Higher-order expansions and efficiencies of tests based on spacings

Abstract

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A class of asymptotically efficient estimators based on sample spacings

“…The summands A k and C k are sums of functions of m-step non-overlapping uniform spacings. Such statistics are well studied in the literature; the results needed are given by Mirakhmedov (2005) and Mirakhmedov and Rao (2013). We will use these facts below.…”

“…We shall use arguments like those on p. 39 in Ghosh (1997). That is, we use a two-term Taylor expansion for g θ 0 (Ũ ( j−1)m+s ) at u ( j−1)m+s , Theorem 2.2(1) of Mirakhmedov and Rao (2013), and Lemma 1. Also, note that the r.v.…”