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ADA096 751 BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS F/6 12/1SIEVES FOR NONPARAMETRIC ESTIMATION OF DENSITIES AND REGRESSION--ETC(U)JAN 81 S GEMAN DAAG29-O8-K-O006
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MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF S;TANDARDS 1963-A
LEVaLSieves for Nonparametric Estimation
of Densities and Regressions
Interim Technical Report
January 1981
U.S. Army Research Office
Grant No. DAAG29-80-K-0006
DT!CDivision of Applied Mathematics MAR 2 4 1981
Brown UniversityProvidence, Rhode Island 02912
F
Approved for Public Release;
'44 Distribution Unlimited
81 3049
Va
The view, opinions, and/or findings contained in this reportare those of the author and should not be construed as anofficial Department of the Army position, policy, or decision,unless so designated by other documentation.
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SECURTiY CLASSIFICATION OF THIS PAGE (25mm, Dat. Entered)READ__ _ INTRCTONREPORT DOCUMENTATION PAGE BZFORE COMPLETIG FORM
IREPORT NUMBER 12. GOVT ACCESSION NO 3. RECIgNH.5 AAOGHME
Sves for Nonparametric Estimation 2Interim Yechnica1 eof Densities and Regressions.,ai
7. -AUTH4OR(.)ATOGRN UBRa
MONITRORING ORANCY^I NAME ANDES~j ADDRS Ife10fo emrelWdOfc) . SECRITYA CLE NTPRJC.AS
Proidece RhodeF.CTIN IslanGRA21G
It. COSTROIBUING STIC AT ME (of DRES SApprovedrm fo ulcReeaseh ditbui on uniited81I Ppo t ic ox 12?11 __- -_u' t4,Et'11111110
17. DISTRIBUTION STATEMENT (of this ep~rft) rdI lek2 I
unfiVfYed //(
IS. SUPPLEMENTARY NOTES TEVE.OIIa.Aef~~ lD"I ~T~~p ~ hSRPR
ARE TNOl E C- C'STIJE,) ASAN 0.71"r7f L oL L~''~ i)E-
IS. KEY WORDS (Continue an reverse side it noceeawy and identify by Wloek ntmber)
nonparametric estimation; probability density functions;regression functions
2!&01A11 rcmirrine r, everse a II j neeeatey sad Ideality by block number)
This report is about the use of least-squares for nonparametricregression and the use of maximum likelihood for nonparametricdensity estimation. Typically, these classical techniquesfail when applied to infinite dimensional problems. Grenander'smethod of sieves is a method for modifying classical estimatorsto make them appropriate for nonclassical problems. Examplesare given here of the application of this method to the, (cont'd)
DDI J 72" W3 EDITON OF I NOV 651 IS 62LETE
SECURITY CLASSIFICATION OF THIS PAGE (Whlen Dole EnOgd
SECUP4lY CLASSIPICATION OF THIS PAGK(Wh Dwo fto*.e~
20. Abstract (Cont.d)
problems of regression and density estimation.
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