Estimating Linear Functionals in Density Estimation Models
The close connection between density estimation and white noise data is extended to the analysis of possible bias-variance tradeoffs. The analysis depends on a modulus of continuity argument based on a chi-square type distance, on a comparison with white noise models and on a nonstandard application of the Cramer-Rao inequality.
KeywordsDensity Estimation Fisher Information Linear Functional Bias Function Finite Sample Size
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- Donoho, D. L. and Liu, R. C. (1988). Geometrizing rates of convergence, I. Technical Report, Department of Statistics, University of California, Berkeley.Google Scholar
- Ibragimov, I. A. and Hasminskii, R. Z. (1981). Statistical Estimation: Asymptotic Theory. Springer-Verlag.Google Scholar
- Liu, R. C. and Brown, L. D. (1992). Non-existence of good unbiased estimators in singular problems. Technical Report.Google Scholar
- Low, M. G. (1992). Bias-Variance tradeoffs in White Noise Models. Technical Report.Google Scholar
- Nussbaum, M. (1992). Asymptotic equivalence of density estimation and white noise. Technical Report.Google Scholar