Convergence rate of the normal approximation for sequential estimators of a probability density and its derivatives

References

• Basu , A.K. and Sahoo , D.K. 1989 . Berry-Esseen type theorems for sequential density estimation . Sequential Anal. , 8 : 119 – 134 .
   Google Scholar
• Bhattacharya , P.K. 1967 . Estimation of a probability density function and its derivatives . SankhyS Ser. , 29 : 373 – 382 .
   Google Scholar
• Carroll , R.J. 1976 . On sequential density estimation . Z. Wahrsch. Verw. Gebiete , 36 : 137 – 151 .
   Web of Science ®Google Scholar
• Davies , H.I. and Wegman , E.J. 1975 . Sequential nonpara-metric density estimation . IEEE Trans. Inform. Theory , 21 : 619 – 628 .
   Web of Science ®Google Scholar
• Devroye , L. and Györfi , L. 1985 . “ Nonparametric Density Estimation ” . In The L1 View , New York : John Wiley & sons .
   Google Scholar
• Isogai , E. 1987 . The convergence rate of fixed-width sequential confidence intervals for a probability density function . Sequential Anal. , 6 : 55 – 69 .
   Google Scholar
• Isogai E. A Berry-Esseen type bound for recursive estimators of a density and its derivatives, to appear in J. Statist. Plann.Inference. 1993
   Google Scholar
• Koronacki , J. and Wertz , W. 1988 . A global stopping rule for recursive density estimators . J. Statist. Plann. Inference , 20 : 23 – 39 .
   Google Scholar
• Loève , M. 1977 . “ Probability Theory I ” . New York : Springer-Verlag .
   Google Scholar
• Martinsek , A.T. 1992 . Using stopping rules to bound the mean integrated squared error in density estimation . Ann. Statist. , 20 : 797 – 806 .
   Web of Science ®Google Scholar
• Michel , R. and Pfanzagl , J. 1971 . The accuracy of the normal approximation for minimum contrast estimates . Z. Wahrsch. Verw. Gebiete , 18 : 73 – 84 .
   Web of Science ®Google Scholar
• Menon , V.V. , Prasad , B. and Singh , R.S. 1984 . Nonparametric recursive estimates of a probability density function and its derivatives . J. Statist. Plann. Inference , 9 : 73 – 82 .
   Google Scholar
• Prakasa Rao , B.L.S. 1983 . “ Nonparametric Functional Estimation ” . Academic press .
   Google Scholar
• Rosenblatt , M. 1956 . Remarks on some nonparametric estimates of a density function . Ann. Math. Statist. , 27 : 832 – 837 .
   Google Scholar
• Samanta , M. and Mugisha , R.X. 1981 . On a class of estimates of the probability density function and mode based on a random number of observations . Cal. Statist. Assoc.Bull , 117 : 23 – 40 .
   Google Scholar
• Schuster , E.F. 1969 . Estimation of a probability density function and its derivatives . Ann. Math. Statist. , 40 : 1187 – 1195 .
   Google Scholar
• Silverman B.W. Density Estimation for Statistics and Data Analysis Chapman and Hall 1986
   Google Scholar
• Singh , R.S. 1977 . Improvement on some known nonparametric uniformly consistent estimators of derivatives of a density . Ann. Statist. , 5 : 394 – 399 .
   Web of Science ®Google Scholar
• Singh , R.S. 1977b . Applications of estimators of a density and its derivatives to certain statistical problems . J. Roy. Statist. Soc, Ser. , 39 : 357 – 363 .
   Google Scholar
• Stute , W. 1983 . Sequential fixed-width confidence intervals for a nonparametric density function . Z. Wahrsch. Verw. Gebiete , 62 : 113 – 123 .
   Web of Science ®Google Scholar