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We introduce kernel estimators for the semicircle law. In this first part ofour general theory on the estimators, we prove the consistency and conductsimulation study to show the performance of the estimators. We also point outthat Wigner's semicircle law for our new estimators and the classical empiricalspectral distributions is still true when the elements of Wigner matrices don'thave finite variances but are in the domain of attraction of normal law.

New estimators of spectral distributions of Wigner matrices