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Could you please write it on paper, thanks a lot 4. (Density estimation; 4+4+2 pts) We study the problem of estimating a probability density function

Could you please write it on paper, thanks a lot

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4. (Density estimation; 4+4+2 pts) We study the problem of estimating a probability density function f, given i.i.d. random variables X1, . .., Xn from the distribution on R that has density f with respect to the Lebesgue measure. Suppose that the density function f belongs to the Holder class E(B, L) defined in class, where L > 0 and 0 0. Consider the kernel density estimator f ( x ) = f (x, X1, . . . , Xn) := K Xi nh i= 1 h defined for all x E R, where h > 0 and the kernel K satisfies 0 0, we have IE [(f(x) - f(2)) 2] S Cn2371

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