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Extra resources for A Central Limit Theorem for the L2 Error of Positive Wavelet Density Estimator

Example text

2) Object quantifier as <1,1> of type < M,f,g » g(o) = = 1 iff {o; 1}. : H £(0) (Hartig's quantifier) = 1} has the same cardinality <1k > : Full. (3) Mixed quantifier of type For each 'V with the usual associated function; <1): of type ~ -state dependent structure U =(0 ,f 1 ,· .. ) = 1 iff for each finite {O, i~ -structure N a finite M £.. U and a state () such that (4) Let few e be a system of small sets on <1'> of type Asff ew « k <1 of type is isomorphic to M ~ structure can be obtained as a sample from , U 6' > there is (each finite U).

Of a state variable s arities respectively satisfying the usual recursiveness condition, quantifiers q , ql" . . With each quantifier q. we associate its kind o 1 k i 4i { ob, st, mx} and its quantifier type (a tuple of ones). The function i--. , s. is a recursive function if the sequence of quantifiers is infinite. 1; if and if . 1S an f' k "1"'" 0 Cf l' (i) are formulae then b ject quantif ier ... , Cf k (qu)( < 1k) f t ype 0 '1 is a k-ary junctor 'If k) is a formula. If q t( ~1' ... , i f u is an 0 b ject varia bl e an d i f are formulae then

Vt of type t as models. , cf. 4}. Note that saying "observational" we assume that the evaluation function of The "part of" ~ 0 ~O is recursive. ( of 1. 1 is now defined as follows: M -< lL iff M is a sample structure from U. t. Sent T and Sent 0 and assume ~ X T CfE 'l' (y,,{,eSent, for simplicity that I is formed by triples Sent 0) . We may consider the following rationality criteria concerning V -truthfulness (V S o o V), just to mention two possibilities: (a) I is rational if for each state dependent structure U and each finite non-empty M s: U we have the following: implies { 6' i Kcr "M(3' E V 0 E } (b) I is rational if for each V o and ':I!

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A Central Limit Theorem for the L2 Error of Positive Wavelet Density Estimator by Ghora J.K.


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