23,762 research outputs found
Estimating linear functionals in nonlinear regression with responses missing at random
We consider regression models with parametric (linear or nonlinear)
regression function and allow responses to be ``missing at random.'' We assume
that the errors have mean zero and are independent of the covariates. In order
to estimate expectations of functions of covariate and response we use a fully
imputed estimator, namely an empirical estimator based on estimators of
conditional expectations given the covariate. We exploit the independence of
covariates and errors by writing the conditional expectations as unconditional
expectations, which can now be estimated by empirical plug-in estimators. The
mean zero constraint on the error distribution is exploited by adding suitable
residual-based weights. We prove that the estimator is efficient (in the sense
of H\'{a}jek and Le Cam) if an efficient estimator of the parameter is used.
Our results give rise to new efficient estimators of smooth transformations of
expectations. Estimation of the mean response is discussed as a special
(degenerate) case.Comment: Published in at http://dx.doi.org/10.1214/08-AOS642 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Inference about the slope in linear regression: an empirical likelihood approach
We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719, 2017), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study
Efficient prediction for linear and nonlinear autoregressive models
Conditional expectations given past observations in stationary time series
are usually estimated directly by kernel estimators, or by plugging in kernel
estimators for transition densities. We show that, for linear and nonlinear
autoregressive models driven by independent innovations, appropriate smoothed
and weighted von Mises statistics of residuals estimate conditional
expectations at better parametric rates and are asymptotically efficient. The
proof is based on a uniform stochastic expansion for smoothed and weighted von
Mises processes of residuals. We consider, in particular, estimation of
conditional distribution functions and of conditional quantile functions.Comment: Published at http://dx.doi.org/10.1214/009053606000000812 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimality of estimators for misspecified semi-Markov models
Suppose we observe a geometrically ergodic semi-Markov process and have a
parametric model for the transition distribution of the embedded Markov chain,
for the conditional distribution of the inter-arrival times, or for both. The
first two models for the process are semiparametric, and the parameters can be
estimated by conditional maximum likelihood estimators. The third model for the
process is parametric, and the parameter can be estimated by an unconditional
maximum likelihood estimator. We determine heuristically the asymptotic
distributions of these estimators and show that they are asymptotically
efficient. If the parametric models are not correct, the (conditional) maximum
likelihood estimators estimate the parameter that maximizes the
Kullback--Leibler information. We show that they remain asymptotically
efficient in a nonparametric sense.Comment: To appear in a Special Volume of Stochastics: An International
Journal of Probability and Stochastic Processes
(http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited
by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of
the IMS Lecture Notes Monograph Series
(http://imstat.org/publications/lecnotes.htm
Variable Metric Random Pursuit
We consider unconstrained randomized optimization of smooth convex objective
functions in the gradient-free setting. We analyze Random Pursuit (RP)
algorithms with fixed (F-RP) and variable metric (V-RP). The algorithms only
use zeroth-order information about the objective function and compute an
approximate solution by repeated optimization over randomly chosen
one-dimensional subspaces. The distribution of search directions is dictated by
the chosen metric.
Variable Metric RP uses novel variants of a randomized zeroth-order Hessian
approximation scheme recently introduced by Leventhal and Lewis (D. Leventhal
and A. S. Lewis., Optimization 60(3), 329--245, 2011). We here present (i) a
refined analysis of the expected single step progress of RP algorithms and
their global convergence on (strictly) convex functions and (ii) novel
convergence bounds for V-RP on strongly convex functions. We also quantify how
well the employed metric needs to match the local geometry of the function in
order for the RP algorithms to converge with the best possible rate.
Our theoretical results are accompanied by numerical experiments, comparing
V-RP with the derivative-free schemes CMA-ES, Implicit Filtering, Nelder-Mead,
NEWUOA, Pattern-Search and Nesterov's gradient-free algorithms.Comment: 42 pages, 6 figures, 15 tables, submitted to journal, Version 3:
majorly revised second part, i.e. Section 5 and Appendi
Fast high--voltage amplifiers for driving electro-optic modulators
We describe five high-voltage (60 to 550V peak to peak), high-speed (1-300ns
rise time; 1.3-300MHz bandwidth) linear amplifiers for driving capacitive or
resistive loads such as electro-optic modulators. The amplifiers use bipolar
transistors in various topologies. Two use electron tubes to overcome the speed
limitations of high-voltage semiconductors. All amplifiers have been built.
Measured performance data is given for each.Comment: 9pages, 6figures, 6tables, to appear in Review of Scientific
Instrument
A simple model of price formation
A simple Ising spin model which can describe the mechanism of price formation
in financial markets is proposed. In contrast to other agent-based models, the
influence does not flow inward from the surrounding neighbors to the center
site, but spreads outward from the center to the neighbors. The model thus
describes the spread of opinions among traders. It is shown via standard Monte
Carlo simulations that very simple rules lead to dynamics that duplicate those
of asset prices.Comment: Version 2: 4 pages, 4 figures; added more stringent statistical
analysis; to appear in Int. J. Modern Physics C, Vol. 13, No. 1 (2002
Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light
We investigate the transmission of focused beams through single subwavelength
holes in a silver film. We use radially and azimuthally polarized light,
respectively, to excite higher order waveguide modes as well as to match the
radial symmetry of the aperture geometry. Remarkably, the transmission
properties can be described by a classical waveguide model even for thicknesses
of the silver film as thin as a quarter of a wavelength
- …