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||Inference of non-centrality parameter of a truncated non-central chi-squared distribution
||Li QZ, Yu K
||Journal of Statistical Planning and Inference
||2009 Jul 1
||Non-central chi-squared distribution plays a vital role in statistical testing procedures. Estima- tion of the non-centrality parameter provides valuable information for the power calculation of the associated test.We are interested in the statistical inference property of the non-centrality parameter estimate based on one observation (usually a summary statistic) from a truncated chi-squared distribution. This work is motivated by the application of the flexible two-stage design in casecontrol studies, where the sample size needed for the second stage of a two- stage study can be determined adaptively by the results of the first stage. We first study the moment estimate for the truncated distribution and prove its existence, uniqueness, and inad- missibility and convergence properties.We then define a new class of estimates that includes the moment estimate as a special case. Among this class of estimates, we recommend to use one member that outperforms the moment estimate in a wide range of scenarios. We also present two methods for constructing confidence intervals. Simulation studies are conducted to evaluate the performance of the proposed point and interval estimates.