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@article{stanton:2001,
author = {Jeffrey M. Stanton},
title = {Galton, Pearson, and the Peas: A Brief History of Linear Regression for Statistics Instructors},
journal = {Journal of Statistics Education},
volume = {9},
number = {3},
pages = {null},
year = {2001},
publisher = {Taylor & Francis},
doi = {10.1080/10691898.2001.11910537},
}
@book{ramsay_silverman:2005,
author = "Ramsay, J.O. and Silverman, B. W.",
year = "2005",
title = "Functional Data Analysis",
edition = "2nd",
publisher = "Springer-Verlag",
location = "New York"}
@article{ramsay:1982,
author = "Ramsay, J.O.",
year = "1982",
title = "When the data are functions",
journal = "Psychometrika",
volume = "47",
pages = "379--396"}
@article{ramsay_dalzell:1991,
ISSN = {00359246},
author = {J. O. Ramsay and C. J. Dalzell},
journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
number = {3},
pages = {539--572},
publisher = {[Royal Statistical Society, Wiley]},
title = {Some Tools for Functional Data Analysis},
urldate = {2023-03-06},
volume = {53},
year = {1991}
}
@article{wang_chiou_muller:2016,
author = {Wang, Jane-Ling and Chiou, Jeng-Min and M\"{u}ller, Hans-Georg},
title = {Functional Data Analysis},
journal = {Annual Review of Statistics and Its Application},
volume = {3},
number = {1},
pages = {257-295},
year = {2016},
doi = {10.1146/annurev-statistics-041715-033624}}
@article{robbins_munro:1951,
author = {Herbert Robbins and Sutton Monro},
title = {{A Stochastic Approximation Method}},
volume = {22},
journal = {The Annals of Mathematical Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {400 -- 407},
year = {1951},
doi = {10.1214/aoms/1177729586}}
@article{kiefer_wolfowitz:1952,
author = {J. Kiefer and J. Wolfowitz},
title = {{Stochastic Estimation of the Maximum of a Regression Function}},
volume = {23},
journal = {The Annals of Mathematical Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {462 -- 466},
year = {1952},
doi = {10.1214/aoms/1177729392}}
@article{nadaraya:1965,
author = "Nadaraya, E. A.",
year = "1965",
title = "On Nonparametric Estimates of Density Functions
and Regression Curves",
journal = "Theory of Applied Probability",
volume = "10",
pages = "186--190"}
@article{watson:1964,
AUTHOR = "Watson, G. S.",
YEAR = "1964",
TITLE = "Smooth Regression Analysis",
JOURNAL = "Sankhya",
VOLUME = "26",
NUMBER = "15",
PAGES = "175--184"}
@article{epanechnikov:1969,
author = "Epanechnikov, V. A.",
year = "1969",
title = "Nonparametric Estimation of a Multidimensional Probability Density",
journal = "Theory of Applied Probability",
volume = "14",
pages = "153--158"}
@Manual{fda,
title = {fda: Functional Data Analysis},
author = {J. O. Ramsay and Spencer Graves and Giles Hooker},
year = {2022},
note = {R package version 6.0.5},
url = {https://CRAN.R-project.org/package=fda},
}
@Manual{fdapace,
title = {fdapace: Functional Data Analysis and Empirical Dynamics},
author = {Yidong Zhou and Satarupa Bhattacharjee and Cody Carroll and Yaqing Chen and Xiongtao Dai and Jianing Fan and Alvaro Gajardo and Pantelis Z. Hadjipantelis and Kyunghee Han and Hao Ji and Changbo Zhu and Hans-Georg Müller and Jane-Ling Wang},
year = {2022},
note = {R package version 0.5.9},
url = {https://CRAN.R-project.org/package=fdapace},
}
@book{kokoszka_reimherr:2017,
author = "Kokoszka, P., and Reimherr, M.",
year = "2017",
booktitle = "Introduction to Functional Data Analysis",
edition = "1st",
publisher = "Chapman and Hall/CRC.",
doi = "https://doi.org/10.1201/9781315117416"}
@book{horvath_kokoszka:2012,
author = "Lajos Horv{\'a}th and Piotr Kokoszka",
title = "Inference for Functional Data with Applications",
volume = "200",
year = "2012",
DOI = "https://doi.org/10.1007/978-1-4614-3655-3",
ISBN = "1-4614-3654-0 (hardcover), 1-4614-3655-9 (e-book)",
series = "Springer Series in Statistics"}
@InProceedings{chan_wood:1998,
author="Chan, Grace
and Wood, Andrew T. A.",
editor="Payne, Roger
and Green, Peter",
title="Simulation of Multifractional Brownian Motion",
booktitle="COMPSTAT",
year="1998",
publisher="Physica-Verlag HD",
address="Heidelberg",
pages="233--238",
abstract="Multifractional Brownian motion (MFBm) is a generalization of Fractional Brownian motion (FBm) in which the Hurst parameter varies with time in a prescribed manner. In this paper we investigate an approximate method for simulating realizations of MFBm on a finite grid.",
isbn="978-3-662-01131-7"
}
@Article{fda.usc,
title = {Statistical Computing in Functional Data Analysis: The {R} Package {fda.usc}},
author = {Manuel Febrero-Bande and Manuel {Oviedo de la Fuente}},
journal = {Journal of Statistical Software},
year = {2012},
volume = {51},
number = {4},
pages = {1--28},
url = {https://www.jstatsoft.org/v51/i04/},
}
@InProceedings{padilla_segarra_et_al:2020,
author="Padilla-Segarra, Adri{\'a}n
and Gonz{\'a}lez-Villacorte, Mabel
and Amaro, Isidro R.
and Infante, Saba",
editor="Rodriguez Morales, Germania
and Fonseca C., Efra{\'i}n R.
and Salgado, Juan Pablo
and P{\'e}rez-Gosende, Pablo
and Orellana Cordero, Marcos
and Berrezueta, Santiago",
title="Brief Review of Functional Data Analysis: A Case Study on Regional Demographic and Economic Data",
booktitle="Information and Communication Technologies",
year="2020",
publisher="Springer International Publishing",
address="Cham",
pages="163--176"}
@phdthesis{tian_renfang:2020,
author={{Tian, Renfang}},
title={On Functional Data Analysis: Methodologies and Applications},
year={2020},
publisher="UWSpace",
url={http://hdl.handle.net/10012/15811}
}
@article{zhang_wang:2016,
author = {Xiaoke Zhang and Jane-Ling Wang},
title = {{From sparse to dense functional data and beyond}},
volume = {44},
journal = {The Annals of Statistics},
number = {5},
publisher = {Institute of Mathematical Statistics},
pages = {2281 -- 2321},
year = {2016},
doi = {10.1214/16-AOS1446}}
@techreport{peltier_vehel:1995,
TITLE = {{Multifractional Brownian Motion : Definition and Preliminary Results}},
AUTHOR = {Peltier, Romain-Fran{\c c}ois and L{\'e}vy V{\'e}hel, Jacques},
URL = {https://hal.inria.fr/inria-00074045},
NOTE = {Projet FRACTALES},
TYPE = {Research Report},
NUMBER = {RR-2645},
INSTITUTION = {{INRIA}},
YEAR = {1995},
KEYWORDS = {FRACTIONAL BROWNIAN MOTION ; FRACTAL ; HOLDER EXPONENT ; HAUSDORFF DIMENSION ; GAUSSIAN PROCESS ; CONTINUOUS PROCESS},
PDF = {https://hal.inria.fr/inria-00074045/file/RR-2645.pdf},
HAL_ID = {inria-00074045},
HAL_VERSION = {v1},
}
@article{mandelbrot_van_ness:1968,
ISSN = {00361445},
URL = {http://www.jstor.org/stable/2027184},
author = {Benoit B. Mandelbrot and John W. Van Ness},
journal = {SIAM Review},
number = {4},
pages = {422--437},
publisher = {Society for Industrial and Applied Mathematics},
title = {Fractional Brownian Motions, Fractional Noises and Applications},
urldate = {2023-02-17},
volume = {10},
year = {1968}
}
@article{brown:1827,
%author = {{Brown, Robert F.R.S. Hon. M.R.S.E. & R.I. Acad. V.P.L.S.}},
author = {Brown, Robert},
title = {XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies},
journal = {The Philosophical Magazine},
volume = {4},
number = {21},
pages = {161-173},
year = {1828},
publisher = {Taylor & Francis},
doi = {10.1080/14786442808674769}}
@article{hall_horowitz:2007,
ISSN = {00905364},
author = {Peter Hall and Joel L. Horowitz},
journal = {The Annals of Statistics},
number = {1},
pages = {70--91},
publisher = {Institute of Mathematical Statistics},
title = {Methodology and Convergence Rates for Functional Linear Regression},
urldate = {2023-03-05},
volume = {35},
year = {2007}
}
@article{horowitz_spokoiny:2001,
journal = {Econometrica},
author = {Joel L. Horowitz and Vladimir G. Spokoiny},
journal = {Econometrica},
number = {3},
pages = {599--631},
publisher = {[Wiley, Econometric Society]},
title = {An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative},
urldate = {2023-02-20},
volume = {69},
year = {2001}
}
@article{golovkine_klutchnikoff_patilea:2022,
author = {Steven Golovkine and Nicolas Klutchnikoff and Valentin Patilea},
title = {{Learning the smoothness of noisy curves with application to online curve estimation}},
volume = {16},
journal = {Electronic Journal of Statistics},
number = {1},
publisher = {Institute of Mathematical Statistics and Bernoulli Society},
pages = {1485 -- 1560},
keywords = {adaptive optimal smoothing, Functional data analysis, Hölder exponent, traffic flow},
year = {2022},
doi = {10.1214/22-EJS1997}}
@article{gloter_hoffmann:2007,
author = {Arnaud Gloter and Marc Hoffmann},
title = {{Estimation of the Hurst parameter from discrete noisy data}},
volume = {35},
journal = {The Annals of Statistics},
number = {5},
publisher = {Institute of Mathematical Statistics},
pages = {1947 -- 1974},
keywords = {adaptive estimation of quadratic functionals, fractional Brownian motion, High frequency data, noisy data, Scaling exponent, Wavelet methods},
year = {2007},
doi = {10.1214/009053607000000316}}
@article{gini_nickl:2010,
author = {Evarist Gin{\'e} and Richard Nickl},
title = {{Confidence bands in density estimation}},
volume = {38},
journal = {The Annals of Statistics},
number = {2},
publisher = {Institute of Mathematical Statistics},
pages = {1122 -- 1170},
keywords = {adaptive estimation, Density estimation, Extremes, Gaussian processes, kernel estimators, limit theorem, wavelet estimators},
year = {2010},
doi = {10.1214/09-AOS738}}
@article{ray:2017,
author = {Kolyan Ray},
title = {{Adaptive Bernstein–von Mises theorems in Gaussian white noise}},
volume = {45},
journal = {The Annals of Statistics},
number = {6},
publisher = {Institute of Mathematical Statistics},
pages = {2511 -- 2536},
keywords = {Adaptation, Bayesian inference, confidence set, Credible set, posterior asymptotics},
year = {2017},
doi = {10.1214/16-AOS1533}}
@article{karhunen:1946,
title={Zur Spektraltheorie stochastischer prozesse},
author={Karhunen, Kari},
year={1946},
journal = {Ann. Acad. Sci. Fenn. Ser. A. I Math.},
volume = "34",
pages = 1--7}
@article{grenander:1950,
author = {Grenander, U.},
title = {Stochastic processes and statistical inference},
journal = {Arkiv Matematik},
volume = {1},
pages = {195--277},
year = {1950}
}
@book{galton:1894,
title={Natural Inheritance},
location="New York",
publisher="Macmillan and Company",
author={Galton, Francis},
edition=5,
year={1894}
}
@article{pearson:1896,
title={VII. Mathematical contributions to the theory of evolution.—III. Regression, heredity, and panmixia},
author={Pearson, Karl},
journal={Philosophical Transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character},
number={187},
pages={253--318},
year={1896},
publisher={The Royal Society London}
}
@unknown{belhakem_et_al:2021,
author = {Belhakem, Ryad and Picard, Franck and Rivoirard, Vincent and Roche, Angelina},
year = {2021},
month = {10},
pages = {},
title = {Minimax estimation of Functional Principal Components from noisy discretized functional data},
doi = "https://doi.org/10.48550/arXiv.2110.12739",
}
@article{cai_low_ma:2014,
ISSN = {01621459},
author = {T. Tony Cai and Mark Low and Zongming Ma},
journal = {Journal of the American Statistical Association},
number = {507},
pages = {1054--1070},
publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
title = {Adaptive Confidence Bands for Nonparametric Regression Functions},
urldate = {2023-03-05},
volume = {109},
year = {2014}
}
@article{cai_yuan:2011,
author = {T. Tony Cai and Ming Yuan},
title = {{Optimal estimation of the mean function based on discretely sampled functional data: Phase transition}},
volume = {39},
journal = {The Annals of Statistics},
number = {5},
publisher = {Institute of Mathematical Statistics},
pages = {2330 -- 2355},
keywords = {functional data, mean function, minimax, phase transition, rate of convergence, reproducing kernel Hilbert space, smoothing splines, Sobolev space},
year = {2011},
doi = {10.1214/11-AOS898},
URL = {https://doi.org/10.1214/11-AOS898}
}
@article{lepski_mammen_spokoiny:1997,
author = {O. V. Lepski and E. Mammen and V. G. Spokoiny},
title = {{Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors}},
volume = {25},
journal = {The Annals of Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {929 -- 947},
keywords = {Bandwidth choice, Besov spaces, kernel estimate, minimax rate of convergence, Spatial adaptation},
year = {1997},
doi = {10.1214/aos/1069362731},
URL = {https://doi.org/10.1214/aos/1069362731}
}
@article{reiss_et_al:2017,
URL = {http://www.jstor.org/stable/44840886},
author = {Philip T. Reiss and Jeff Goldsmith and Han Lin Shang and R. Todd Ogden},
journal = {International Statistical Review / Revue Internationale de Statistique},
number = {2},
pages = {228--249},
publisher = {[Wiley, International Statistical Institute (ISI)]},
title = {Methods for Scalar-on-Function Regression},
urldate = {2023-03-05},
volume = {85},
year = {2017}
}
@article{aneiros_et_al:2019,
title = {Recent advances in functional data analysis and high-dimensional statistics},
journal = {Journal of Multivariate Analysis},
volume = {170},
pages = {3-9},
year = {2019},
note = {Special Issue on Functional Data Analysis and Related Topics},
issn = {0047-259X},
doi = {https://doi.org/10.1016/j.jmva.2018.11.007},
url = {https://www.sciencedirect.com/science/article/pii/S0047259X1830561X},
author = {Germán Aneiros and Ricardo Cao and Ricardo Fraiman and Christian Genest and Philippe Vieu},
keywords = {Functional data analysis, High-dimensional statistics},
}
@article{levitin_et_al:2007,
title={Introduction to Functional Data Analysis},
author={Daniel J. Levitin and Regina L. Nuzzo and Bradley W. Vines and James O. Ramsay},
journal={Canadian Psychology},
year={2007},
volume={48},
pages={135-155}
}