MARC Record from marc_columbia

LEADER: 02348cam a22003373i 4500
001 10579592
005 20180618182502.0
006 m o d
007 cr |n||||a||||
008 131223s2012 nyu|||| om 00| ||eng d
035 $a(OCoLC)867755874
035 $a(OCoLC)ocn867755874
035 $a(NNC)ACfeed:legacy_id:ac:164424
035 $a(NNC)ACfeed:doi:10.7916/D8P55VVD
035 $a(NNC)10579592
040 $aNNC$beng$erda$cNNC
100 1 $aXiong, Wei.
245 10 $aSparse functional regression models :$bminimax rates and contamination /$cWei Xiong.
264 1 $a[New York, N.Y.?] :$b[publisher not identified],$c2012.
300 $a1 online resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
502 $aThesis (Ph.D.)--Columbia University, 2012.
500 $aDepartment: Biostatistics.
500 $aThesis advisor: Ian W. McKeague.
520 $aIn functional linear regression and functional generalized linear regression models, the effect of the predictor function is usually assumed to be spread across the index space. In this dissertation we consider the sparse functional linear model and the sparse functional generalized linear models (GLM), where the impact of the predictor process on the response is only via its value at one point in the index space, defined as the sensitive point. We are particularly interested in estimating the sensitive point. The minimax rate of convergence for estimating the parameters in sparse functional linear regression is derived. It is shown that the optimal rate for estimating the sensitive point depends on the roughness of the predictor function, which is quantified by a "generalized Hurst exponent". The least squares estimator (LSE) is shown to attain the optimal rate. Also, a lower bound is given on the minimax risk of estimating the parameters in sparse functional GLM, which also depends on the generalized Hurst exponent of the predictor process.
520 $aThe order of the minimax lower bound is the same as that of the weak convergence rate of the maximum likelihood estimator (MLE), given that the functional predictor behaves like a Brownian motion.
653 0 $aBiometry
856 40 $uhttps://doi.org/10.7916/D8P55VVD$zClick for full text
852 8 $blweb$hDISSERTATIONS