466
Views
2
CrossRef citations to date
0
Altmetric
Functional, Graph, and Tree-Based Approaches

Improving Estimation in Functional Linear Regression With Points of Impact: Insights Into Google AdWords

, &
Pages 814-826 | Received 25 May 2018, Accepted 30 Mar 2020, Published online: 19 May 2020

References

  • Cardot, H., Crambes, C., Kneip, A., and Sarda, P. (2007), “Smoothing Splines Estimators in Functional Linear Regression With Errors-in-Variables,” Computational Statistics & Data Analysis, 51, 4832–4848. DOI: 10.1016/j.csda.2006.07.029.
  • Cardot, H., Mas, A., and Sarda, P. (2007), “CLT in Functional Linear Regression Models,” Probability Theory and Related Fields, 138, 325–361. DOI: 10.1007/s00440-006-0025-2.
  • Chiou, J.-M. (2012), “Dynamical Functional Prediction and Classification, With Application to Traffic Flow Prediction,” The Annals of Applied Statistics, 6, 1588–1614. DOI: 10.1214/12-AOAS595.
  • Choi, H., and Reimherr, M. (2018), “A Geometric Approach to Confidence Regions and Bands for Functional Parameters,” Journal of the Royal Statistical Society, Series B, 80, 239–260. DOI: 10.1111/rssb.12239.
  • Crambes, C., Kneip, A., and Sarda, P. (2009), “Smoothing Splines Estimators for Functional Linear Regression,” The Annals of Statistics, 37, 35–72. DOI: 10.1214/07-AOS563.
  • de Boor, C. (2001), A Practical Guide to Splines, New York: Springer.
  • Doty, D., Sruoginis, K., and Silverman, D. (2016), “IAB/PwC Internet Advertising Revenue Report,” available at www.iab.com/adrevenuereport.
  • Ferraty, F., Hall, P., and Vieu, P. (2010), “Most-Predictive Design Points for Functional Data Predictors,” Biometrika, 97, 807–824. DOI: 10.1093/biomet/asq058.
  • Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis—Theory and Practice, New York: Springer.
  • Fraiman, R., Gimenez, Y., and Svarc, M. (2016), “Feature Selection for Functional Data,” Journal of Multivariate Analysis, 146, 191–208. DOI: 10.1016/j.jmva.2015.09.006.
  • Geddes, B. (2014), Advanced Google AdWords, Hoboken, NJ: Wiley.
  • Gellar, J. E., Colantuoni, E., Needham, D. M., and Crainiceanu, C. M. (2014), “Variable-Domain Functional Regression for Modeling ICU Data,” Journal of the American Statistical Association, 109, 1425–1439. DOI: 10.1080/01621459.2014.940044.
  • Goldsmith, J., Bobb, J., Crainiceanu, C. M., Caffo, B., and Reich, D. (2010), “Penalized Functional Regression,” Journal of Computational and Graphical Statistics, 20, 830–851. DOI: 10.1198/jcgs.2010.10007.
  • Goldsmith, J., Crainiceanu, C. M., Caffo, B., and Reich, D. (2012), “Longitudinal Penalized Functional Regression for Cognitive Outcomes on Neuronal Tract Measurements,” Journal of the Royal Statistical Society, Series C, 61, 453–469. DOI: 10.1111/j.1467-9876.2011.01031.x.
  • Gromenko, O., Kokoszka, P., and Sojka, J. (2017), “Evaluation of the Cooling Trend in the Ionosphere Using Functional Regression With Incomplete Curves,” The Annals of Applied Statistics, 11, 898–918. DOI: 10.1214/17-AOAS1022.
  • Hall, P., and Horowitz, J. L. (2007), “Methodology and Convergence Rates for Functional Linear Regression,” The Annals of Statistics, 35, 70–91. DOI: 10.1214/009053606000000957.
  • Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models (Vol. 43), Boca Raton, FL: CRC Press.
  • Horváth, L., and Kokoszka, P. (2012), Inference for Functional Data With Applications, New York: Springer.
  • Hsing, T., and Eubank, R. (2015), Theoretical Foundations of Functional Data Analysis, With an Introduction to Linear Operators, Chichester: Wiley.
  • Kneip, A., Poss, D., and Sarda, P. (2016), “Functional Linear Regression With Points of Impact,” The Annals of Statistics, 44, 1–30. DOI: 10.1214/15-AOS1323.
  • Koeppe, R., Zhu, J., Nan, B., and Wang, X. (2014), “Regularized 3D Functional Regression for Brain Image Data via Haar Wavelets,” The Annals of Applied Statistics, 8, 1045–1064. DOI: 10.1214/14-AOAS736.
  • Lindquist, M. A., and McKeague, I. W. (2009), “Logistic Regression With Brownian-Like Predictors,” Journal of the American Statistical Association, 104, 1575–1585. DOI: 10.1198/jasa.2009.tm08496.
  • Liu, B., and Müller, H.-G. (2008), “Functional Data Analysis for Sparse Auction Data,” in Statistical Methods in eCommerce Research, eds. W. Jank and G. Shmueli, New York: Wiley, pp. 269–290.
  • Maronna, R. A., and Yohai, V. J. (2013), “Robust Functional Linear Regression Based on Splines,” Computational Statistics & Data Analysis, 65, 46–55. DOI: 10.1016/j.csda.2011.11.014.
  • Matsui, H., and Konishi, S. (2011), “Variable Selection for Functional Regression Models via the L1 Regularization,” Computational Statistics & Data Analysis, 55, 3304–3310. DOI: 10.1016/j.csda.2011.06.016.
  • McKeague, I. W., and Sen, B. (2010), “Fractals With Point Impact in Functional Linear Regression,” The Annals of Statistics, 38, 2559–2586. DOI: 10.1214/10-aos791.
  • Poß, D., Liebl, D., Kneip, A., Eisenbarth, H., Wager, T. D., and Barrett, L. F. (2020), “Super-Consistent Estimation of Points of Impact in Nonparametric Regression With Functional Predictors,” Working Paper, arXiv no. 1905.09021.
  • Ramsay, J., and Silverman, B. (2005), Functional Data Analysis (2nd ed.), New York: Springer.
  • R Core Team (2017), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Reddy, S. K., and Dass, M. (2006), “Modeling On-Line Art Auction Dynamics Using Functional Data Analysis,” Statistical Science, 21, 179–193. DOI: 10.1214/088342306000000196.
  • Reiss, P. T., Goldsmith, J., Shang, H. L., and Ogden, R. T. (2016), “Methods for Scalar-on-Function Regression,” International Statistical Review, 85, 228–249. DOI: 10.1111/insr.12163.
  • Torrecilla, J. L., Berrendero, J. R., and Cuevas, A. (2016), “Variable Selection in Functional Data Classification: A Maxima-Hunting Proposal,” Statistica Sinica, 26, 619–638. DOI: 10.5705/ss.202014.0014.
  • Wang, S., Jank, W., and Shmueli, G. (2008), “Explaining and Forecasting Online Auction Prices and Their Dynamics Using Functional Data Analysis,” Journal of Business & Economic Statistics, 26, 144–160. DOI: 10.1198/073500106000000477.
  • Wang, S., Jank, W., Shmueli, G., and Smith, P. (2008), “Modeling Price Dynamics in eBay Auctions Using Differential Equations,” Journal of the American Statistical Association, 103, 1100–1118. DOI: 10.1198/016214508000000670.
  • Zhang, S., Jank, W., and Shmueli, G. (2010), “Real-Time Forecasting of Online Auctions via Functional k-Nearest Neighbors,” International Journal of Forecasting, 26, 666–683. DOI: 10.1016/j.ijforecast.2009.08.006.

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.