could I remove outliers in really small data?

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I have data that should resemble a parabola when plotted into a figure. However, near the center, there is a "high" value for the data.
x = [-9.0000 -8.0000 -7.0000 -6.0000 -5.0000 -4.0000 -3.0000 -2.0000 -1.0000 0 1.0000 ...
2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000];
y = [0.0173 0.0169 0.0168 0.0166 0.0166 0.0167 0.0165 0.0165 0.0166 0.0167 0.0168 ...
0.0177 0.0189 0.0173 0.0176 0.0178 0.0180 0.0181 0.0182 0.0185];
The values I would like Matlab to see as an outlier are x = 2 --> y = 0.0177, and x = 3, --> y = 0.0189, because I should not expected the parabola to grow in the middle, and then decrease. However, it does not count this points as outliers because, of course, Matlab does not know that I should be expecting a parabola-like shape. How could I do this? Thank you!
  6 Comments
Juan Manuel Hussein Belda
Juan Manuel Hussein Belda on 22 Nov 2021
Thank you both! By the way, John, your function inpaint_nans is a life saver!!! (Do not worry, I have properly cited it everytime I used it :) )

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Accepted Answer

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 21 Nov 2021
Linear interpolation might be good to use here, e.g.:
x = [-9.0000 -8.0000 -7.0000 -6.0000 -5.0000 -4.0000 -3.0000 -2.0000 -1.0000 0 1.0000 ...
2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000];
y = [0.0173 0.0169 0.0168 0.0166 0.0166 0.0167 0.0165 0.0165 0.0166 0.0167 0.0168 ...
0.0177 0.0189 0.0173 0.0176 0.0178 0.0180 0.0181 0.0182 0.0185];
plot(x,y, 'linewidth', 2), shg
% Linear Interpolation
x1 = 2; y1 = 0.0177;
x2 = 3; y2 = 0.0189;
Idx = find(x==x1 | x==x2);
y(Idx) = interp1([x(Idx(1)-1),x(Idx(2)+1)], [y(Idx(1)-1),y(Idx(2)+1)], x(Idx));
hold on
plot(x, y, 'r--', 'linewidth', 2), grid on; legend('Raw: x vs. y', 'Fixed: x vs. y')

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