On the theory of moving average graduation

References

• Borgan , Ø. 1977 . “ Graduation by moving averages ” . In Statistical Research Report No. 9 , Vol. 1977 , Institute of Mathematics, University of Oslo .
   Google Scholar
• Elphinstone , M. D. W. 1951 . Summation and other methods of graduation . Trans. Fac. Act. , 20 : 15 – 57 .
   Google Scholar
• Gerber , H. 1977 . “ Applications of linear algebra in graduation and other disciplines of actuarial sciences ” . In Preprint , Ann Arbor : Dept. of Math., Univ. of Michigan .
   Google Scholar
• Greville , T. N. E. 1947 . Actuarial note: Adjusted average graduation formulas of maximum smoothness . Record Am. Inst. Act. , 36 ( 2 ) : 249 – 264 .
   Google Scholar
• Greville , T. N. E. 1948 . Actuarial note: Tables of coefficients in adjusted average graduation formulas of maximum smoothness . Record Am. Inst. Act. , 37 ( 1 ) : 11 – 30 .
   Google Scholar
• Greville , T. N. E. 1957 . On smoothing a finite table: A matrix approach . J. Soc. Industr. Appl. Math. , 5 ( 3 ) : 137 – 154 .
   Web of Science ®Google Scholar
• Greville , T. N. E. 1966 . On stability of linear smoothing formulas . SIAM J. Numer. Anal. , 3 ( 1 ) : 157 – 170 .
   Google Scholar
• Greville , T. N. E. 1972 . “ Part V. Supplementary study note on graduation ” . In Preprint , Univ. of Wisconsin .
   Google Scholar
• Greville , T. N. E. 1974 . On a problem of E . L. De Forest in iterated smoothing. SIAM J. Math. Anal. , 5 ( 3 ) : 376 – 398 .
   Web of Science ®Google Scholar
• Henrici , P. 1964 . Elements of numerical analysis , New York : Wiley .
   Google Scholar
• Jecklin , H. & Strickler . 1954 . Wahrscheinlichkeitstheoretische Begründung mechanischer Ausgleichung und deren praktische Anwendung . Mitteilungen , 54 ( 2 ) : 125 – 161 .
   Google Scholar
• Kockelkorn , U. and Rüger , B. 1974 . Die Schätzung der glatten Komponente von Zeitreihen ohne Saisonfigur mit Hilfe gleitender Durchschnitte bei Verwendung von Polynomen ersten bis dritten Grades . Blätter Deutschen Ver. Versich. Math. , 11 ( 3 ) : 319 – 329 .
   Google Scholar
• Michalup , E. 1956 . Entwicklung und Weiterbildung von mechanischen Ausgleichungsformeln . Stat. Vierteljahresschrift , 9 ( 2 ) : 64 – 69 .
   Google Scholar
• Miller , M. D. 1946 . Elements of graduation , New York : Actuarial Society of America .
   Google Scholar
• Pollard , J. H. 1971a . “ On optimal error-reducing formula and optimal smoothing formula ” . In Preprint , Macquarie University .
   Google Scholar
• Pollard , J. H. 1971b . “ Non-symmetric graduation formula ” . In Preprint , Macquarie University .
   Google Scholar
• Scheffe , H. 1959 . The analysis of variance , New York : Wiley .
   Google Scholar
• Sheppard , W. F. 1913 . Reduction of errors by means of negligible differences . Proc. 5th. Int. Congr. Math. , 2 : 348 – 384 .
   Google Scholar
• Sheppard , W. F. 1914a . Fitting of polynomial by method of least squares. (Solution in terms of differences or sums.) . Proc. London Math. Soc. , 13 ( 2 ) : 97 – 108 .
   Google Scholar
• Sheppard , W. F. 1914b . Graduation by reduction of mean square of error (I) . J. Inst. Act. , 48 ( 2 ) : 171 – 185 .
   Google Scholar
• Sheppard , W. F. 1914c . Graduation by reduction of mean square of error (II) . J. Inst. Act. , 48 ( 4 ) : 390 – 412 .
   Google Scholar
• Sheppard , W. F. 1915 . Graduation by reduction of mean square of error (III) . J. Inst. Act. , 49 ( 2 ) : 149 – 157 .
   Google Scholar
• Sheppard , W. F. 1921 . Reduction of error by linear compounding . Philosophical Trans. Royal Soc. London. Ser. A. , 221 : 199 – 237 .
   Google Scholar
• Stigler , S. S. 1978 . Mathematical statistics in the early states . Ann. Statist. , 6 ( 2 ) : 239 – 265 .
   Web of Science ®Google Scholar
• Sverdrup , E. 1967 . Laws and chance variations , Vol. I , Amsterdam : North-Holland .
   Google Scholar
• Weichselberger , K. 1964 . Über eine Theorie der gleitenden Durchschnitte und verschiedene Anwendungen dieser Theorie . Metrika , 8 ( 2 ) : 185 – 230 .
   Web of Science ®Google Scholar
• Whittaker , E. T. and Robinson , G. 1924 . The calculus of observations , London : Blackie and Son .
   Google Scholar
• Wolfenden , H. H. 1924 . On the development of formulae for graduation by linear compounding. With special reference to the work of Erastus L. De Forest . Trans. Am. Soc. Act. , 26 : 81 – 121 .
   Google Scholar