Abstract
Functional analysis of variance (FANOVA) models have been utilized by several authors and proven to be useful in several fields.
Guard against the prestige of great names; see that your judgments are your own; and do not shrink from disagreement; no trusting without testing.
Lord Acton Dalberg (1834–1902)
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Bibliography
F. Abramovich, C. Angelini, Testing in mixing effects FANOVA models. J. Stat. Plan. Inference 136, 4326–4348 (2006)
F. Abramovich, A. Antoniadis, T. Sapatinas, B. Vidakovic, Optimal testing in a fixed effects functional analysis of variance model. Int. J. Wavelets Multiresolution Inf. Process. 2(4), 323–349 (2004)
L.D. Brown, M. Low, Asymptotic equivalence of nonparametric regression and white noise. Ann. Stat. 24(6), 2384–2398 (1996)
I. Daubechies, Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61 (Society for Industrial and Applied Mathematics, Philadelphia, 1992)
D. Donoho, I.M. Johnstone, Minimax estimation via wavelet shrinkage. Ann. Stat. 26(3), 879–921 (1998)
D. Donoho, I.M. Johnstone, Asymptotic minimaxity of wavelet estimators with sampled data. Stat. Sin. 9, 1–32 (1999)
J. Fan, S.-K. Lin, Test of significance when data are curves. J. Am. Stat. Assoc. 93(443), 1007–1021 (1998)
R.A. Fisher, The fiducial argument in statistical inference. Ann. Eugenics 6, 391–398 (1935)
J.L. Horowitz, V.G. Spokoiny, An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica, 69, 599–631 (2001)
Y.I. Ingster, Asymptotically minimax hypothesis testing for nonparametric alternatives: I. Math. Methods Stat. 2, 85–114 (1993a)
Y.I. Ingster, Asymptotically minimax hypothesis testing for nonparametric alternatives: II. Math. Methods Stat. 3, 171–189 (1993b)
Y.I. Ingster, Asymptotically minimax hypothesis testing for nonparametric alternatives: III. Math. Methods Stat. 4, 249–268 (1993c)
J. Klemalä, Sharp adaptive estimation of quadratic functionals. Probab. Theory Relat. Fields 134(4), 539–564 (2006)
L. Le Cam, Asymptotic Methods in Statistical Decision Theory (Springer, New York, 1986)
O. Lepski, V.G. Spokoiny, Minimax nonparametric hypothesis testing: the case of inhomogeneous alternative. Bernoulli 5, 333–358 (1999)
Y. Meyer, Wavelets and Operators (Cambridge University Press, Cambridge, 1992)
P.A. Morettin, Waves and Wavelets: From Fourier to Wavelet Analysis of Time Series (University of São Paulo Press, São Paulo, 2014)
M. Nussbaum, Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Stat. 25(4), 2399–2430 (1996)
J.O. Ramsay, B.W. Silverman, Functional Data Analysis, 2nd edn. (Springer, New York, 2006)
V.G. Spokoiny, Adaptive hypothesis testing using wavelets. Ann. Stat. 24, 2477–2498 (1996)
P. Wojtaszczyk, A Mathematical Introduction to Wavelets (Cambridge University Press, Cambridge, 1999)
G.W. Wornell, Signal Processing with Fractals: A Wavelet Based Approach (Prentice Hall, Englewood Cliffs, NJ, 1996)
J.T. Zhang, Analysis of Variance for Functional Data (Chapman & Hall, Boca Raton, FL, 2014)
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Morettin, P.A., Pinheiro, A., Vidakovic, B. (2017). Functional ANOVA. In: Wavelets in Functional Data Analysis. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-59623-5_5
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DOI: https://doi.org/10.1007/978-3-319-59623-5_5
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