119,008 research outputs found
The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation Probabilities
For the zone of moderate deviation probabilities the local asymptotic minimax
lower bound of asymptotic efficiency of estimators is established. The
estimation parameter is multidimensional. The lower bound admits the
interpretation as the lower bound of asymptotic efficiency in confidence
estimation
The Guarded Lambda-Calculus: Programming and Reasoning with Guarded Recursion for Coinductive Types
We present the guarded lambda-calculus, an extension of the simply typed
lambda-calculus with guarded recursive and coinductive types. The use of
guarded recursive types ensures the productivity of well-typed programs.
Guarded recursive types may be transformed into coinductive types by a
type-former inspired by modal logic and Atkey-McBride clock quantification,
allowing the typing of acausal functions. We give a call-by-name operational
semantics for the calculus, and define adequate denotational semantics in the
topos of trees. The adequacy proof entails that the evaluation of a program
always terminates. We introduce a program logic with L\"ob induction for
reasoning about the contextual equivalence of programs. We demonstrate the
expressiveness of the calculus by showing the definability of solutions to
Rutten's behavioural differential equations.Comment: Accepted to Logical Methods in Computer Science special issue on the
18th International Conference on Foundations of Software Science and
Computation Structures (FoSSaCS 2015
Moment conditions in strong laws of large numbers for multiple sums and random measures
The validity of the strong law of large numbers for multiple sums of
independent identically distributed random variables , , with
-dimensional indices is equivalent to the integrability of
, where is the typical summand. We consider the
strong law of large numbers for more general normalisations, without assuming
that the summands are identically distributed, and prove a multiple sum
generalisation of the Brunk--Prohorov strong law of large numbers. In the case
of identical finite moments of irder with integer , we show that
the strong law of large numbers holds with the normalisation for any
. The obtained results are also formulated in the setting of
ergodic theorems for random measures, in particular those generated by marked
point processes.Comment: 15 page
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