2,544 research outputs found
The semiparametric Bernstein-von Mises theorem
In a smooth semiparametric estimation problem, the marginal posterior for the
parameter of interest is expected to be asymptotically normal and satisfy
frequentist criteria of optimality if the model is endowed with a suitable
prior. It is shown that, under certain straightforward and interpretable
conditions, the assertion of Le Cam's acclaimed, but strictly parametric,
Bernstein-von Mises theorem [Univ. California Publ. Statist. 1 (1953) 277-329]
holds in the semiparametric situation as well. As a consequence, Bayesian
point-estimators achieve efficiency, for example, in the sense of H\'{a}jek's
convolution theorem [Z. Wahrsch. Verw. Gebiete 14 (1970) 323-330]. The model is
required to satisfy differentiability and metric entropy conditions, while the
nuisance prior must assign nonzero mass to certain Kullback-Leibler
neighborhoods [Ghosal, Ghosh and van der Vaart Ann. Statist. 28 (2000)
500-531]. In addition, the marginal posterior is required to converge at
parametric rate, which appears to be the most stringent condition in examples.
The results are applied to estimation of the linear coefficient in partial
linear regression, with a Gaussian prior on a smoothness class for the
nuisance.Comment: Published in at http://dx.doi.org/10.1214/11-AOS921 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Development of flight check-out system Final report
Flight checkout system breadboard design, construction and testin
On a semiparametric survival model with flexible covariate effect.
A semiparametric hazard model with parametrized time but general covariate dependency is formulated and analyzed inside the framework of counting process theory. A profile likelihood principle is introduced for estimation of the parameters: the resulting estimator is n1/2-consistent, asymptotically normal and achieves the semiparametric efficiency bound. An estimation procedure for the nonparametric part is also given and its asymptotic properties are derived. We provide an application to mortality data.
The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA?
We consider the Bayesian analysis of a few complex, high-dimensional models
and show that intuitive priors, which are not tailored to the fine details of
the model and the estimated parameters, produce estimators which perform poorly
in situations in which good, simple frequentist estimators exist. The models we
consider are: stratified sampling, the partial linear model, linear and
quadratic functionals of white noise and estimation with stopping times. We
present a strong version of Doob's consistency theorem which demonstrates that
the existence of a uniformly -consistent estimator ensures that the
Bayes posterior is -consistent for values of the parameter in subsets
of prior probability 1. We also demonstrate that it is, at least, in principle,
possible to construct Bayes priors giving both global and local minimax rates,
using a suitable combination of loss functions. We argue that there is no
contradiction in these apparently conflicting findings.Comment: Published in at http://dx.doi.org/10.1214/14-STS483 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An efficiency upper bound for inverse covariance estimation
We derive an upper bound for the efficiency of estimating entries in the
inverse covariance matrix of a high dimensional distribution. We show that in
order to approximate an off-diagonal entry of the density matrix of a
-dimensional Gaussian random vector, one needs at least a number of samples
proportional to . Furthermore, we show that with samples, the
hypothesis that two given coordinates are fully correlated, when all other
coordinates are conditioned to be zero, cannot be told apart from the
hypothesis that the two are uncorrelated.Comment: 7 Page
Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk
When a parameter of interest is nondifferentiable in the probability, the
existing theory of semiparametric efficient estimation is not applicable, as it
does not have an influence function. Song (2014) recently developed a local
asymptotic minimax estimation theory for a parameter that is a
nondifferentiable transform of a regular parameter, where the nondifferentiable
transform is a composite map of a continuous piecewise linear map with a single
kink point and a translation-scale equivariant map. The contribution of this
paper is two fold. First, this paper extends the local asymptotic minimax
theory to nondifferentiable transforms that are a composite map of a Lipschitz
continuous map having a finite set of nondifferentiability points and a
translation-scale equivariant map. Second, this paper investigates the
discontinuity of the local asymptotic minimax risk in the true probability and
shows that the proposed estimator remains to be optimal even when the risk is
locally robustified not only over the scores at the true probability, but also
over the true probability itself. However, the local robustification does not
resolve the issue of discontinuity in the local asymptotic minimax risk
Data-driven efficient score tests for deconvolution problems
We consider testing statistical hypotheses about densities of signals in
deconvolution models. A new approach to this problem is proposed. We
constructed score tests for the deconvolution with the known noise density and
efficient score tests for the case of unknown density. The tests are
incorporated with model selection rules to choose reasonable model dimensions
automatically by the data. Consistency of the tests is proved
Ablation debris control by means of closed thick film filtered water immersion
The performance of laser ablation generated debris control by means of open immersion techniques have been shown to be limited by flow surface ripple effects on the beam and the action of ablation plume pressure loss by splashing of the immersion fluid. To eradicate these issues a closed technique has been developed which ensured a controlled geometry for both the optical interfaces of the flowing liquid film. This had the action of preventing splashing, ensuring repeatable machining conditions and allowed for control of liquid flow velocity. To investigate the performance benefits of this closed immersion technique bisphenol A polycarbonate samples have been machined using filtered water at a number of flow velocities. The results demonstrate the efficacy of the closed immersion technique: a 93% decrease in debris is produced when machining under closed filtered water immersion; the average debris particle size becomes larger, with an equal proportion of small and medium sized debris being produced when laser machining under closed flowing filtered water immersion; large debris is shown to be displaced further by a given flow velocity than smaller debris, showing that the action of flow turbulence in the duct has more impact on smaller debris. Low flow velocities were found to be less effective at controlling the positional trend of deposition of laser ablation generated debris than high flow velocities; but, use of excessive flow velocities resulted in turbulence motivated deposition. This work is of interest to the laser micromachining community and may aide in the manufacture of 2.5D laser etched patterns covering large area wafers and could be applied to a range of wavelengths and laser types
Effects of different energy intakes before and after calving on food intake, performance and blood hormones and metabolites in dairy cows
An experiment with 25 dairy cows was performed to investigate the effects of different energy intakes on food intake, performance and blood hormone and metabolite levels during the last 70 days of pregnancy and the first 125 days after parturition. Compared with animals fed ad libitum before parturition, cows fed only according to requirements during the same time showed no decrease of food intake at calving. Cows fed at a restricted level also showed a faster increase in food intake, a smaller energy deficiency at the onset of lactation and a smaller weight loss after parturition. Peak milk yield was also lower, but the peak was maintained for a longer period, and during the first 2 months of lactation these cows had higher concentrations of glucose and lactic acid, and lower concentrations of non-esterified fatty acids and ketone bodies in the blood. Weight losses, and decrease of milk production during the 1st weeks of lactation were higher in cows fed only 0¡75 of requirements during the first 60 days of lactation than in animals whose energy intake was planned to cover energy requirements, and during the first 2 months of lactation levels of unesterified fatty acids, ketone bodies and urea were higher, whereas levels of insulin, thyroxine and triiodothyronine were lower. Endocrine and metabolic changes seen during early lactation suggested improved glucose homeostasis, diminished fat mobilization and ketogenesis in cows given reduced amounts of energy during the dry period compared to animals fed ad libitum. To prevent the development of acetonaemia an adequate energy supply during the first part of lactation is, however, of greater importanc
Statistical mechanics of a colloidal suspension in contact with a fluctuating membrane
Surface effects are generally prevailing in confined colloidal systems. Here
we report on dispersed nanoparticles close to a fluid membrane. Exact results
regarding the static organization are derived for a dilute solution of
non-adhesive colloids. It is shown that thermal fluctuations of the membrane
broaden the density profile, but on average colloids are neither accumulated
nor depleted near the surface. The radial correlation function is also
evaluated, from which we obtain the effective pair-potential between colloids.
This entropically-driven interaction shares many similarities with the familiar
depletion interaction. It is shown to be always attractive with range
controlled by the membrane correlation length. The depth of the potential well
is comparable to the thermal energy, but depends only indirectly upon membrane
rigidity. Consequenses for stability of the suspension are also discussed
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