Expansions and Asymptotics for Statistics

By Christopher G. Small. 2010

104 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/07c48c65e49e35b7cbca66660734789dd40379ca

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Citations in the corpus

Fixing Variational Bayes: Deterministic Variational Inference for Bayesian Neural Networks (2018, unknown): “However, using the second-order Delta method (Small, 2010), we find the expansion EaL∼q̃(aL) [ log p(y|aL) ] = 〈 aL 〉 − EaL∼q̃(aL) [ logsumexp(aL) ] ≈ 〈 aL 〉 − logsumexp( 〈 aL 〉 )− 12 ( p> diag(ΣL)− p>ΣLp ) , (21) To derive this expansion, we first state the second order expansion for the…”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, methodology): “t;z)jand thus may be considered as a bound on the rate of convergence in the delta method for vector statistics; it is the latter bound that took more of our time and eort. The reader is referred to [110] for a rather detailed description of the delta method and its applications; see [57,101] for a ”
Debiasing Evidence Approximations: On Importance-weighted Autoencoders and Jackknife Variational Inference (2018, methodology): “One classic method is the delta method for bias correction Small (2010).”
On the Laplace Transform of the Lognormal Distribution (2014, methodology): “Finally, we discuss the approximation obtained by using the so-called asymptotic saddlepoint methodology [11, 23].”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, methodology): “s It turns out that the bias analysis in estimation, albeit widely studied in statistics, seems to still largely bear an asymptotic and expansion nature in the mainstream statistical literature [53], [54]. In particular, the bootstrap [55] as a method for estimating functionals was essentially only ”
Cleaning Crowdsourced Labels Using Oracles For Statistical Classification (2018, unknown): “, approximate E[ Y ] as E[X] E[Y ] [21, 29, 34, 38].”