Show that the estimates of the Fourier coefficients in orthogonal series density estimation XXXXXXXXXXare unbiased. Generate a sample of n = 400 observations from the t3 distribution (Section 11.3,...

Show that the estimates of the Fourier coefficients in orthogonal series density estimation (12.2.7) are unbiased.

Generate a sample of n = 400 observations from the t3 distribution (Section 11.3, Algorithm C5). Estimate the upper .05 and .01 percentile points using estimates cˆ1, cˆ2, cˆ3, cˆ4, and compare to the true values.