@misc{AronowKallusLopatto2026,
  author = {Aronow, P. M. and Kallus, N. and Lopatto, P.},
  title  = {Nearly minimax rates for functional estimation under rough random design},
  year   = {2026},
  note   = {\href{https://hexagonmath.org/2610.00157?version=1}{hexagon:2610.00157v1}}
}

@misc{AronowLopatto2026v1,
  author = {Aronow, P. M. and Lopatto, P.},
  title  = {On rates attainable under random design: A negative answer to a problem of {Robins}},
  year   = {2026},
  note   = {\href{https://arxiv.org/abs/2607.13170v1}{arXiv:2607.13170v1}}
}

@misc{AronowLopatto2026v2,
  author = {Aronow, P. M. and Lopatto, P.},
  title  = {On rates attainable under random design: A negative answer to a problem of {Robins}},
  year   = {2026},
  note   = {\href{https://arxiv.org/abs/2607.13170v2}{arXiv:2607.13170v2}}
}

@misc{AronowLopatto2026v3,
  author = {Aronow, P. M. and Lopatto, P.},
  title  = {Nearly-minimax variance estimation under rough random design},
  year   = {2026},
  note   = {\href{https://arxiv.org/abs/2607.13170v3}{arXiv:2607.13170v3}}
}

@article{BrownLevine2007,
  author  = {Brown, L. D. and Levine, M.},
  title   = {Variance estimation in nonparametric regression via the difference sequence method},
  journal = {The Annals of Statistics},
  volume  = {35},
  number  = {5},
  pages   = {2219--2232},
  year    = {2007},
  doi     = {10.1214/009053607000000145}
}

@article{BrownLow1996,
  author  = {Brown, L. D. and Low, M. G.},
  title   = {A constrained risk inequality with applications to nonparametric functional estimation},
  journal = {The Annals of Statistics},
  volume  = {24},
  number  = {6},
  pages   = {2524--2535},
  year    = {1996},
  doi     = {10.1214/aos/1032181166}
}

@article{CaiLevineWang2009,
  author  = {Cai, T. T. and Levine, M. and Wang, L.},
  title   = {Variance function estimation in multivariate nonparametric regression with fixed design},
  journal = {Journal of Multivariate Analysis},
  volume  = {100},
  number  = {1},
  pages   = {126--136},
  year    = {2009},
  doi     = {10.1016/j.jmva.2008.03.007}
}

@article{CaiLow2011,
  author  = {Cai, T. T. and Low, M. G.},
  title   = {Testing composite hypotheses, {Hermite} polynomials and optimal estimation of a nonsmooth functional},
  journal = {The Annals of Statistics},
  volume  = {39},
  number  = {2},
  pages   = {1012--1041},
  year    = {2011},
  doi     = {10.1214/10-AOS849}
}

@book{CartierFoata1969,
  author    = {Cartier, P. and Foata, D.},
  title     = {Probl{\`e}mes Combinatoires de Commutation et R{\'e}arrangements},
  series    = {Lecture Notes in Mathematics},
  volume    = {85},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1969},
  doi       = {10.1007/BFb0079468}
}

@misc{ChenLiuMukherjee2024,
  author = {Chen, X. and Liu, L. and Mukherjee, R.},
  title  = {Method-of-moments inference for {GLMs} and doubly robust functionals under proportional asymptotics},
  year   = {2025},
  note   = {\href{https://arxiv.org/abs/2408.06103v3}{arXiv:2408.06103v3}}
}

@article{DetteEtAl1998,
  author  = {Dette, H. and Munk, A. and Wagner, T.},
  title   = {Estimating the variance in nonparametric regression---what is a reasonable choice?},
  journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume  = {60},
  number  = {4},
  pages   = {751--764},
  year    = {1998},
  doi     = {10.1111/1467-9868.00152}
}

@misc{DLMF,
  key          = {DLMF},
  title        = {{NIST Digital Library of Mathematical Functions}},
  howpublished = {\url{https://dlmf.nist.gov/}, Release 1.2.8 of 2026-09-15},
  year         = {2026},
  note         = {F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, eds.}
}

@misc{DobribanEtAl2026,
  author = {Dobriban, E. and Mukherjee, R. and Robins, J. M. and Wang, Z.},
  title  = {Improved variance estimation in homoskedastic nonparametric random-design regression via a two-scale approach},
  year   = {2026},
  note   = {\href{https://arxiv.org/abs/2609.08783v1}{arXiv:2609.08783v1}}
}

@incollection{Dobrushin1996,
  author    = {Dobrushin, R. L.},
  title     = {Estimates of semi-invariants for the {Ising} model at low temperatures},
  booktitle = {Topics in Statistical and Theoretical Physics},
  series    = {American Mathematical Society Translations, Series 2},
  volume    = {177},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  pages     = {59--81},
  year      = {1996},
  doi       = {10.1090/trans2/177/05}
}

@article{DonohoNussbaum1990,
  author  = {Donoho, D. L. and Nussbaum, M.},
  title   = {Minimax quadratic estimation of a quadratic functional},
  journal = {Journal of Complexity},
  volume  = {6},
  number  = {3},
  pages   = {290--323},
  year    = {1990},
  doi     = {10.1016/0885-064X(90)90025-9}
}

@article{DuSchick2009,
  author  = {Du, J. and Schick, A.},
  title   = {A covariate-matched estimator of the error variance in nonparametric regression},
  journal = {Journal of Nonparametric Statistics},
  volume  = {21},
  number  = {3},
  pages   = {263--285},
  year    = {2009},
  doi     = {10.1080/10485250802626873}
}

@article{FanYao1998,
  author  = {Fan, J. and Yao, Q.},
  title   = {Efficient estimation of conditional variance functions in stochastic regression},
  journal = {Biometrika},
  volume  = {85},
  number  = {3},
  pages   = {645--660},
  year    = {1998},
  doi     = {10.1093/biomet/85.3.645}
}

@article{GasserEtAl1986,
  author  = {Gasser, T. and Sroka, L. and Jennen-Steinmetz, C.},
  title   = {Residual variance and residual pattern in nonlinear regression},
  journal = {Biometrika},
  volume  = {73},
  number  = {3},
  pages   = {625--633},
  year    = {1986},
  doi     = {10.1093/biomet/73.3.625}
}

@article{GineNickl2008,
  author  = {Gin{\'e}, E. and Nickl, R.},
  title   = {A simple adaptive estimator of the integrated square of a density},
  journal = {Bernoulli},
  volume  = {14},
  number  = {1},
  pages   = {47--61},
  year    = {2008},
  doi     = {10.3150/07-BEJ110}
}

@article{HallEtAl1990,
  author  = {Hall, P. and Kay, J. W. and Titterington, D. M.},
  title   = {Asymptotically optimal difference-based estimation of variance in nonparametric regression},
  journal = {Biometrika},
  volume  = {77},
  number  = {3},
  pages   = {521--528},
  year    = {1990},
  doi     = {10.1093/biomet/77.3.521}
}

@article{HallMarron1990,
  author  = {Hall, P. and Marron, J. S.},
  title   = {On variance estimation in nonparametric regression},
  journal = {Biometrika},
  volume  = {77},
  number  = {2},
  pages   = {415--419},
  year    = {1990},
  doi     = {10.1093/biomet/77.2.415}
}

@article{Hoeffding1948,
  author  = {Hoeffding, W.},
  title   = {A class of statistics with asymptotically normal distribution},
  journal = {The Annals of Mathematical Statistics},
  volume  = {19},
  number  = {3},
  pages   = {293--325},
  year    = {1948},
  doi     = {10.1214/aoms/1177730196}
}

@article{HuangFan1999,
  author  = {Huang, L.-S. and Fan, J.},
  title   = {Nonparametric estimation of quadratic regression functionals},
  journal = {Bernoulli},
  volume  = {5},
  number  = {5},
  pages   = {927--949},
  year    = {1999},
  doi     = {10.2307/3318450}
}

@misc{JiaoEtAl2015,
  author = {Jiao, J. and Venkat, K. and Han, Y. and Weissman, T.},
  title  = {Minimax estimation of functionals of discrete distributions},
  year   = {2015},
  note   = {\href{https://arxiv.org/abs/1406.6956v5}{arXiv:1406.6956v5}}
}

@inproceedings{KongValiant2018,
  author    = {Kong, W. and Valiant, G.},
  title     = {Estimating learnability in the sublinear data regime},
  booktitle = {Advances in Neural Information Processing Systems},
  volume    = {31},
  pages     = {5455--5464},
  year      = {2018},
  url       = {https://papers.nips.cc/paper_files/paper/2018/hash/8bd39eae38511daad6152e84545e504d-Abstract.html},
  note      = {Locators refer to \href{https://arxiv.org/abs/1805.01626v3}{arXiv:1805.01626v3}}
}

@misc{KrausEtAl2012,
  author = {Kraus, J. K. and Vassilevski, P. S. and Zikatanov, L. T.},
  title  = {Polynomial of best uniform approximation to $x^{-1}$ and smoothing in two-level methods},
  year   = {2012},
  note   = {\href{https://arxiv.org/abs/1002.1859v3}{arXiv:1002.1859v3}}
}

@book{LastPenrose2018,
  author    = {Last, G. and Penrose, M.},
  title     = {Lectures on the {Poisson} Process},
  series    = {Institute of Mathematical Statistics Textbooks},
  volume    = {7},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2018},
  doi       = {10.1017/9781316104477}
}

@article{Laurent1996,
  author  = {Laurent, B.},
  title   = {Efficient estimation of integral functionals of a density},
  journal = {The Annals of Statistics},
  volume  = {24},
  number  = {2},
  pages   = {659--681},
  year    = {1996},
  doi     = {10.1214/aos/1032894458}
}

@book{LehmannCasella1998,
  author    = {Lehmann, E. L. and Casella, G.},
  title     = {Theory of Point Estimation},
  edition   = {Second},
  publisher = {Springer},
  address   = {New York},
  year      = {1998},
  doi       = {10.1007/b98854}
}

@article{LepskiEtAl1999,
  author  = {Lepski, O. and Nemirovski, A. and Spokoiny, V.},
  title   = {On estimation of the {$L_r$} norm of a regression function},
  journal = {Probability Theory and Related Fields},
  volume  = {113},
  number  = {2},
  pages   = {221--253},
  year    = {1999},
  doi     = {10.1007/s004409970006}
}

@article{LiuEtAl2021,
  author  = {Liu, L. and Mukherjee, R. and Robins, J. M. and Tchetgen Tchetgen, E.},
  title   = {Adaptive estimation of nonparametric functionals},
  journal = {Journal of Machine Learning Research},
  volume  = {22},
  number  = {99},
  pages   = {1--66},
  year    = {2021},
  url     = {https://jmlr.org/papers/v22/19-892.html}
}

@article{LiuMukherjeeRobins2020,
  author  = {Liu, L. and Mukherjee, R. and Robins, J. M.},
  title   = {Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning},
  journal = {Statistical Science},
  volume  = {35},
  number  = {3},
  pages   = {545--554},
  year    = {2020},
  doi     = {10.1214/20-STS804},
  note    = {Section~4 is cited from \href{https://arxiv.org/abs/2008.03288v1}{arXiv:2008.03288v1}}
}

@book{MasonHandscomb2003,
  author    = {Mason, J. C. and Handscomb, D. C.},
  title     = {{Chebyshev} Polynomials},
  publisher = {Chapman \& Hall/CRC},
  address   = {Boca Raton, FL},
  year      = {2003}
}

@article{Mathar2006,
  author  = {Mathar, R. J.},
  title   = {Chebyshev series expansion of inverse polynomials},
  journal = {Journal of Computational and Applied Mathematics},
  volume  = {196},
  number  = {2},
  pages   = {596--607},
  year    = {2006},
  doi     = {10.1016/j.cam.2005.10.013},
  note    = {Locators refer to \href{https://arxiv.org/abs/math/0403344v4}{arXiv:math/0403344v4}}
}

@article{McCleanEtAl2024,
  author  = {McClean, A. and Balakrishnan, S. and Kennedy, E. H. and Wasserman, L.},
  title   = {Double cross-fit doubly robust estimators: Beyond series regression},
  journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume  = {88},
  number  = {4},
  pages   = {1469--1491},
  year    = {2026},
  doi     = {10.1093/jrsssb/qkag057},
  note    = {Locators refer to \href{https://arxiv.org/abs/2403.15175v3}{arXiv:2403.15175v3}}
}

@incollection{McDiarmid1989,
  author    = {McDiarmid, C.},
  title     = {On the method of bounded differences},
  booktitle = {Surveys in Combinatorics, 1989},
  editor    = {Siemons, J.},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  pages     = {148--188},
  year      = {1989},
  doi       = {10.1017/CBO9781107359949.008}
}

@misc{MukherjeeNeweyRobins2017,
  author = {Mukherjee, R. and Newey, W. K. and Robins, J. M.},
  title  = {Semiparametric efficient empirical higher order influence function estimators},
  year   = {2017},
  note   = {\href{https://arxiv.org/abs/1705.07577v1}{arXiv:1705.07577v1}}
}

@article{MullerEtAl2003,
  author  = {M{\"u}ller, U. U. and Schick, A. and Wefelmeyer, W.},
  title   = {Estimating the error variance in nonparametric regression by a covariate-matched {U}-statistic},
  journal = {Statistics},
  volume  = {37},
  number  = {3},
  pages   = {179--188},
  year    = {2003},
  doi     = {10.1080/0233188031000078051}
}

@article{MunkEtAl2005,
  author  = {Munk, A. and Bissantz, N. and Wagner, T. and Freitag, G.},
  title   = {On difference-based variance estimation in nonparametric regression when the covariate is high dimensional},
  journal = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume  = {67},
  number  = {1},
  pages   = {19--41},
  year    = {2005},
  doi     = {10.1111/j.1467-9868.2005.00486.x}
}

@misc{NeweyRobins2018,
  author = {Newey, W. K. and Robins, J. M.},
  title  = {Cross-fitting and fast remainder rates for semiparametric estimation},
  year   = {2018},
  note   = {\href{https://arxiv.org/abs/1801.09138v1}{arXiv:1801.09138v1}}
}

@article{OReillyTran2022,
  author  = {O'Reilly, E. and Tran, N. M.},
  title   = {Stochastic geometry to generalize the {Mondrian} process},
  journal = {SIAM Journal on Mathematics of Data Science},
  volume  = {4},
  number  = {2},
  pages   = {531--552},
  year    = {2022},
  doi     = {10.1137/20M1354490},
  note    = {Locators refer to \href{https://arxiv.org/abs/2002.00797v3}{arXiv:2002.00797v3}}
}

@misc{Park2026,
  author = {Park, S.},
  title  = {Minimax estimation of the expected conditional covariance under bounds on the covariate density},
  year   = {2026},
  note   = {\href{https://arxiv.org/abs/2610.05006v1}{arXiv:2610.05006v1}}
}

@article{Rice1984,
  author  = {Rice, J.},
  title   = {Bandwidth choice for nonparametric regression},
  journal = {The Annals of Statistics},
  volume  = {12},
  number  = {4},
  pages   = {1215--1230},
  year    = {1984},
  doi     = {10.1214/aos/1176346788}
}

@article{RichardsonRotnitzky2014,
  author  = {Richardson, T. S. and Rotnitzky, A.},
  title   = {Causal etiology of the research of {James M. Robins}},
  journal = {Statistical Science},
  volume  = {29},
  number  = {4},
  pages   = {459--484},
  year    = {2014},
  doi     = {10.1214/14-STS505}
}

@book{Rivlin1990,
  author    = {Rivlin, T. J.},
  title     = {{Chebyshev} Polynomials: From Approximation Theory to Algebra and Number Theory},
  edition   = {Second},
  publisher = {Wiley},
  address   = {New York},
  year      = {1990}
}

@incollection{RobinsEtAl2008,
  author    = {Robins, J. and Li, L. and Tchetgen, E. and van der Vaart, A.},
  title     = {Higher order influence functions and minimax estimation of nonlinear functionals},
  editor    = {Nolan, D. and Speed, T.},
  booktitle = {Probability and Statistics: Essays in Honor of {David A. Freedman}},
  series    = {Institute of Mathematical Statistics Collections},
  volume    = {2},
  pages     = {335--421},
  publisher = {Institute of Mathematical Statistics},
  address   = {Beachwood, OH},
  year      = {2008},
  doi       = {10.1214/193940307000000527}
}

@article{RobinsEtAl2009EJS,
  author  = {Robins, J. and Tchetgen Tchetgen, E. and Li, L. and van der Vaart, A.},
  title   = {Semiparametric minimax rates},
  journal = {Electronic Journal of Statistics},
  volume  = {3},
  pages   = {1305--1321},
  year    = {2009},
  doi     = {10.1214/09-EJS479}
}

@article{RobinsEtAl2017,
  author  = {Robins, J. M. and Li, L. and Mukherjee, R. and Tchetgen Tchetgen, E. and van der Vaart, A.},
  title   = {Minimax estimation of a functional on a structured high-dimensional model},
  journal = {The Annals of Statistics},
  volume  = {45},
  number  = {5},
  pages   = {1951--1987},
  year    = {2017},
  doi     = {10.1214/16-AOS1515}
}

@article{ScottSokal2005,
  author  = {Scott, A. D. and Sokal, A. D.},
  title   = {The repulsive lattice gas, the independent-set polynomial, and the {Lov{\'a}sz} local lemma},
  journal = {Journal of Statistical Physics},
  volume  = {118},
  number  = {5--6},
  pages   = {1151--1261},
  year    = {2005},
  doi     = {10.1007/s10955-004-2055-4},
  note    = {Locators refer to \href{https://arxiv.org/abs/cond-mat/0309352v2}{arXiv:cond-mat/0309352v2}}
}

@article{ShenGaoWittenHan2020,
  author  = {Shen, Y. and Gao, C. and Witten, D. and Han, F.},
  title   = {Optimal estimation of variance in nonparametric regression with random design},
  journal = {The Annals of Statistics},
  volume  = {48},
  number  = {6},
  pages   = {3589--3618},
  year    = {2020},
  doi     = {10.1214/20-AOS1944},
  note    = {Locators refer to \href{https://arxiv.org/abs/1902.10822v2}{arXiv:1902.10822v2}}
}

@misc{Song2026,
  author = {Song, X.},
  title  = {Batched and complete {U}-statistics for trace-polynomial estimation from classical shadows},
  year   = {2026},
  note   = {\href{https://arxiv.org/abs/2608.22962v1}{arXiv:2608.22962v1}}
}

@article{Spokoiny2002,
  author  = {Spokoiny, V.},
  title   = {Variance estimation for high-dimensional regression models},
  journal = {Journal of Multivariate Analysis},
  volume  = {82},
  number  = {1},
  pages   = {111--133},
  year    = {2002},
  doi     = {10.1006/jmva.2001.2023},
  note    = {Locators refer to the \href{https://www.wias-berlin.de/people/spokoiny/publications/6_Spokoiny_a4_02/jmva99n.pdf}{author manuscript}}
}

@article{Stanley1986,
  author  = {Stanley, R. P.},
  title   = {Two poset polytopes},
  journal = {Discrete \& Computational Geometry},
  volume  = {1},
  number  = {1},
  pages   = {9--23},
  year    = {1986},
  doi     = {10.1007/BF02187680}
}

@article{vanDerVaart2014,
  author  = {van der Vaart, A.},
  title   = {Higher order tangent spaces and influence functions},
  journal = {Statistical Science},
  volume  = {29},
  number  = {4},
  pages   = {679--686},
  year    = {2014},
  doi     = {10.1214/14-STS478}
}

@incollection{Viennot1986,
  author    = {Viennot, G. X.},
  title     = {Heaps of pieces, {I}: Basic definitions and combinatorial lemmas},
  booktitle = {Combinatoire {\'e}num{\'e}rative},
  editor    = {Labelle, G. and Leroux, P.},
  series    = {Lecture Notes in Mathematics},
  volume    = {1234},
  publisher = {Springer},
  address   = {Berlin},
  pages     = {321--350},
  year      = {1986},
  doi       = {10.1007/BFb0072524}
}

@article{WangBrownCaiLevine2008,
  author  = {Wang, L. and Brown, L. D. and Cai, T. T. and Levine, M.},
  title   = {Effect of mean on variance function estimation in nonparametric regression},
  journal = {The Annals of Statistics},
  volume  = {36},
  number  = {2},
  pages   = {646--664},
  year    = {2008},
  doi     = {10.1214/009053607000000901}
}

@article{WuYang2016,
  author  = {Wu, Y. and Yang, P.},
  title   = {Minimax rates of entropy estimation on large alphabets via best polynomial approximation},
  journal = {IEEE Transactions on Information Theory},
  volume  = {62},
  number  = {6},
  pages   = {3702--3720},
  year    = {2016},
  doi     = {10.1109/TIT.2016.2548468}
}

@article{WuYang2019,
  author  = {Wu, Y. and Yang, P.},
  title   = {Chebyshev polynomials, moment matching, and optimal estimation of the unseen},
  journal = {The Annals of Statistics},
  volume  = {47},
  number  = {2},
  pages   = {857--883},
  year    = {2019},
  doi     = {10.1214/17-AOS1665},
  note    = {Locators refer to \href{https://arxiv.org/abs/1504.01227v2}{arXiv:1504.01227v2}}
}