Adaptive window for local polynomial regression from noisy nonuniform samples

We consider the problem of local polynomial regression of noisy nonuniform samples of a time-varying signal in the presence of observation noise. We formulate the problem in the time domain and use the pointwise minimum mean square error (MMSE) as the cost function. The choice of the window length for local regression introduces a bias-variance tradeoff which we solve by using the intersection-of-confidence-intervals (ICI) technique. This results in an adaptive pointwise MMSE-optimal window length. The performance of the adaptive window technique is superior to the conventional fixed window approaches. Simulation results show that the improvement in reconstruction accuracy can be as much as 9 dB for 3 dB input signal-to-noise ratio (SNR).