# What are variance and bias in spectral estimation (specifically periodogram spectral estimation)?

So far, I have read that all the non-parametric estimation techniques decrease the frequency resolution in order to decrease the variance in the spectral estimate

What is the general "overview" meaning of variance and what is the advantage in decreasing the variance of spectral estimate?

The PSD can be calculated from the autocorrelation function of a signal by taking its Fourier transform, called the periodogram. In general the variance of the estimate $P_{xx}(f)$ does not decay to zero as $N$ tends to infinity. Thus, "the periodogram is not a consistent estimate of the true power density spectrum", i.e., it does not converge to the true power density spectrum. Thus, the estimated spectrum suffers from the smoothing effects and the leakage embodied in the Barlett window. The smoothing and leakage ultimately limit our ability to resolve closely spaced spectra. The methods Barlett along with Blackman, Tukey, and Welch are classical methods and make no assumption about how the data were generated and are hence called non-parametric methods.

In this method for reducing the variance in the periodogram involves three steps:

1. First the $N$-point sequence is subdivided into $K$ non-overlapping segments, where each segment has length $M$.
2. For each segment we compute the periodogram.
3. Finally, we average the periodograms for the $K$ segments to obtain the Barlett power spectrum estimate.