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Competitive Stats
Q26Section I (Objective (Q1–Q80))26 of 80

Statistical Inference — lower bound for the variance of the sample variance under Poisson

To estimate the parameter λ\lambda (variance) of Poisson distribution, a statistic is defined as S2=∑i=1n(Xi−Xˉ)2n−1S^2=\frac{\sum_{i=1}^n(X_i-\bar X)^2}{n-1} from a random sample of size n from the distribution. Then Var⁡(S2)\operatorname{Var}(S^2) will be always greater than or equal to

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