852,261 research outputs found
Efficient information theoretic inference for conditional moment restrictions
The generalized method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first order equivalent semi-parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel-weighted version of the Cressie-Read power divergence family of discrepancies. This approach is similar in spirit to the empirical likelihood methods of Kitamura, Tripathi and Ahn (2004) and Tripathi and Kitamura (2003). These efficient local methods avoid the necessity of explicit estimation of the conditional Jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations.Conditional Moment Restrictions, Local Cressie-Read Minimum Discrepancy, GMM, Semi-Parametric Efficiency
On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions
Full likelihood-based inference for high-dimensional multivariate extreme
value distributions, or max-stable processes, is feasible when incorporating
occurrence times of the maxima; without this information, -dimensional
likelihood inference is usually precluded due to the large number of terms in
the likelihood. However, some studies have noted bias when performing
high-dimensional inference that incorporates such event information,
particularly when dependence is weak. We elucidate this phenomenon, showing
that for unbiased inference in moderate dimensions, dimension should be of
a magnitude smaller than the square root of the number of vectors over which
one takes the componentwise maximum. A bias reduction technique is suggested
and illustrated on the extreme value logistic model.Comment: 7 page
Bayesian inference with information content model check for Langevin equations
The Bayesian data analysis framework has been proven to be a systematic and
effective method of parameter inference and model selection for stochastic
processes. In this work we introduce an information content model check which
may serve as a goodness-of-fit, like the chi-square procedure, to complement
conventional Bayesian analysis. We demonstrate this extended Bayesian framework
on a system of Langevin equations, where coordinate dependent mobilities and
measurement noise hinder the normal mean squared displacement approach.Comment: 10 pages, 7 figures, REVTeX, minor revision
Statistical Mechanics of High-Dimensional Inference
To model modern large-scale datasets, we need efficient algorithms to infer a
set of unknown model parameters from noisy measurements. What are
fundamental limits on the accuracy of parameter inference, given finite
signal-to-noise ratios, limited measurements, prior information, and
computational tractability requirements? How can we combine prior information
with measurements to achieve these limits? Classical statistics gives incisive
answers to these questions as the measurement density . However, these classical results are not
relevant to modern high-dimensional inference problems, which instead occur at
finite . We formulate and analyze high-dimensional inference as a
problem in the statistical physics of quenched disorder. Our analysis uncovers
fundamental limits on the accuracy of inference in high dimensions, and reveals
that widely cherished inference algorithms like maximum likelihood (ML) and
maximum-a posteriori (MAP) inference cannot achieve these limits. We further
find optimal, computationally tractable algorithms that can achieve these
limits. Intriguingly, in high dimensions, these optimal algorithms become
computationally simpler than MAP and ML, while still outperforming them. For
example, such optimal algorithms can lead to as much as a 20% reduction in the
amount of data to achieve the same performance relative to MAP. Moreover, our
analysis reveals simple relations between optimal high dimensional inference
and low dimensional scalar Bayesian inference, insights into the nature of
generalization and predictive power in high dimensions, information theoretic
limits on compressed sensing, phase transitions in quadratic inference, and
connections to central mathematical objects in convex optimization theory and
random matrix theory.Comment: See http://ganguli-gang.stanford.edu/pdf/HighDimInf.Supp.pdf for
supplementary materia
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