Recursive kernel estimator in a semiparametric regression model

References

• Amiri, A. (2009), ‘Sur une famille paramétrique d'estimateurs séquentiels de la densité pour un processus fortement mélangeant’, Comptes Rendus de L'académie Des Sciences I, 347, 309–314.
   Google Scholar
• Aragon, Y., and Sarraco, J. (1997), ‘Sliced Inverse Regression (SIR): An Appraisal of Small Sample Alternatives to Slicing’, Computational Statistics, 12, 109–130.
   Web of Science ®Google Scholar
• Bercu, B., Nguyen, T., and Sarraco, J. (2012), ‘A New Approach on Recursive and Non-recursive Sir Methods’, Journal of the Korean Statistical Society, 41, 17–36.
   Web of Science ®Google Scholar
• Cook, R. (1994), ‘Using Dimension Reduction Subspaces to Identify Important Inputs in Models of Physical Systems’, in Proceedings of the Section on Physical and Engineering Sciences, American Statistical Association, pp. 18–25.
   Google Scholar
• Cook, R. (1996), ‘Graphics for Regressions with a Binary Response’, Journal of the American Statistical Association, 91, 983–992.
   Web of Science ®Google Scholar
• Cook, R., and Weisberg, S. (1991), ‘Sliced Inverse Regression for Dimension Reduction: Comment’, Journal of the American Statistical Association, 86, 328–332.
   Web of Science ®Google Scholar
• Cook, R., and Weisberg, S. (2000), ‘Discussion to “sliced Inverse Regression for Dimension Reduction”’, Journal of the American Statistical Association, 86, 316–342.
   Google Scholar
• Davies, H. (1972), ‘Strong Consistency of a Sequential Estimator of a Probability Density Function’, Kyushu University Institutional Repository.
   Google Scholar
• Devroye, L. (1979), ‘On the Pointwise and Integral Convergence of Recursive Kernel Estimates of Probability Densities’, Utilitas Mathematica, 15, 113–128.
   Google Scholar
• Duan, N., and Li, K. (1991), ‘Slicing Regression: A Link-Free Regression Method’, The Annals of Statistics, 19, 505–530.
   Web of Science ®Google Scholar
• Ferré, L., and Yao, A. (2005), ‘Smoothed Functional Inverse Regression’, Statistica Sinica, 15, 665–683.
   Web of Science ®Google Scholar
• Galambos, J., and Seneta, E. (1973), ‘Regularly Varying Sequences’, Proceedings of the American Mathematical Society, 41, 110–116.
   Web of Science ®Google Scholar
• Li, K. (1991), ‘Sliced Inverse Regression for Dimension Reduction’, Journal of the American Statistical Association, 86, 316–327.
   Web of Science ®Google Scholar
• Li, Y., and Zhu, L. (2007), ‘Asymptotics for Sliced Average Variance Estimation’, The Annals of Statistics, 35, 41–69.
   Web of Science ®Google Scholar
• Mokkadem, A., and Pelletier, M. (2007), ‘A Companion for the Kiefer-wolfowitz-blum Stochastic Approximation Algorithm’, The Annals of Statistics, 35, 1749–1772.
   Web of Science ®Google Scholar
• Mokkadem, A., and Pelletier, M. (2008), ‘Compact Law of the Iterated Logarithm for Matrix-normalized Sums of Random Vectors’, Theory of Probability and Its Applications, 52, 636–650.
   Web of Science ®Google Scholar
• Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009a), ‘Revisiting Révész Stochastic Approximation Method for the Estimation of a Regression Function’, ALEA. Latin American Journal of Probability and Mathematical Statistics, 6, 63–114.
   Web of Science ®Google Scholar
• Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009b), ‘The Stochastic Approximation Method for the Estimation of a Multivariate Probability Density’, Journal of Statistical Planning and Inference, 139, 2459–2478.
   Web of Science ®Google Scholar
• Nguyen, T.N., and Saracco, J. (2010), ‘Estimation récursive en régression inverse par tranches (Sliced Inverse Regression)’, Journal de la Société Française de Statistique, 151(2), 19–46.
   Google Scholar
• Nkiet, G. (2008), ‘Consistent Estimation of the Dimensionality in Sliced Inverse Regression’, Annals of the Institute of Statistical Mathematics, 60, 257–271.
   Web of Science ®Google Scholar
• Nkou, E. (2022), ‘Strong Consistency of Kernel Method for Sliced Average Variance Estimation’, Communications in Statistics – Theory and Methods.
   PubMed Web of Science ®Google Scholar
• Nkou, E., and Nkiet, G. (2019), ‘Strong Consistency of Kernel Estimator in a Semiparametric Regression Model’, Statistics, 53, 1289–1305.
   Web of Science ®Google Scholar
• Nkou, E., and Nkiet, G. (2022), ‘Wavelet – Based Estimation in a Semiparametric Regression Model’, International Journal of Wavelets, Multiresolution and Information Processing, 20, Article ID 2150056.
   Web of Science ®Google Scholar
• Powell, J., Stock, J., and Stoker, T. (1989), ‘Semiparametric Estimation of Index Coefficients’, Econometrica, 57, 1403–1430.
   Web of Science ®Google Scholar
• Révész, P. (1973), ‘Robbins-monro Procedure in a Hilbert Space and Its Application in the Theory of Learning Processes’, Studia Scientiarum Mathematicarum Hungarica, 8, 391–398.
   Google Scholar
• Révész, P. (1977), ‘How to Apply the Method of Stochastic Approximation in the Non-parametric Estimation of a Regression Function’, Series Statistics, 8, 119–126.
   Google Scholar
• Slaoui, Y. (2013), ‘Large and Moderate Principles for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method’, Serdica Mathematical Journal, 39, 53–82.
   Google Scholar
• Slaoui, Y. (2014), ‘Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method’, Journal of Probability and Statistics, 2014, Article ID 739640, 1–11.
   Google Scholar
• Slaoui, Y. (2015), ‘Plug-in Bandwidth Selector for Recursive Kernel Regression Estimators Defined by Stochastic Approximation Method’, Statistica Neerlandica, 69, 483–509.
   Web of Science ®Google Scholar
• Stone, C. (1984), ‘An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates’, The Annals of Statistics, 12, 1285–1297.
   Web of Science ®Google Scholar
• Tsybakov, A.B. (1990), ‘Recurrent Estimation of the Mode of a Multidimensional Distribution’, Problems of Information Transmission, 8, 119–126.
   Google Scholar
• Wolverton, C., and Wagner, T. (1969), ‘Asymptotically Optimal Discriminant Functions for Pattern Classification’, Institute of Electrical and Electronics Engineers Transactions on Information Theory, 15, 258–265.
   Web of Science ®Google Scholar
• Yamato, H. (1971), ‘Sequential Estimation of a Continuous Probability Density Function and Mode’, Bulletin of Mathematical Statistics, 14, 1–12.
   Google Scholar
• Zhu, L., and Fang, K. (1996), ‘Asymptotics for Kernel Estimate of Sliced Inverse Regression’, The Annals of Statistics, 24, 1053–1068.
   Web of Science ®Google Scholar
• Zhu, L., and Zhu, L. (2007), ‘On Kernel Method for Sliced Average Variance Estimation’, Journal of Multivariate Analysis, 98, 970–991.
   Web of Science ®Google Scholar