Randomized consistent statistical inference for random processes and fields

Arkady Tempelman
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Arkady Tempelman: The Pennsylvania State University

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 3, No 8, 599-627

Abstract: Abstract We propose a randomized approach to the consistent statistical analysis of random processes and fields on $${\mathbb {R}}^m$$ R m and $${\mathbb {Z}}^m, m=1,2,...$$ Z m , m = 1 , 2 , . . . , which is valid in the case of strong dependence: the parameter of interest $$\theta $$ θ only has to possesses a consistent sequence of estimators $${\hat{\theta }}_n$$ θ ^ n . The limit theorem is related to consistent sequences of randomized estimators $${\hat{\theta }}_n^*$$ θ ^ n ∗ ; it is used to construct consistent asymptotically efficient sequences of confidence intervals and tests of hypotheses related to the parameter $$\theta $$ θ . Upper bounds for “admissible” sequences of normalizing coefficients in the limit theorem are established for some statistical models in Part 2.

Keywords: Consistency; Statistical inference; Randomization; Random process; Random field; Primary 62F05; 62F12; Secondary 37A30; 60F05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-022-09270-y

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