Доверительное оценивание демографических коэффициентов на примере коэффициентов смертности
Аннотация
В большинстве случаев демографы игнорируют стохастическую природу демографических коэффициентов, в том числе коэффициентов смертности. Но рост интереса к смертности и долголетию малых групп населения требует надежных решений для доверительного оценивания соответствующих показателей смертности. В статье предлагается формула апостериорного распределения коэффициента смертности в однородной группе населения. На ее основе строится доверительная область значений коэффициента смертности. Методами стохастической симуляции строятся доверительные области для кумулятивных характеристик смертности, в том числе для продолжительности жизни.
Скачивания
Литература
Agresti A., Coull B. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. // The American Statistician,. 52: 119–126.
Andreev E.M.; Shkolnikov V.M. (2010). Spreadsheet for calculation of confidence limits for any life table or healthy-life table quantity MPIDR // Technical Report TR-2010-005.
Buckland S.T. (1983). Monte Carlo methods for confidence interval estimation using the bootstrap technique. // Journal of Applied Statistics, 10 (2): 194-212.
Buckland S.T. (1984). Monte Carlo confidence intervals. // Biometrics, 40: 811-817
Carpenter J., Bithell J. (2000). Bootstrap condence intervals: when, which, what? A practical guide for medical statisticians. // Statistics in Medicine 19: 1141–1164
Caselli G., Vallin J., Wunsch G. (2006). Demography: Analysis and Synthesis. Elsevier. London.
Chiang C.L. (1960a). A stochastic study of the life table and its applications: I. Probability distributions of the biometric functions. // Biometrics 6: 618-635.
Chiang C.L. (l960b). A stochastic study of the life table and its applications: 11. Sample variance of the observed expectation of life and other biomelric functions. // Human Bioilogy. 32: 221-238.
Chiang C.L. (1961). A stochastic study of the life table and its applications: III. The follow-up study with the consideration of competing risks. // Biometrics. 17: 57-78.
Chiang C.L. (1984). The life table and its applications. Robert E. Krieger publishing company. Malabar, Florida.
Demograficheskii entsiklopedicheskii slovar' (1985). [Demographic Encyclopedic Dictionary]. Valentei D.I. ed. Moscow. Sovetskaia entsiklopediia.
Fishman G.S. (1996). Monte Carlo: concepts, algorithms, and applications / G.S.Fishman. - New York: Springer, - 698 p. - (Springer series in operations research).
Gnedenko B.V. (2001). Ocherk po istorii teorii veroiatnostei. M. [Essay on the history of probability theory]. Moscow. URSS, 88 p.
Keyfitz N. (1976). Mathematical Demography: A Bibliographical Essay. // Population Index, 42, (1): 9-38.
Keyfitz N. (1977). Applied mathematical demography. New York, John Wiley & Son, 388 p. (Reedited in 1985 by Springer-Verlag, New York, 442 p).
Lewis J.R., Sauro J. (2006). When 100% Really Isn’t 100%: Improving the Accuracy of Small-Sample Estimates of Completion Rates. // Journal of usability studies. 1 (3): 136-150.
Lewis J.R., Sauro J. (2012). Quantifying the User Experience Practical Statistics for User Research. Elsevier Science & Technology.
Linnik U.V., Khalfina N.M. (1979). Doveritel'noe otsenivanie [Confidence estimation]. Matematicheskaia entsiklopediia. Vol. 2. Moscow. Sovetskaia entsiklopediia: 365-367.
Paevskii V.V. (1934). Ob izmerenii smertnosti migriruiuchshikh mass naseleniia [On measuring mortality of migratory population]. In: Trudy Demograficheskogo instituta Akademii nauk SSSR. Vol. 1. Leningrad: 63-134.
Preston S.H., Heuveline P., Guillot M. (2001). Demography. Measuring and Modeling Population Processes. Blackwell Publishers Inc. Maiden, Massachusetts.
Sachs L. (1982). Applied Statistics. A Handbook of Techniques. Springer-Verlag, New York - Heidelberg - Berlin.
Sauro J., Lewis J.R. (2005). Estimating Completion Rates from Small Samples using Binomial Confidence Intervals: Comparisons and Recommendations. // Proceedings of the Human Factors and Ergonomics Society Annual Meeting Orlando, FL.
Scherbov S., Ediev D.M. (2011). Significance of life table estimates for small populations: Simulation-based study of standard errors. // Demographic Research, 24(22): 527-550.
Shryock H.S., Siegel J.S. (1980). The methods and materials of demography, Vol. 1 - 2, , Washington DC.
Silcocks P.B.S., Jenner D.A., Reza R. (2001). Life expectancy as a summary of mortality in a population: statistical considerations and suitability for use by health authorities // Journal of Epidemiology & Community Health. 55:38–43.
Toson B., Baker A. (2003). Life expectancy at birth: methodological options for small populations. Office for National Statistics (ONS) UK. http://www.statistics.gov.uk/statbase/Product.asp?vlnk=8841
Wilson E.B. (1927). Probable inference, the law of succession, and statistical inference. // Journal of the American Statistical Association. 22: 209–212.