143
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Minimax wavelet estimation for multisample heteroscedastic nonparametric regression

, &
Pages 238-261 | Received 01 Apr 2016, Accepted 02 Sep 2017, Published online: 27 Nov 2017

References

  • Amato, U., and Sapatinas, T. (2005), ‘Wavelet Shrinkage Approaches to Baseline Signal Estimation from Repeated Noisy Measurements’, Advances and Applications in Statistics, 51, 21–50.
  • Antoniadis, A., and Fan, J. (2001), ‘Regularization of Wavelet Approximations’, Journal of the American Statistical Association, 96, 939–967. doi: 10.1198/016214501753208942
  • Antoniadis, A., and Lavergne, C. (1995), ‘Variance Function Estimation in Regression by Wavelet Methods’, Lecture Notes in Statistics ‘Wavelets and Statistics’, 103, 31–42. doi: 10.1007/978-1-4612-2544-7_3
  • Antoniadis, A., and Sapatinas, T. (2007), ‘Estimation and Inference in Functional Mixed-Effects Models’, Computational Statistics & Data Analysis, 51, 4793–4813. doi: 10.1016/j.csda.2006.09.038
  • Antoniadis, A., Bigot, J., Lambert-Lacroix, S., and Letue, F. (2007), ‘Non Parametric Pre-Processing Methods and Inference Tools for Analyzing Time-of-Flight Mass Spectrometry Data’, Current Analytical Chemistry, 3, 127–147. doi: 10.2174/157341107780361718
  • Arribas-Gil, A., Bertin, K., Meza, C., and Rivoirard, V. (2014), ‘LASSO-Type Estimators for Semiparametric Nonlinear Mixed-Effects Models Estimation’, Statistics and Computing, 24, 443–460. doi: 10.1007/s11222-013-9380-x
  • Cai, T.T., and Brown, L.D. (1998), ‘Wavelet Shrinkage for Nonequispaced Samples’, The Annals of Statistics, 26, 1783–1799. doi: 10.1214/aos/1024691357
  • Cai, T.T., and Wang, L. (2008), ‘Adaptive variance function estimation in heteroscedastic nonparametric regression’, The Annals of Statistics, 36, 2025–2054. doi: 10.1214/07-AOS509
  • Coifman, R., and Donoho, D. (1995), ‘Translation Invariant De-Noising’, Wavelets and Statistics, 103, 125–150. doi: 10.1007/978-1-4612-2544-7_9
  • Delyon, B., and Juditsky, A. (1997), ‘On the Computation of Wavelet Coefficients’, Journal of Approximation Theory, 88, 47–79. doi: 10.1006/jath.1996.3008
  • DeVore, R., and Lorentz, G (1993), Constructive Approximation, Heidelberg: Springer Verlag.
  • Donoho, D. (1994), ‘Smooth Wavelet Decompositions with Blocky Coefficient Kernels’, Recent Advances in Wavelet Analysis, ed. L. Schumaker. Boston: Academic Press.
  • Donoho, D., and Johnstone, I. (1994), ‘Ideal Spatial Adaptation by Wavelet Shrinkage’, Biometrika, 81, 425–455. doi: 10.1093/biomet/81.3.425
  • Donoho, D.L., and Johnstone, I.M. (1995), ‘Adapting to Unknown Smoothness via Wavelet Shrinkage’, Journal of the American Statistical Association, 90, 1200–1224. doi: 10.1080/01621459.1995.10476626
  • Donoho, D., Johnstone, I., Kerkyacharian, G., and Picard, D. (1995), ‘Wavelet Shrinkage: Asymptopia’, Journal of the Royal Statistical Society, Series B, 57, 371–394.
  • Eckel-Passow, J.E., Oberg, A.L., Therneau, T.M., and Bergen, H.R. (2009), ‘An Insight Into High-Resolution Mass-Spectrometry Data’, Biostatistics, 10, 481–500. doi: 10.1093/biostatistics/kxp006
  • Fan, J., and Li, R. (2001), ‘Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties’, Journal of the American Statistical Association, 96, 1348–1360. doi: 10.1198/016214501753382273
  • Frazier, M., Jawerth, B., and Weiss, G (1991), Littlewood–Paley Theory and the Study of Function Spaces, Vol. 79, Providence: American Mathematical Society.
  • Gasser, T., Stroka, L., and Jennen-Steinmetz, C. (1989), ‘Residual Variance and Residual Pattern in Nonlinear Regression’, Biometrika, 73, 625–633. doi: 10.1093/biomet/73.3.625
  • Giacofci, M., Lambert-Lacroix, S., Marot, G., and Picard, F. (2013), ‘Wavelet-Based Clustering for Mixed-Effects Functional Models in High Dimension’, Biometrics, 69, 31–40. doi: 10.1111/j.1541-0420.2012.01828.x
  • Hall, P., and Turlach, B.A. (1997), ‘Interpolation Methods for Nonlinear Wavelet Regression with Irregularly Spaced Design’, The Annals of Statistics, 25, 1912–1925. doi: 10.1214/aos/1069362378
  • Härdle, W., Kerkyacharian, G., Picard, D., and Tsybakov, A (1998), Wavelets, Approximation and Statistical Applications, New York: Springer.
  • Johnstone, I.M., and Silverman, B.W. (1997), ‘Wavelet Threshold Estimators for Data with Correlated Noise’, Journal of the Royal Statistical Society, Series B, 59, 319–351. doi: 10.1111/1467-9868.00071
  • Juditsky, A., and Delyon, B. (1996), ‘On Minimax Wavelet Estimators’, Applied and computational harmonic analysis, 3, 215–228. doi: 10.1006/acha.1996.0017
  • Kovac, A., and Silverman, B.W. (2000), ‘Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding’, Journal of the American Statistical Association, 95, 172–183. doi: 10.1080/01621459.2000.10473912
  • Mallat, S. (1999), A Wavelet Tour of Signal Processing, San Diego: Academic Press.
  • Morris, J.S., and Carroll, R.J. (2006), ‘Wavelet-Based Functional Mixed Models’, Journal of the Royal Statistical Society Series B Statistical Methodology, 68, 179–199. doi: 10.1111/j.1467-9868.2006.00539.x
  • Morris, J., Brown, P., Herrick, R., Baggerly, K., and Coombes, K.R. (2008), ‘Bayesian Analysis of Mass Spectrometry Proteomic Data using Wavelet-Based Functional Mixed Models’, Biometrics, 64, 479–489. doi: 10.1111/j.1541-0420.2007.00895.x
  • Nason, G. (2008), Wavelet Methods in Statistics with R, New York: Springer.
  • Ogden, R.T. (1997), ‘On Preconditioning the Data for the Wavelet Transform when the Sample Size is Not a Power of Two’, Communications in Statistics - Simulation and Computation, 26, 467–486. doi: 10.1080/03610919708813391
  • Park, C. (2010), ‘Block Thresholding Wavelet Regression using {SCAD} Penalty’, Journal of Statistical Planning and Inference, 140, 2755–2770. doi: 10.1016/j.jspi.2010.03.035
  • Pensky, M., and Vidakovic, B. (2001), ‘On Non-Equally Spaced Wavelet Regression’, Annals of the Institute of Statistical Mathematics, 53, 681–690. doi: 10.1023/A:1014640632666
  • Petricoin, E.F., Ardekani, A.M., Hitt, B.A., Levine, P.J., Fusaro, V.A., Steinberg, S.M., Mills, G.B., Simone, C., Fishman, D.A., Kohn, E.C., and Liotta, L.A. (2002), ‘Use of Proteomic Patterns in Serum to Identify Ovarian Cancer’, The Lancet, 359, 572–577. doi: 10.1016/S0140-6736(02)07746-2
  • Scheipl, F., Staicu, A.M., and Greven, S. (2015), ‘Functional Additive Mixed Models’, Journal of Computational and Graphical Statistics, 24, 477–501. doi: 10.1080/10618600.2014.901914
  • Stein, C.M. (1981), ‘Estimation of the Mean of a Multivariate Normal Distribution’, The Annals of Statistics, 9, 1135–1151. doi: 10.1214/aos/1176345632
  • von Sachs, R., and MacGibbon, B. (2000), ‘Non-parametric Curve Estimation by Wavelet Thresholding with Locally Stationary Errors’, Scandinavian Journal of Statistics, 27, 475–499. doi: 10.1111/1467-9469.00202

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.