Let X be a random variable with values in R and K be a function defined over R such tha [K(2)dz = 1; K(2)dz = 0. Let fi (x; T)- K(r X) denote the kernel density estimator given a training set T = (X1,..., XN) formed with L.i.d. copies of X. Assume that the true distribution of X is uniform on [0, 1]. Letting Q be the function Q(x) = / K(2)dz. %3D Prove that, for æ € (0,1): E(İ(1;T)) = Q (,") -(-) h
Let X be a random variable with values in R and K be a function defined over R such tha [K(2)dz = 1; K(2)dz = 0. Let fi (x; T)- K(r X) denote the kernel density estimator given a training set T = (X1,..., XN) formed with L.i.d. copies of X. Assume that the true distribution of X is uniform on [0, 1]. Letting Q be the function Q(x) = / K(2)dz. %3D Prove that, for æ € (0,1): E(İ(1;T)) = Q (,") -(-) h
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Let X be a random variable with values in R and K be a function defined over R such that
| K(z)dæ = 1; zK(æ)dæ = 0.
Let
N
FA(2; T)
N2K(x - X)
k=1
denote the kernel density estimator given a training set T = (X1,..., XN) formed with N
L.i.d. copies of X.
Assume that the true distribution of X is uniform on [0, 1]. Letting
Q be the function
Q(x) = | K(2)dz.
00
Prove that, for æ E (0,1):
E( fala: T) = Q () -()
1
h](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa055ad3a-499c-43ec-a457-d599c6f4bfea%2F61c6d188-f783-4d83-b9b3-dc622140abff%2Fsdqibie_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X be a random variable with values in R and K be a function defined over R such that
| K(z)dæ = 1; zK(æ)dæ = 0.
Let
N
FA(2; T)
N2K(x - X)
k=1
denote the kernel density estimator given a training set T = (X1,..., XN) formed with N
L.i.d. copies of X.
Assume that the true distribution of X is uniform on [0, 1]. Letting
Q be the function
Q(x) = | K(2)dz.
00
Prove that, for æ E (0,1):
E( fala: T) = Q () -()
1
h
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