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2013 | nr 152 Metody wnioskowania statystycznego w badaniach ekonomicznych | 32--41
Tytuł artykułu

On Kernel Smoothing and Horvitz-Thompson Estimation

Autorzy
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Estimation of the total value of fixed characteristic of interest in a finite population is considered for a complex sampling scheme featuring unknown inclusion probabilities. The general empirical Horvitz-Thompson statistic is adopted as an estimator for the unknown total. In the presence of additional knowledge on inclusion probabilities taking form of inequality constraints it is proposed to use the well-known kernel estimator for individual inclusion probabilities. For a fixed-cost sequential sampling scheme this leads to a new nonparametric empirical Horvitz-Thompson estimator of a total. Its properties are compared to known alternatives in a simulation study.(original abstract)
Twórcy
  • Uniwersytet Ekonomiczny w Katowicach
Bibliografia
  • Aires N. (2000): Techniques to Calculate Exact Inclusion Probabilities for Conditional Poisson Sampling and Pareto πps Sampling Designs, Phd thesis, Chalmers, Göteborg University, Göteborg.
  • Ayer M., Brunk H.D., Ewing G.M., Reid W.T., Silverman E. (1955): An Empirical Distribution Function for Sampling with Incomplete Information. The Annals of Mathematical Statistics 6(4), s. 641-647.
  • Best M.J., Chakravarti N. (1990): Active Set Algorithms for Isotonic Regression. A Unifying Framework. Mathematical Programming 47, s. 425-439.
  • Fattorini L., Ridolfi G. (1997): A Sampling Design for Areal Units Based on Spatial Variability. Metron 55, s. 59-72.
  • Fattorini L. (2006): Appling the Horvitz-Thompson Criterion in Complex Designs: A Computer- Intensive Perspective for Estimating Inclusion Probabilities. "Biometrica", 93(2), s. 269-278.
  • Gamrot W. (2012) Simulation-Assisted Horvitz-Thompson Statistic and Isotonic Regression. Proceedings of the 30th International Conference on Mathematical Methods in Economics 2012 (accepted).
  • Giommi A. (1987): Nonparametric Methods for Estimating Individual Response Probabilities. "Survey Methodology", Vol. 13, No. 2, s. 127-134.
  • Härdle W. (1992): Applied Nonparametric Regression. Cambridge University Press.
  • Kulczycki P. (2005): Estymatory jądrowe w analizie systemowej. WNT, Warszawa.
  • Kremers W.K. (1985): The Statistical Analysis of Sum-Quota Sampling. Unpublished PHD thesis. Cornell University.
  • Pathak K. (1976): Unbiased Estimation in Fixed-Cost Sequential Sampling Schemes. "Annals of Statistics", 4 (5), s. 1012-1017.
  • Robertson T., Wright F.T., Dykstra R.L. (1988): Order Restricted Statistical Inference. Wiley, New York.
  • Rosén B. (1997): On Sampling with Probability Proportional to Size. "Journal of Statistical Planning and Inference", 62, s. 159-191.
  • Rosenblatt M. (1956): Remarks on Some Nonparametric Estimates for the Density Function. "Annals of Mathematical Statistics", No. 27, s. 832-837.
  • Schuster P. (2000): Taming Combinatorial Explosion. Proceedings of the National Academy of Sciences of the United States of America, 97 (14), s. 7678-7680.
  • Sheather S.J., Jones M.C. (1991): A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. "Journal of the Royal Statistical Society", B, 53(3), s. 683-690.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171268653

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