Registration for Exponential Family Functional Data

2017 ◽  
pp. 271-277
Author(s):  
Julia Wrobel ◽  
Jeff Goldsmith
Keyword(s):  
Functional Data ◽  
Exponential Family

Exponential Family Functional data analysis via a low‐rank model

Biometrics ◽  
2018 ◽  
Vol 74 (4) ◽  
pp. 1301-1310 ◽  
Author(s):  
Gen Li ◽  
Jianhua Z. Huang ◽  
Haipeng Shen
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Exponential Family ◽  
Low Rank

Registration for exponential family functional data

Biometrics ◽  
2018 ◽  
Vol 75 (1) ◽  
pp. 48-57 ◽  
Author(s):  
Julia Wrobel ◽  
Vadim Zipunnikov ◽  
Jennifer Schrack ◽  
Jeff Goldsmith
Keyword(s):  
Functional Data ◽  
Exponential Family

An Introduction to Statistical Models for Networks

2020 ◽  
pp. 218-233
Author(s):  
Valentina Kuskova ◽  
Stanley Wasserman
Keyword(s):  
Social System ◽  
Exponential Family ◽  
Behavioral Science ◽  
Social Science Research ◽  
Science Research ◽  
Uniform Distributions ◽  
The Social ◽  
Special Cases ◽  
Social And Behavioral Science ◽  
Network Methods

Network theoretical and analytic approaches have reached a new level of sophistication in this decade, accompanied by a rapid growth of interest in adopting these approaches in social science research generally. Of course, much social and behavioral science focuses on individuals, but there are often situations where the social environment—the social system—affects individual responses. In these circumstances, to treat individuals as isolated social atoms, a necessary assumption for the application of standard statistical analysis is simply incorrect. Network methods should be part of the theoretical and analytic arsenal available to sociologists. Our focus here will be on the exponential family of random graph distributions, p*, because of its inclusiveness. It includes conditional uniform distributions as special cases.

scholarly journals On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1568
Author(s):  
Shaul K. Bar-Lev
Keyword(s):  
Power Function ◽  
Exponential Family ◽  
Probability Distributions ◽  
Infinite Divisibility ◽  
Variance Function ◽  
Exponential Families ◽  
Natural Exponential Family ◽  
Natural Exponential Families ◽  
Convolution Properties ◽  
The Relationship

Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ) such that L(αn∑i=1nXi)=Fgn(θ)∈F. In this paper, we prove that a natural exponential family F is reproducible iff it possesses a variance function which is a power function of its mean. Such a result generalizes that of Bar-Lev and Enis (1986, The Annals of Statistics) who proved a similar but partial statement under the assumption that F is steep as and under rather restricted constraints on the forms of αn and gn(θ). We show that such restrictions are not required. In addition, we examine various aspects of reproducibility, both theoretically and practically, and discuss the relationship between reproducibility, convolution and infinite divisibility. We suggest new avenues for characterizing other classes of families of distributions with respect to their reproducibility and convolution properties .

scholarly journals Bounding uncertainty in functional data: A case study

2021 ◽  
Vol 33 (1) ◽  
pp. 178-188
Author(s):  
Caleb King ◽  
Nevin Martin ◽  
James Derek Tucker
Keyword(s):  
Functional Data
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