| The Weighted Bootstrap Softcover Repri Edition Contributor(s): Barbe, Philippe (Author), Bertail, Patrice (Author) |
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ISBN: 0387944788 ISBN-13: 9780387944784 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback Published: February 1995 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General |
| Dewey: 519.544 |
| LCCN: 95005885 |
| Series: Ima Volumes in Mathematics and Its Applications |
| Physical Information: 0.51" H x 6.14" W x 9.21" (0.76 lbs) 230 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |