home4 - [0 1 are bounded 3 Problem 19.4 in van der Vaart 4...

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Stat 210B Homework Assignment 4 (due March 15) 1. Let X be a real-valued random variable with distribution P . (a) For 0 < M < and a R , let f ( x, t ) = | x - t | , and F = { f ( x, t ) : | t - a | ≤ M } . (b) For a R , let g ( x, t ) = | x - t | - | x - a | , and G = { g ( x, t ) : | t - a | ≤ M } . Show that the bracketing number N 1 ,B ( ², P, F ) < for every ² > 0 for the class F if E | X | < , and for the class G without the hypothesis E | X | < . 2. Show that the functions in D
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Unformatted text preview: [0 , 1] are bounded. 3. Problem 19.4 in van der Vaart. 4. Problem 5.19 in van der Vaart. 5. Consider the following two location models: (a) p θ ( x ) = 1 π 1 1+( x-θ ) 2 (b) p θ ( x ) = 1 2 exp(-| x-θ | ). For each of these models compute the quadratic mean derivative and the Fisher information....
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