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- W262472783 abstract "Suppose that X1, X2, …, Xn, … is a sequence of independent identically distributed (i.i.d.) random variables. We assume that a parameter space (H) is an open subset in a Euclidean p-space. In the textbook discussion of asymptotic theory, it is usually shown that the asymptotically best (in some sense or other) estimator ({rm{hat theta }}_{rm{n}}^*) has an asymptotic distribution of order (sqrt {rm{n}} ) , in the sense that the distribution of (sqrt {rm{n}} ({rm{hat theta }}_{rm{n}}^* - {rm{theta }})) converges to some probability law (in most cases normal). There are sporadic examples where the distribution of (sqrt {rm{n}} ({rm{hat theta }}_{rm{n}}^* - {rm{theta }})) or (sqrt {{rm{n log n}}} ({rm{hat theta }}_{rm{n}}^* - {rm{theta }})) converges to some law (Woodroofe [57]) when Xi’s are i.i.d. random variables with an uniform distribution or a truncated distribution. The purpose of this chapter is to give a systematic treatment to the problem of whether for a given sequence ({ {{rm{c}}_{rm{n}}}} ,{{rm{c}}_{rm{n}}}({rm{hat theta }}_{rm{n}}^* - {rm{theta }})) converges to some law, and what is the possible bound for such a sequence. In the location parameter case it will be shown that such a bound can be explicitely given. The asymptotic distribution of ({{rm{c}}_{rm{n}}}(hat theta _{rm{n}}^* - theta )) and the bound for it in non-regular cases is discussed by Akahira [2]. Also some results in terms of the asymptotic distribution of estimators are given in Takeuchi [42]. Asymptotic sufficiency of consistent estimators is discussed by Akahira [5] in non-regular cases." @default.
- W262472783 created "2016-06-24" @default.
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- W262472783 date "1981-01-01" @default.
- W262472783 modified "2023-10-01" @default.
- W262472783 title "Consistency of Estimators and Order of Consistency" @default.
- W262472783 doi "https://doi.org/10.1007/978-1-4612-5927-5_2" @default.
- W262472783 hasPublicationYear "1981" @default.
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