Let (hat{f}_{n}(t)) denote a kernel density estimator with kernel function (k) computed on a sample (X_{1}, ldots,

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Let \(\hat{f}_{n}(t)\) denote a kernel density estimator with kernel function \(k\) computed on a sample \(X_{1}, \ldots, X_{n}\). Prove that,

\[E\left[\int_{-\infty}^{\infty} \hat{f}_{h}(t) f(t) d tight]=h^{-1} E\left[\int_{-\infty}^{\infty} k\left(\frac{t-X}{h}ight) f(t) d tight]\]

where the expectation on the right hand side of the equation is taken with respect to \(X\).

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 11:00 PM

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Let (hat{f}_{n}(t)) denote a kernel density estimator with kernel function (k) computed on a sample (X_{1}, ldots,

Question:

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Introduction To Statistical Limit Theory

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