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The Weighted Bootstrap (Lecture Notes in Statistics, 98, Band 98) - Softcover

Buch 6 von 72: Lecture Notes in Statistics

Barbe, Philippe; Bertail, Patrice

 
9780387944784: The Weighted Bootstrap (Lecture Notes in Statistics, 98, Band 98)
Softcover
ISBN 10: 0387944788 ISBN 13: 9780387944784
Verlag: Springer, 2013

Inhaltsangabe

INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n • • LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn • • P T(P ) conditionally on := mn l: i =1 a • ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.

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INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n ¿ ¿ LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn ¿ ¿ P T(P ) conditionally on := mn l: i =1 a ¿ ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
0387944788
ISBN 13 
9780387944784
Einband
Taschenbuch
Anzahl der Seiten
238
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