Hypothesis testing for Markovian models with random time observations

Barsotti, Flavia; Philippe, Anne; Rochet, Paul

doi:10.1016/j.jspi.2015.12.009

Cited by 7 publications

(7 citation statements)

References 15 publications

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“…The identifiability conditions in this model rely on the existence of a sparse matrix in the commutant. Similar problems and applications are studied in [3,13,15,17].…”

Section: Notations and Preliminary Resultsmentioning

confidence: 94%

Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs

Espinasse

Rochet

2016

Graphs and Combinatorics

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A walk in a directed graph is defined as a finite sequence of contiguous edges. Seeing the edges as indeterminates, walks are investigated as monomials and endowed with a partial order that extends to possibly unconnected objects called hikes. Analytical transformations of the weighted adjacency matrix reveal a relation between walks and self-avoiding hikes, giving rise to interesting combinatorial properties such as an expression of the number of ways to travel a walk in function of its self-avoiding divisors.

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“…The identifiability conditions in this model rely on the existence of a sparse matrix in the commutant. Similar problems and applications are studied in [3,13,15,17].…”

Section: Notations and Preliminary Resultsmentioning

confidence: 94%

Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs

Espinasse

Rochet

2016

Graphs and Combinatorics

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“…The fourth step in the guided inquiry is collecting data, information needed to test the proposed hypothesis (Saarinen et al, 2017, Depoy & Gitlin, 2016Deufemia et al 2014;Majid 2015). The fifth step in the guided inquiry is to test the hypothesis, the process of determining the answer that is deemed to be accepted in accordance with the data or information obtained on the basis of data collection (Donnarumma et al 2017;Zhou et al 2017;Barsotti et al 2016, Majid, 2015. The last step in the guided inquiry is to formulate a conclusion, a process of describing the findings obtained on the basis of hypothesis testing (Lucena-Molina, 2016;Tan, 2017;Majid, 2015).…”

Section: Discussionmentioning

confidence: 99%

Improving Student Learning Outcomes With a Staffing Administration Module Based Guided Inquiry in Basic Competencies Suggested Leave Regulations

Sari

Suputra

Chasanah³

2017

JPBM

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The purpose of this study is to (1) produce personnel administration learning module Guided Inquiry-based for XI graders of Vocational School, particularly for office administration expertise program based on basic competence point 3.6 (proposing leave regulation) and 4.6 (reciting leave regulation), (2) validate the product through the validation test, (3) and find out the different learning outcome for those who used and did not used this product. there are different learning outcomes from those who belong to the control and experimental class namely 10,81 (control class average score= 82,58 and experimental class average score= 93,39).

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“…where Σ is a N 2 × N 2 covariance matrix (either known or that can be estimated). For instance, one can think of K as the empirical covariance when observing a sample of vectors of covariance K. This condition is verified for instance in the framework considered in Barsotti et al (2014Barsotti et al ( , 2016. Note that asymptotic normality is a standard ground base investigating any least-squares procedure.…”

Section: Assumptionsmentioning

confidence: 93%

“…We begin with an example treated in the companion papers Barsotti et al (2014Barsotti et al ( , 2016. Consider a Markov chain (X n ) n∈N with finite state space [1, N ] and transition matrix P ∈ R N ×N .…”

Section: Markov Chainsmentioning

confidence: 99%

Reconstructing undirected graphs from eigenspaces

Castro¹,

Espinasse²,

Rochet³

2016

Preprint

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In this paper, we aim at recovering an undirected weighted graph of N vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix W. For instance, this situation arises for stationary signals on graphs or for Markov chains observed at random times. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator AB − BA between symmetric matrices A and B.In the Erdős-Rényi model with no self-loops, we show that identifiability (i.e., the ability to reconstruct W from the knowledge of its eigenspaces) follows a sharp phase transition on the expected number of edges with threshold function N log N/2.Given an estimation of the eigenspaces based on a n-sample, we provide support selection procedures from theoretical and practical point of views. In particular, when deleting an edge from the active support, our study unveils that our test statistic is the order of O(1/n) when we overestimate the true support and lower bounded by a positive constant when the estimated support is smaller than the true support. This feature leads to a powerful practical support estimation procedure. Simulated and real life numerical experiments assert our new methodology.

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Hypothesis testing for Markovian models with random time observations

Cited by 7 publications

References 15 publications

Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs

Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs

Improving Student Learning Outcomes With a Staffing Administration Module Based Guided Inquiry in Basic Competencies Suggested Leave Regulations

Reconstructing undirected graphs from eigenspaces

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