References
- I. Ahmad and Q. Li, Testing symmetry of an unknown density function by kernel method, J. Nonparametr. Stat. 7 (1997), pp. 279–293. doi: 10.1080/10485259708832704
- M.G. Akritas and I. Van Keilegom, Non-parametric estimation of the residual distribution, Scand. J. Statist. 28 (2001), pp. 549–567. doi: 10.1111/1467-9469.00254
- G. Aneiros-Pérez, F. Ferraty and P. Vieu, Variable selection in partial linear regression with functional covariate, Statist.: A J. Theor. Appl. Statist. 49 (2015), pp. 1322–1347. doi: 10.1080/02331888.2014.998675
- G. Aneiros-Pérez and P. Vieu, Semi-functional partial linear regression, Stat. Probab. Lett. 76 (2006), pp. 1102–1110. doi: 10.1016/j.spl.2005.12.007
- G. Aneiros-Pérez and P. Vieu, Partial linear modelling with multi-functional covariates, Comput. Stat. 30 (2015), pp. 647–671. doi: 10.1007/s00180-015-0568-8
- J. Barrientos-Marin, F. Ferraty and P. Vieu, Locally modelled regression and functional data, J. Nonparametr. Stat. 22 (2010), pp. 617–632. doi: 10.1080/10485250903089930
- K. Benhenni, F. Ferraty, M. Rachdi, and P. Vieu, Local smoothing regression with functional data, Comput. Stat. 22 (2007), pp. 353–369. doi: 10.1007/s00180-007-0045-0
- A. Berlinet, A. Elamine, and A. Mas, Local linear regression for functional data, Ann. Inst. Stat. Math. 63 (2011), pp. 1047–1075. doi: 10.1007/s10463-010-0275-8
- E. Boj, P. Delicado, and J. Fortiana, Distance-based local linear regression for functional predictors, Comput. Stat. Data Anal. 54 (2010), pp. 429–437. doi: 10.1016/j.csda.2009.09.010
- A.W. Bowman, An alternative method of cross-validation for the smoothing of density estimates, Biometrika 71 (1984), pp. 353–360. doi: 10.1093/biomet/71.2.353
- F. Burba, F. Ferraty, and P. Vieu, k-nearest neighbour method in functional nonparametric regression, J. Nonparametr. Stat. 21 (2009), pp. 453–469. doi: 10.1080/10485250802668909
- H. Cardot, F. Ferraty, and P. Sarda, Spline estimators for the functional linear model, Stat. Sin. 13 (2003), pp. 571–591.
- H. Chen, R. Smyth, and X. Zhang, A Bayesian sampling approach to measuring the price responsiveness of gasoline demand using a constrained partially linear model, Energy Econ. 67 (2017), pp. 346–354. doi: 10.1016/j.eneco.2017.08.029
- L.-H. Chen, M.-Y. Cheng, and L. Peng, Conditional variance estimation in heteroscedastic regression models, J. Stat. Plan. Inference 139 (2009), pp. 236–245. doi: 10.1016/j.jspi.2008.04.020
- F. Cheng and S. Sun, A goodness-of-fit test of the errors in nonlinear autoregressive time series models, Stat. Probab. Lett. 78 (2008), pp. 50–59. doi: 10.1016/j.spl.2007.05.003
- V. Chernozhukov and H. Hong, An MCMC approach to classical estimation, J. Econom. 115 (2003), pp. 293–346. doi: 10.1016/S0304-4076(03)00100-3
- S. Chib, Marginal likelihood from the Gibbs output, J. Amer. Statist. Assoc.: Theory Method 90 (1995), pp. 1313–1321. doi: 10.1080/01621459.1995.10476635
- R. Davidson and J.G. MacKinnon, Several tests for model specification in the presence of alternative hypotheses, Econometrica 49 (1981), pp. 781–793. doi: 10.2307/1911522
- C. de Boor, A Practical Guide to Splines, Revised ed., volume 27 of Applied Mathematical Sciences. Springer, New York, 2001.
- S. Efromovich, Estimation of the density of regression errors, Ann. Stat. 33 (2005), pp. 2194–2227. doi: 10.1214/009053605000000435
- P.H.C. Eilers, B. Li, and B.D. Marx, Multivariate calibration with single-index signal regression, Chemometr. Intell. Lab. Syst. 96 (2009), pp. 196–202. doi: 10.1016/j.chemolab.2009.02.001
- J.C. Escanciano and D.T. Jacho-Chávez, n uniformly consistent density estimation in nonparametric regression models, J. Econom. 167 (2012), pp. 305–316. doi: 10.1016/j.jeconom.2011.09.017
- F. Ferraty, P. Hall, and P. Vieu, Most-predictive design points for functional data predictors, Biometrika 97 (2010), pp. 807–824. doi: 10.1093/biomet/asq058
- F. Ferraty, A. Laksaci, and P. Vieu, Functional time series prediction via conditional mode estimation, C. R. Acad. Sci. Paris Ser. I 340 (2005), pp. 389–392. doi: 10.1016/j.crma.2005.01.016
- F. Ferraty, I. Van Keilegom, and P. Vieu, On the validity of the bootstrap in non-parametric functional regression, Scand. J. Statist. 37 (2010), pp. 286–306. doi: 10.1111/j.1467-9469.2009.00662.x
- F. Ferraty and P. Vieu, The functional nonparametric model and application to spectrometric data, Comput. Stat. 17 (2002), pp. 545–564. doi: 10.1007/s001800200126
- F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis: Theory and Practice, Springer, New York, 2006.
- F. Ferraty and P. Vieu, Additive prediction and boosting for functional data, Comput. Stat. Data Anal. 53 (2009), pp. 1400–1413. doi: 10.1016/j.csda.2008.11.023
- F. Ferraty and P. Vieu, Richesse et complexité des données fonctionnelles, Revue MODULAD 43 (2011), pp. 25–43.
- J. Friedman, T. Hastie, and R. Tibshirani, Regularization paths for generalized linear models via coordinate descent, J. Stat. Softw. 33 (2010), pp. 1–22. doi: 10.18637/jss.v033.i01
- P.H. Garthwaite, Y. Fan, and S.A. Sisson, Adaptive optimal scaling of Metropolis-Hastings algorithms using the Robbins-Monro process, Comm Statist Theory Methods 45 (2016), pp. 5098–5111. doi: 10.1080/03610926.2014.936562
- A.E. Gelfand and D.K. Dey, Bayesian model choice: Asymptotics and exact calculations, J. R. Stat. Soc. Ser. B 56 (1994), pp. 501–514.
- J. Goldsmith, J. Bobb, C.M. Crainiceanu, B. Caffo, and D. Reich, Penalized functional regression, J. Comput. Graph. Stat. 20 (2011), pp. 830–851. doi: 10.1198/jcgs.2010.10007
- J. Goldsmith and F. Scheipl, Estimator selection and combination in scalar-on-function regression, Comput. Stat. Data Anal. 70 (2014), pp. 362–372. doi: 10.1016/j.csda.2013.10.009
- C. Gourieroux, A. Monfort, and A. Trognon, Pseudo maximum likelihood methods: Theory, Econometrica 52 (1984), pp. 681–700. doi: 10.2307/1913471
- C. Goutis, Second-derivative functional regression with applications to near infra-red spectroscopy, J. R. Stat. Soc. Ser. B 60 (1998), pp. 103–114. doi: 10.1111/1467-9868.00111
- R.E. Kass and A.E. Raftery, Bayes factors, J. Amer. Statist. Assoc.: Rev. Paper 90 (1995), pp. 773–795. doi: 10.1080/01621459.1995.10476572
- S. Kim, N. Shephard, and S. Chib, Stochastic volatility: Likelihood inference and comparison with ARCH models, Rev. Econ. Stud. 65 (1998), pp. 361–393. doi: 10.1111/1467-937X.00050
- N. Krämer, A.-L. Boulesteix, and G. Tutz, Penalized partial least squares with application to B-spline transformations and functional data, Chemometr. Intell. Lab. Syst. 94 (2008), pp. 60–69. doi: 10.1016/j.chemolab.2008.06.009
- S. Kullback, Information Theory and Statistics, Wiley, New York, 1959.
- A. Laksaci, M. Lemdani, and E.O. Saïd, Asymptotic results for an L1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology, Sankhyā 73-A (2011), pp. 125–141. doi: 10.1007/s13171-011-0002-4
- H. Lian, Functional partial linear model, J. Nonparametr. Stat. 23 (2011), pp. 115–128. doi: 10.1080/10485252.2010.500385
- N. Ling, G. Aneiros, and P. Vieu, kNN estimation in functional partial linear modeling, Statist. Papers 61 (2020), pp. 423–444. doi: 10.1007/s00362-017-0946-0
- J.S. Marron and M.P. Wand, Exact mean integrated squared error, Ann. Stat. 20 (1992), pp. 712–736. doi: 10.1214/aos/1176348653
- A. Mas and B. Pumo, Functional linear regression with derivatives, J. Nonparametr. Stat. 21 (2009), pp. 19–40. doi: 10.1080/10485250802401046
- R. Meyer and J. Yu, BUGS for a Bayesian analysis of stochastic volatility models, Econom. J. 3 (2000), pp. 198–215. doi: 10.1111/1368-423X.00046
- B. Muhsal and N. Neumeyer, A note on residual-based empirical likelihood kernel density estimation, Electron. J. Stat. 4 (2010), pp. 1386–1401. doi: 10.1214/10-EJS586
- U. Müller, Risk of Bayesian inference in misspecified models, and the sandwich covariance matrix, Econometrica 81 (2013), pp. 1805–1849. doi: 10.3982/ECTA9097
- N. Neumeyer and H. Dette, Testing for symmetric error distribution in nonparametric regression models, Stat. Sin. 17 (2007), pp. 775–795.
- M. Rachdi and P. Vieu, Nonparametric regression for functional data: Automatic smoothing parameter selection, J. Stat. Plan. Inference 137 (2007), pp. 2784–2801. doi: 10.1016/j.jspi.2006.10.001
- J. Ramsay and B. Silverman, Functional Data Analysis, 2nd ed., Springer, New York, 2005.
- P.T. Reiss, J. Goldsmith, H.L. Shang, and R.T. Ogden, Methods for scalar-on-function regression, Int. Statist. Rev. 85 (2017), pp. 228–249. doi: 10.1111/insr.12163
- P.T. Reiss and R.T. Ogden, Functional principal component regression and functional partial least squares, J. Am. Stat. Assoc. 102 (2007), pp. 984–996. doi: 10.1198/016214507000000527
- G.O. Roberts and J.S. Rosenthal, Examples of adaptive MCMC, J. Comput. Graph. Stat. 18 (2009), pp. 349–367. doi: 10.1198/jcgs.2009.06134
- H.L. Shang, Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density, Comput. Stat. Data Anal. 67 (2013), pp. 185–198. doi: 10.1016/j.csda.2013.05.006
- H.L. Shang, Bayesian bandwidth estimation for a nonparametric functional regression model with mixed types of regressors and unknown error density, J. Nonparametr. Stat. 26 (2014), pp. 599–615. doi: 10.1080/10485252.2014.916806
- H.L. Shang, Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density, Comput. Stat. 29 (2014), pp. 829–848. doi: 10.1007/s00180-013-0463-0
- H.L. Shang, A Bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-function quantile regression with unknown error density and dependent functional data, J. Multivar. Anal. 146 (2016), pp. 95–104. doi: 10.1016/j.jmva.2015.06.015
- H.L. Shang, Estimation of a functional single index model with dependent errors and unknown error density, Comm Statist Simulation Computation (2020). Available at https://www.tandfonline.com/doi/abs/10.1080/03610918.2018.1535068?journalCode=lssp20.
- R. Shibata, An optimal selection of regression variables, Biometrika 68 (1981), pp. 45–54. doi: 10.1093/biomet/68.1.45
- S.N. Wood, Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models, J. R. Stat. Soc. Ser. B 73 (2011), pp. 3–36. doi: 10.1111/j.1467-9868.2010.00749.x
- J. You and X. Zhou, Statistical inference in a panel data semiparametric regression model with serially correlated errors, J. Multivar. Anal. 97 (2006), pp. 844–873. doi: 10.1016/j.jmva.2005.04.005
- X. Zhang and M.L. King, Bayesian semiparametric GARCH models, Working Paper 24, Monash University, 2011. Available at https://www.monash.edu/business/econometrics-and-business-statistics/research/publications/ebs/wp24-11.pdf.
- X. Zhang, M.L. King, and H.L. Shang, Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density, Working Paper 10, Monash University, 2011. Available at https://www.monash.edu/business/econometrics-and-business-statistics/research/publications/ebs/wp10-11.pdf.