A Simple Formula for Mixing Estimators With Different Convergence Rates

REFERENCES

• Ahmed, S.E., Nicol, C.J. (2012), An Application of Shrinkage Estimation to the Nonlinear Regression Model, Computational Statistics & Data Analysis, 56, 3309–3321.
   Web of Science ®Google Scholar
• Bierens, H.J. (1987), “Kernel Estimators of Regression Functions,” in Advances in Econometrics: Fifth World Congress (Vol. 110), eds. TrumanF. Bewley, Cambridge: Cambridge University Press, pp. 99–144
   Google Scholar
• Carroll, R.J., Ruppert, D., Welsh, A.H. (1998), Local Estimating Equations, The Journal of the American Statistical Association, 93, 214–227.
   Web of Science ®Google Scholar
• Chacón, J.E., Duong, T., Wand, M.P. (2011), Asymptotics for General Multivariate Kernel Density Derivative Estimators, Statistica Sinica, 21, 807–840.
   Web of Science ®Google Scholar
• Chen, Y.-H., Chatterjee, N., Carroll, R.J. (2009), Shrinkage Estimators for Robust and Efficient Inference in Haplotype-Based Case-Control Studies, The Journal of the American Statistical Association, 104, 220–233.
   PubMed Web of Science ®Google Scholar
• Fan, J., and Gijbels, I. (1996), Local Polynomial Modeling and Its Applications, London: Chapman and Hall.
   Google Scholar
• Fan, J., Heckman, N.E., Wand, M.P. (1995), Local Polynomial Kernel Regression for Generalized Linear Models and Quasi-Likelihood Functions, The Journal of the American Statistical Association, 90, 477–489.
   Web of Science ®Google Scholar
• Fan, Y., Ullah, A. (1999), Asymptotic Normality of a Combined Regression Estimator, Journal of Multivariate Analysis, 71, 191–240.
   Web of Science ®Google Scholar
• Götze, F., Hipp, C. (1983), Asymptotic Expansions for Sums of Weakly Dependent Random Vectors, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 64, 211–39.
   Web of Science ®Google Scholar
• Götze, F., Künsch, H.R. (1996), Second-Order Correctness of the Blockwise Bootstrap for Stationary Observations, The Annals of Statistics, 24, 1914–1933.
   Web of Science ®Google Scholar
• Hall, P., Horowitz, J.L., Jing, B.-Y. (1995), On Blocking Rules for the Bootstrap With Dependent Data, Biometrika, 82, 561–574.
   Web of Science ®Google Scholar
• Hastie, T., Tibshirani, R. (1993), Varying-Coefficient Models, Journal of the Royal Statistical Society, Series B, 55, 757–796.
   Google Scholar
• Kouassi, D.A., Singh, J. (1997), A Semiparametric Approach to Hazard Estimation With Randomly Censored Observations, Journal of the American Statistical Association, 92, 1351–1355.
   Web of Science ®Google Scholar
• Mays, J.E., Birch, J.B., Starnes, B.A. (2001), Model Robust Regression: Combining Parametric, Nonparametric, and Semiparametric Methods, Journal of Nonparametric Statistics, 13, 245–277.
   Web of Science ®Google Scholar
• Nottingham, Q.J., Birch, J.B. (2000), A Semiparametric Approach to Analysing Dose-Response Data, Statistics in Medicine, 19, 389–404.
   PubMed Web of Science ®Google Scholar
• Olkin, I., Spiegelman, C.H. (1987), A Semiparametric Approach to Density Estimation, Journal of the American Statistical Association, 82, 858–865.
   Web of Science ®Google Scholar
• Pötscher, B.M., Leeb, H. (2009), On the Distribution of Penalized Maximum Likelihood Estimators: The Lasso, Scad and Thresholding, Journal of Multivariate Analysis, 100, 2065–2082.
   Web of Science ®Google Scholar
• Rice, J. (1984), Bandwidth Choice for Nonparametric Regression, The Annals of Statistics, 12, 1215–1230.
   Web of Science ®Google Scholar
• Rousseeuw, P.J., Croux, C. (1993), Alternatives to the Median Absolute Deviation, Journal of the American Statistical Association, 88, 1273–1283.
   Web of Science ®Google Scholar
• Singh, R.S. (1977), Applications of Estimators of a Density and Its Derivatives to Certain Statistical Problems, Journal of the Royal Statistical Society, Series B, 39, 357–363.
   Google Scholar
• (1981), Speed of Convergence in Nonparametric-Estimation of a Multivariate μ-Density and Its Mixed Partial Derivatives, Journal of Statistical Planning and Inference, 5, 287–298.
   Web of Science ®Google Scholar
• Soleymani, M., Lee, S. M.S. (2014), A Bootstrap Procedure for Local Semiparametric Density Estimation Amid Model Uncertainties, Journal of Statistical Planning and Inference, 153, 75–86.
   Web of Science ®Google Scholar
• Tibshirani, R., Hastie, T. (1987), Local Likelihood Estimation, Journal of the American Statistical Association, 82, 559–567.
   Web of Science ®Google Scholar
• Tsybakov, A.B. (2009), Introduction to Nonparametric Estimation, New York: Springer.
   Google Scholar
• Wasserman, L. (2006), All of Nonparametric Statistics, New York: Springer.
   Google Scholar
• Wei, Y., Ma, Y., Carroll, R.J. (2012), Multiple Imputation in Quantile Regression, Biometrika, 99, 423–438.
   PubMed Web of Science ®Google Scholar
• Wu, T.J. (1997), Root n Bandwidth Selectors for Kernel Estimation of Density Derivatives, Journal of the American Statistical Association, 92, 536–547.
   Web of Science ®Google Scholar
• Yuan, Y., Yin, G. (2011), Dose-Response Curve Estimation: A Semiparametric Mixture Approach, Biometrics, 67, 1543–1554.
   PubMed Web of Science ®Google Scholar