Non-central chi-squared distribution plays a vital role in commonly used statistical testing procedures. The non-centrality parameter A provides valuable information on the power of the associated test. In this paper. based on one observation X sampled from a chi-squared distribution with p degrees of freedom and non-centrality parameter S, we study a new class of non-centrality parameter estimators (delta) over cap (beta)(X) = max {X - p. beta X), 0 <= beta < 1, and investigate their statistical properties under the quadratic loss function. Theoretical and simulation studies indicate that <(delta)over cap>(1/(1+p))(X) generally works well compared with other existing estimators, especially for relatively small and moderate delta.
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