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by: Providenci Mosciski Sr.

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# ADV THRY STAT INFER STAT 583

Providenci Mosciski Sr.
UW
GPA 3.66

Staff

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COURSE
PROF.
Staff
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PAGES
2
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KARMA
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## Popular in Statistics

This 2 page Class Notes was uploaded by Providenci Mosciski Sr. on Wednesday September 9, 2015. The Class Notes belongs to STAT 583 at University of Washington taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/192515/stat-583-university-of-washington in Statistics at University of Washington.

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Date Created: 09/09/15
STAT 583 SPRING 2008 Lecture Notes 1 Statistical Functionals The Gateux derivative of a statistical functional TF is the limit T F G F T F dJFG F lxigol M x If Q0 TF 7 G F has a McLaurin expansion we get an expansion the von Mises expansion of T by noting that Q0TF QlTG Q0 d1TFG F etc yielding 1 TG TF dkTFG FRmG We are usually particularly interested in G F n and we write RmFn Rmn T has a differential at F with respect to a norm if there is a linear functional F A such that for all G TG TF TFG F oG F T is called the Frechet derivative of T Theorem 1 If T has a differential atF with respect to then for any G the Gateux derivative dLTFG F exists and equals TFG F Theorem 2 Let T have a differential at F with respect to Let X1Xn be observations P IF F 0131 Then JZRM gt0 from F not necessarily independent such that J Define the in uence curve of T at F by hF x d1F itX F where z x is the cdf of point mass at x Theorem 3 Suppose T has a linear derivative satisfying a 0 lt VathFX lt 00 P b JZRM gt0 Define pTF EFhFX and 02TF VathFX Then TFn N AsNTF uTF0392TF n STAT 583 SPRING 2008 Theorem 4 Assume that T has an in uence curve which is identically zero and a bilinear second GateuX derivative with symmetric kernel hFuv such that a 0 lt VathFX1X2 lt 00 P b nRZn gt 0 c EFFxX 0 as a function ofx Then 0 no nTFn TltFgtgt 2W 1 where the are iid x12 random variables and k is the eigenvalue of the operator Agx hFxygydFy corresponding to the eigenfunction gjx

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