main.bib

@article{koppel2017breaking,
    title   = {Breaking bellman’s curse of dimensionality: Efficient kernel gradient temporal difference},
    author  = {Koppel, Alec and Warnell, G and Stump, E and Stone, P and Ribeiro, Alejandro},
    journal = {arXiv preprint arXiv:1709.04221},
    year    = {2017}
}

@misc{stackexchange_nball,
    title        = {n-Ball Volume and surface with n → $\infty$},
    author       = {Contributors, StackExchange},
    year         = {2023},
    howpublished = {\url{https://math.stackexchange.com/questions/584774/n-ball-volume-and-surface-with-n-rightarrow-infty}},
    note         = {Accessed: 2023-11-08}
}

@misc{kaist_lec8,
    title        = {Lecture 8: High-dimensional Space},
    author       = {KAIST},
    year         = {2021},
    howpublished = {\url{https://alinlab.kaist.ac.kr/resource/2021_AI503_Lec8.pdf}},
    note         = {Accessed: 2023-11-08}
}

@article{brown2020language,
    title   = {Language models are few-shot learners},
    author  = {Brown, Tom and Mann, Benjamin and Ryder, Nick and Subbiah, Melanie and Kaplan, Jared D and Dhariwal, Prafulla and Neelakantan, Arvind and Shyam, Pranav and Sastry, Girish and Askell, Amanda and others},
    journal = {Advances in neural information processing systems},
    volume  = {33},
    pages   = {1877--1901},
    year    = {2020}
}

@article{10.1214/aos/1176345969,
    author    = {Charles J. Stone},
    title     = {{Optimal Global Rates of Convergence for Nonparametric Regression}},
    volume    = {10},
    journal   = {The Annals of Statistics},
    number    = {4},
    publisher = {Institute of Mathematical Statistics},
    pages     = {1040 -- 1053},
    abstract  = {Consider a $p$-times differentiable unknown regression function $\theta$ of a $d$-dimensional measurement variable. Let $T(\theta)$ denote a derivative of $\theta$ of order $m$ and set $r = (p - m)/(2p + d)$. Let $\hat{T}_n$ denote an estimator of $T(\theta)$ based on a training sample of size $n$, and let $\| \hat{T}_n - T(\theta)\|_q$ be the usual $L^q$ norm of the restriction of $\hat{T}_n - T(\theta)$ to a fixed compact set. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for $\| \hat{T}_n - T(\theta)\|_q$ is $n^{-r}$ if $0 < q < \infty$; while $(n^{-1} \log n)^r$ is the optimal rate if $q = \infty$.},
    keywords  = {Nonparametric regression, Optimal rate of convergence},
    year      = {1982},
    doi       = {10.1214/aos/1176345969},
    url       = {https://doi.org/10.1214/aos/1176345969}
}

@article{mammen1999existence,
    title     = {The existence and asymptotic properties of a backfitting projection algorithm under weak conditions},
    author    = {Mammen, Enno and Linton, Oliver and Nielsen, Janni},
    journal   = {The Annals of Statistics},
    volume    = {27},
    number    = {5},
    pages     = {1443--1490},
    year      = {1999},
    publisher = {Institute of Mathematical Statistics}
}

@book{hastie1990generalized,
    title     = {Generalized Additive Models},
    author    = {Hastie, T.J. and Tibshirani, R.J.},
    isbn      = {9780412343902},
    lccn      = {99015185},
    series    = {Chapman \& Hall/CRC Monographs on Statistics \& Applied Probability},
    url       = {https://books.google.fr/books?id=qa29r1Ze1coC},
    year      = {1990},
    publisher = {Taylor \& Francis}
}

@article{lee2018estimation, 
title={Estimation of errors-in-variables partially linear additive models}, 
author={Lee, Eun Ryung and Han, Kyunghee and Park, Byeong U.}, 
journal={Statistica Sinica}, 
volume={28}, 
number={5}, 
pages={2353–2373}, 
year={2018}, 
doi={https://doi.org/10.5705/ss.202017.0101}
}

@article{han2018smooth,
  title={Smooth backfitting for errors-in-variables additive models},
  author={Han, Kyunghee and Park, Byeong U.},
  journal={The Annals of Statistics},
  volume={46},
  number={5},
  pages={2216--2250},
  year={2018},
  publisher={Institute of Mathematical Statistics}
}

@book{Ryan2002,
    author    = {Ryan, Raymond A.},
    note     = {The Radon-Nikod{\'y}m Property : pages 93--126 -- ISBN : 978-1-4471-3903-4},
    title = {Introduction to Tensor Products of Banach Spaces},
    year      = {2002},
    publisher = {Springer London},
    address   = {London},
    pages     = {93--126},
    abstract  = {In this chapter we introduce the Radon-Nikod{\'y}m property for Banach spaces. We begin with a study of vector measures, that is, measures with values in a Banach space. Those spaces for which the classical Radon---Nikod{\'y}m Theorem extends to vector valued measures are said to have the Radon---Nikod{\'y}m property. The identification of injective and projective tensor products of spaces of scalar measures in terms of spaces of vector measures sheds some light on this property. We then examine the representability of various types of operators on C(K) and L1($\mu$) spaces and we uncover some classes of Banach spaces, such as the reflexive spaces and the separable dual spaces, that possess the Radon-;Nikod{\'y}m property. We also relate the possession of this property to the coincidence of the integral and nuclear operators Finally, we give some applications of the Radon-Nikod{\'y}m property, including the Principle of Local Reflexivity.},
    isbn      = {978-1-4471-3903-4},
    doi       = {10.1007/978-1-4471-3903-4_5},
    url       = {https://doi.org/10.1007/978-1-4471-3903-4_5}
}


@article{delaigle2010defining,
    title     = {Defining probability density for a distribution of random functions},
    author    = {Delaigle, Aurore and Hall, Peter},
    journal   = {The Annals of Statistics},
    pages     = {1171--1193},
    year      = {2010},
    publisher = {JSTOR}
}

@article{azais2013remark,
    title   = {Remark on the finite-dimensional character of certain results of functional statistics},
    author  = {Aza{\"\i}s, Jean-Marc and Fort, Jean-Claude},
    journal = {Comptes Rendus. Math{\'e}matique},
    volume  = {351},
    number  = {3-4},
    pages   = {139--141},
    year    = {2013}
}

@online{leGall2006,
    author       = {Jean François Le Gall},
    title        = {Intégration, Probabilités et Processus Aléatoires},
    year         = 2006,
    url          = {https://www.imo.universite-paris-saclay.fr/~jean-francois.le-gall/IPPA2.pdf},
    howpublished = {
        \href{https://www.imo.universite-paris-saclay.fr/~jean-francois.le-gall/IPPA2.pdf}{[télécharger]}
    },
    organization = {Département Mathématiques et Applications, École normale supérieure de Paris}
}

@article{selk2023nonparametric,
    title     = {Nonparametric regression and classification with functional, categorical, and mixed covariates},
    author    = {Selk, Leonie and Gertheiss, Jan},
    journal   = {Advances in Data Analysis and Classification},
    volume    = {17},
    number    = {2},
    pages     = {519--543},
    year      = {2023},
    publisher = {Springer}
}

@article{jeon2020additive,
    title  = {Additive regression with Hilbertian responses},
    author = {Jeon, Jeong Min and Park, Byeong U},
    year   = {2020}
}

@article{cho2023partially,
    title     = {Partially Linear Additive Regression with a General Hilbertian Response},
    author    = {Cho, Sungho and Jeon, Jeong Min and Kim, Dongwoo and Yu, Kyusang and Park, Byeong U},
    journal   = {Journal of the American Statistical Association},
    pages     = {1--15},
    year      = {2023},
    publisher = {Taylor \& Francis}
}

@article{jeon2022additive,
    title   = {Additive Regression with General Imperfect Variables},
    author  = {Jeon, Jeong Min and Van Bever, Germain},
    journal = {arXiv preprint arXiv:2212.05745},
    year    = {2022}
}
@article{lee2023hilbertian,
    title     = {Hilbertian additive regression with parametric help},
    author    = {Lee, Young Kyung and Mammen, Enno and Park, Byeong U},
    journal   = {Journal of Nonparametric Statistics},
    pages     = {1--20},
    year      = {2023},
    publisher = {Taylor \& Francis}
}

@article{bradley2005basic,
    title  = {Basic properties of strong mixing conditions. A survey and some open questions},
    author = {Bradley, Richard C},
    year   = {2005}
}


@article{horowitz2006optimal,
    title     = {Optimal estimation in additive regression models},
    author    = {Horowitz, Joel and Klemel{\"a}, Jussi and Mammen, Enno},
    journal   = {Bernoulli},
    volume    = {12},
    number    = {2},
    pages     = {271--298},
    year      = {2006},
    publisher = {Bernoulli Society for Mathematical Statistics and Probability}
}