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Research Article

Nonparametric estimation of single-index models in scale-space

, &
Pages 2414-2443 | Received 14 May 2020, Accepted 01 Mar 2021, Published online: 12 Mar 2021

References

  • Sharpe WF. A simplified model for portfolio analysis. Manage Sci. 1963;9:277–293.
  • Hall P. On projection pursuit regression. Ann Stat. 1989;17:573–588.
  • Härdle W, Hall P, Ichimula H. Optimal smoothing in single index models. Ann Stat. 1993;21:157–178.
  • Bellman RE. Adaptive control processes. Princeton, NJ: Princeton University Press; 1961.
  • Ruppert D, Wand MP. Multivariate locally weighted least squares regression. Ann Stat. 1994;22:1346–1370.
  • Silverman BW. Density estimation for statistics and data analysis. London: Chapman and Halls; 1986.
  • Härdle W. Applied nonparametric regression. Cambridge: Cambridge University Press; 1990.
  • Friedman JH, Stuetzle W. Projection pursuit regression. J Am Stat Assoc. 1981;76:817–823.
  • Härdle W, Stoker T. Investigating smooth multiple regression by the method of average derivatives. J Am Stat Assoc. 1989;84:986–995.
  • Nadaraya EA. On estimating regression. Theory Probab Appl. 1964;9:141–142.
  • Watson GS. Smooth regression analysis. Sankhya: Indian J Stat Ser A. 1964;26:359–372.
  • Powell J, Stock J, Stoker T. Semiparametric estimation of index coefficients. Econometrica. 1989;57:1403–1430.
  • Huh J, Park BU. Likelihood-based local polynomial fitting for single-index models. J Multivariate Anal. 2002;80:302–321.
  • Li Q, Lu X, Ullah A. Multivariate local polynomial regression for estimating average derivatives. J Nonparametric Stat. 2003;15:607–624.
  • Lambert-Lacroix S, Peyre J. Local likelihood regression in generalized linear single-index models with applications to microarray data. Comput Stat Data Anal. 2006;51:2091–2113.
  • Escanciano JC, Song K. Testing single-index restrictions with a focus on average derivatives. J Econ. 2010;156:377–391.
  • Cattaneo MD, Crump RK, Jansson M. Bootsrapping density-weighted average derivatives. Econ Theory. 2014;30:1135–1164.
  • Cattaneo MD, Crump RK, Jansson M. Generalized jackknife estimators of weighted average derivatives. J Am Stat Assoc. 2013;108:1243–1256.
  • Li C, Wang Y. Gradient-based bandwidth selection for estimating average derivatives. Econ Lett. 2016;140:19–22.
  • Luo S, Ghosal S. Forward selection and estimation in high dimensional single index models. Stat Methodol. 2016;33:172–179.
  • Chaudhuri P, Marron JS. SiZer for exploration of structures in curves. J Am Stat Assoc. 1999;94:807–823.
  • Chaudhuri P, Marron JS. Scale space view of curve estimation. Ann Stat. 2000;28:408–428.
  • Hannig J, Marron JS. Advanced distribution theory for SiZer. J Am Stat Assoc. 2006;101:484–499.
  • Godtliebsen F, Øigård TA. A visual display device for significant features in complicated signals. Comput Stat Data Anal. 2005;48:317–343.
  • Erästö P, Holmström L. Bayesian multiscale smoothing for making inferences about features in scatter plots. J Comput Graph Stat. 2005;14:569–589.
  • Øigård TA, Rue H, Godtliebsen F. Bayesian multiscale analysis for time series data. Comput Stat Data Anal. 2006;51:1719–1730.
  • Erästö P, Holmström L. Bayesian analysis of features in a scatter plot with dependent observations and errors in predictors. J Stat Comput Simul. 2007;77:421–431.
  • Holmström L, Pasanen L. Bayesian scale space analysis of differences in images. Technometrics. 2012;54:16–29.
  • Zhang JT, Marron JS. SiZer for smoothing splines. Comput Stat. 2005;20:481–502.
  • Li R, Marron JS. Local likelihood SiZer map. Sankhya. 2005;67:476–498.
  • Park C, Huh J. Statistical inference and visualization in scale-space using local likelihood. Comput Stat Data Anal. 2013;57:336–348.
  • Hannig J, Lee T. Robust SiZer for exploration of regression structures and outlier detection. J Comput Graph Stat. 2006;15:101–117.
  • Park C, Lee T, Hannig J. Multiscale exploratory analysis of regression quantiles using quantile SiZer. J Comput Graph Stat. 2010;19:497–513.
  • Park C, Kang K. SiZer analysis for the comparison of regression curves. Comput Stat Data Anal. 2008;52:3954–3970.
  • Park C, Hannig J, Kang KH. Nonparametric comparison of multiple regression curves in scale-space. J Comput Graph Stat. 2014;23:657–677.
  • Park C, Huh J. Nonparametric estimation of a log-variance function in scale-space. J Stat Plan Inference. 2013;143:1766–1780.
  • Zhang HG, Mei CL. SiZer inference for varying coefficient models. Commun Stat Simul Comput. 2012;41:1944–1959.
  • Park C, Marron JS, Rondonotti V. Dependent SiZer: goodness of fit tests for time series models. J Appl Stat. 2004;31:999–1017.
  • Rondonotti V, Marron JS, Park C. SiZer for time series: a new approach to the analysis of trends. Electron J Stat. 2007;1:268–289.
  • Olsen LR, Chaudhuri P, Godtliebsen F. Multiscale spectral analysis for detecting short and long range change points in time series. Comput Stat Data Anal. 2008;52:3310–3330.
  • Olsen LR, Sorbye SH, Godtliebsen F. A scale-space approach for detecting non-stationarities in time series. Scand J Stat. 2008;35:119–138.
  • Park C, Hannig J, Kang K. Improved SiZer for time series. Stat Sin. 2009;19:1511–1530.
  • Park C, Vaughan A, Hannig J, et al. Sizer analysis for the comparison of time series. J Stat Plan Inference. 2009;139:3974–3988.
  • Godtliebsen F, Marron JS, Chaudhuri P. Significance in scale space for bivariate density estimation. J Comput Graph Stat. 2002;11:1–21.
  • Godtliebsen F, Marron JS, Chaudhuri P. Statistical significance of features in digital images. Image Vis Comput. 2004;22:1093–1104.
  • González-Manteiga W, Martinez-Miranda MD, Raya-Miranda R. SiZer map for inference with additive models. Stat Comput. 2008;18:297–312.
  • Vaughan A, Jun M, Park C. Statistical inference and visualization in scale-space for spatially dependent images. J Korean Stat Soc. 2012;41:115–135.
  • Oliveira M, Crujeiras R, Rodráguez-Casal A. CircSiZer: an exploratory tool for circular data. Environ Ecol Stat. 2014;21:143–159.
  • Holmström L, Pasanen L. Statistical scale space methods. Int Stat Rev. 2017;85:1–30.
  • Fan J, Gijbels I. Local polynomial modelling and its applications. London: Chapman & Hall; 1996.
  • Fan J, Heckman NE, Wand MP. Local polynomial kernel regression for generalized linear models and quasi-likelihood functions. J Am Stat Assoc. 1995;90:141–150.
  • R Core Team. R: a language and environment for statistical computing. Vienna R Foundation for Statistical Computing; 2013. Available from: http://www.R-project.org/
  • Ruppert D, Sheather SJ, Wand MP. An effective bandwidth selector for local least squares regression. J Am Stat Assoc. 1995;90:1257–1270.

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