Summary
We study the increase in statistical information obtained by adding independent observations, as measured by the LeCam-deficiencyδ. The main object of our study is the case where the observations follow a 1-parameter exponential law. We show that when the parameter set is a compact, non-degenerate interval andr is a fixed integer, then
where δ(ℰ n, ℰn+r) is the deficiency ofℰ n with respect toℰ n+r, andℰ n is the experiment consisting in takingn independent observations fromℰ.
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References
Ferguson, R.: Mathematical Statistics. New York-London: Academic Press 1967
Hengartner, W., Theodorescu, R.: Concentration Functions. New York-London: Academic Press 1973
LeCam, L.: Sufficiency and approximate sufficiency. Ann. Math. Statist.35, 1419–1455 (1964)
LeCam, L.: Notes on asymptotic methods in statistical decision theory. Montreal: Centre de Recherches Math., Univ. de Montréal 1974 a
LeCam, L.: On the information contained in additional observations. Ann. Statist.2, 630–649 (1974b)
Lehmann, E.: Testing statistical hypotheses. New York: Wiley 1959.
Loéve, M.: Probability theory. 3rd Edition. Princeton: Van Nostrand 1963
Neveu, J.: Mathematical foundations of the calculations of probability. San Francisco: Holden-Day 1965
Torgersen, E.: Comparison of translation experiments. Ann. Math. Statist.43, 1383–1399 (1972)
Torgersen, E.: Asymptotic behaviour of powers of dichotomies. Stat. res. rep., Univ. of Oslo (1974)
Torgersen, E.: Deviations from total information and from total ignorance as measures of information. Stat. res. rep., Univ. of Oslo (1976)
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Helgeland, J. Additional observations and statistical information in the case of 1-parameter exponential distributions. Z. Wahrscheinlichkeitstheorie verw Gebiete 59, 77–100 (1982). https://doi.org/10.1007/BF00575527
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DOI: https://doi.org/10.1007/BF00575527