Generalised kernel smoothing for non-negative stationary ergodic processes

References

• Andrews , D. W.K. 1984 . Non-strong Mixing Autoregressive Processes . Journal of Applied Probability , 21 : 930 – 934 .
   Web of Science ®Google Scholar
• Bagai , I. and Prakasa Rao , B. L.S. 1996 . Kernel Type Density Estimates for Positive Valued Random Variables . Sankhya, Series A , 57 : 56 – 67 .
   Google Scholar
• Bosq , D. 1998 . Nonparametric Statistics for Stochastic Processes , New York : Springer Verlag . Lecture Note in Statistics
   Google Scholar
• Chaubey , Y. P. and Sen , P. K. 1996 . On Smooth Estimation of Survival and Density Functions . Statistics and Decisions , 14 : 1 – 22 .
   Google Scholar
• Chaubey , Y. P. , Sen , A. and Sen , P. K. 2007 . “ A New Smooth Density Estimator for Non-negative Random Variables ” . Montreal, , Canada : Department of Mathematics & Statistics, Concordia University . Technical Report
   Google Scholar
• Chen , S. X. 2000 . Probability Density Function Estimation Using Gamma Kernels . Annals of the Institute of Statistical Mathematics , 52 : 471 – 480 .
   Web of Science ®Google Scholar
• Chen , S. X. 2002 . “Local Linear Smoothers Using Asymmetric Kernels . Annals of the Institute of Statistical Mathematics , 54 : 312 – 323 .
   Web of Science ®Google Scholar
• Chernick , M. R. 1981 . A Limit Theorem for the Maximum of Autoregressive Processes with Uniform Marginal Distributions . Annals of Probability , 9 : 145 – 149 .
   Web of Science ®Google Scholar
• Chow , Y. S. and Teicher , H. 1988 . Probabilty Theory , 2 , New York : Springer Verlag .
   Google Scholar
• Diaconis , P. and Freedman , D. 1999 . Iterated Random Functions . SIAM Review , 41 : 41 – 76 .
   Google Scholar
• Engle , R. F. 1982 . Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation . Econometrica , 50 : 987 – 1007 .
   Web of Science ®Google Scholar
• Fan , J. 1993 . Local Linear Regression Smoothers and their Minimax Efficiencies . Annals of Statistics , 21 : 196 – 216 .
   Web of Science ®Google Scholar
• Fan , J. and Gijbels , I. 1992 . Variable Bandwidth and Local Linear Regression Smoothers . Annals of Statistics , 20 : 2008 – 2036 .
   Web of Science ®Google Scholar
• Fan , J. and Gijbels , I. 1996 . Local Polynomial Modeling and its Applications , London : Chapman and Hall .
   Google Scholar
• Feller , W. 1965 . An Introduction to Probability Theory and its Applications , Vol. II , New York : John Wiley and Sons .
   Google Scholar
• Gasser , T. and Müller , H. G. 1979 . “ Kernel Estimation of Regression Functions ” . In Smoothing Techniques for Curve Estimation , Edited by: Gasser , Rosenblatt . Heidelberg, , Germany : Springer-Verlag .
   Google Scholar
• Grenander , U. 1956 . On the Theory of Mortality Measurement. II . Skand. Aktuarietidskr , 39 : 125 – 153 .
   Google Scholar
• Guégan , D. and Ladoucette , S. 2001 . Non-mixing Properties of Long Memory Processes . Comptes Rendus de l'Académie des sciences Paris. Séries I , 333 : 373 – 376 .
   Google Scholar
• Györfi , L. and Lugosi , G. 1992 . Kernel Density Estimation from Ergodic Sample is not Universally Consistent . Computational Statistics & Data Analysis , 14 : 437 – 442 .
   Web of Science ®Google Scholar
• Haggan , V. and Ozaki , T. 1981 . Modelling Nonlinear Random Vibrations Using an Amplitude-dependent Autoregressive Time Series Model . Biometrika , 68 : 189 – 196 .
   Web of Science ®Google Scholar
• Hall , P. and Heyde , C. 1980 . Martingale Limit Theory and its Application , New York : Academic Press .
   Google Scholar
• Hall , P. and Wehrly , T. E. 1991 . A Geometrical Method for Removing Edge Effects from Kernel-type Nonparametric Estimators . Journal of the American Statistical Association , 86 : 665 – 672 .
   Web of Science ®Google Scholar
• Härdle , W. 1990 . Applied Nonparametric Regression , Cambridge, , UK : Cambridge University Press .
   Google Scholar
• Kulikov , V. N. and Lopuhaä , H. P. 2006 . The Behavior of the NPMLE of a Decreasing Density Near the Boundaries of the Support . Annals of Statistics , 34 : 742 – 768 .
   Web of Science ®Google Scholar
• Laïb , N. 1999 . Exponential-type Inequalities for Martingale Difference Sequences: Application to Nonparametric Regression Estimation . Communication in Statistics, Theory and Methods, Series A , 28 : 1565 – 1576 .
   Web of Science ®Google Scholar
• Laïb , N. 2005 . Kernel Estimates of the Mean and the Volatility Functions in a Nonlinear Autoregressive Model with ARCH Errors . Journal of Statistical Planing and Inference , 134 : 116 – 139 .
   Web of Science ®Google Scholar
• Müller , H. G. 1984 . “ Boundary Effects in Nonparametric Curve Estimation Models ” . In COMPSTAT , Vol. 1984 , 84 – 89 . Heidelberg : Physica Verlag .
   Google Scholar
• Rice , J. A. 1984 . Boundary Modification for Kernel Regression . Communication in Statistics, Series A , 13 : 893 – 900 .
   Web of Science ®Google Scholar
• Scaillet , O. 2004 . Density Esimation Using Inverse Gaussian and Reciprocal Inverse Gaussian Kernels . Journal of Nonparametric Statistics , 16 : 217 – 226 .
   Web of Science ®Google Scholar
• Seifer , B. and Gasser , Th. 1996 . Finite Sample Variance of Local Polynomials: Analysis and Solutions . Journal of the American Statistical Association , 96 : 267 – 275 .
   Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
   Google Scholar
• Tong , H. 1990 . Non-linear Time Series: A Dynamical System Approach , Oxford University Press .
   Google Scholar
• Tran , L. T. 1994 . Density Estimation for Time Series by Histograms . Journal of Statistical Planing and Inference , 40 : 61 – 79 .
   Web of Science ®Google Scholar
• Wand , M. P. , Marron , J. S. and Ruppert , D. 1991 . Transformations in Density Estimation . Journal of the American Statistical Association , 86 : 343 – 361 .
   Web of Science ®Google Scholar
• Wu , W. B. 2003 . “ Nonparametric Estimation for Stationary Processes ” . University of Chicago . Technical Report 536
   Google Scholar
• Wu , W. B. and Shao , X. 2004 . Limit Theorems for Iterated Random Functions . Journal of Applied Probability , 41 : 425 – 436 .
   Web of Science ®Google Scholar
• Zhang , S. , Karunamuni , R. J. and Jones , M. C. 1999 . An Improved Estimator of the Density Function at the Boundary . Journal of the American Statistical Association , 94 : 1231 – 1241 .
   Web of Science ®Google Scholar