Asymptotic Sampling Distribution for Polynomial Chaos Representation of Data: A Maximum Entropy and Fisher information approach

2006 ◽  
Author(s):  
Sonjoy Das ◽  
Roger Ghanem ◽  
James C. Spall
Keyword(s):  
Maximum Entropy ◽  
Fisher Information ◽  
Polynomial Chaos ◽  
Sampling Distribution ◽  
Information Approach ◽  
Asymptotic Sampling

scholarly journals Asymptotic Inference for Optimal Rerandomization Designs

2021 ◽  
Vol 1 (1) ◽  
pp. 49-58
Author(s):  
Mårten Schultzberg ◽  
Per Johansson
Keyword(s):  
Experimental Design ◽  
Normal Distribution ◽  
Mahalanobis Distance ◽  
Design Strategy ◽  
Sampling Distribution ◽  
Optimal Designs ◽  
Asymptotic Inference ◽  
Optimal Allocations ◽  
Asymptotic Sampling

AbstractRecently a computational-based experimental design strategy called rerandomization has been proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to remove, from consideration, those allocations with large imbalances in observed covariates according to a balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations. Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling distribution derived by Li et al. (2018), is well approximated by a normal distribution.

scholarly journals Closed-Form Asymptotic Sampling Distributions under the Coalescent with Recombination for an Arbitrary Number of Loci

2012 ◽  
Vol 44 (2) ◽  
pp. 391-407 ◽  
Author(s):  
Anand Bhaskar ◽  
Yun S. Song
Keyword(s):  
Asymptotic Expansion ◽  
Closed Form ◽  
Recombination Rate ◽  
Functional Form ◽  
Asymptotic Series ◽  
Sampling Distribution ◽  
Challenging Problem ◽  
Sampling Distributions ◽  
Asymptotic Sampling ◽  
New Framework

Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on an asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.

scholarly journals Closed-Form Asymptotic Sampling Distributions under the Coalescent with Recombination for an Arbitrary Number of Loci

2012 ◽  
Vol 44 (02) ◽  
pp. 391-407 ◽  
Author(s):  
Anand Bhaskar ◽  
Yun S. Song
Keyword(s):  
Asymptotic Expansion ◽  
Closed Form ◽  
Recombination Rate ◽  
Functional Form ◽  
Asymptotic Series ◽  
Sampling Distribution ◽  
Challenging Problem ◽  
Sampling Distributions ◽  
Asymptotic Sampling ◽  
New Framework

Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on an asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.

Sign in / Sign up

Export Citation Format

Share Document