643 research outputs found
Regularization-free estimation in trace regression with symmetric positive semidefinite matrices
Over the past few years, trace regression models have received considerable
attention in the context of matrix completion, quantum state tomography, and
compressed sensing. Estimation of the underlying matrix from
regularization-based approaches promoting low-rankedness, notably nuclear norm
regularization, have enjoyed great popularity. In the present paper, we argue
that such regularization may no longer be necessary if the underlying matrix is
symmetric positive semidefinite (\textsf{spd}) and the design satisfies certain
conditions. In this situation, simple least squares estimation subject to an
\textsf{spd} constraint may perform as well as regularization-based approaches
with a proper choice of the regularization parameter, which entails knowledge
of the noise level and/or tuning. By contrast, constrained least squares
estimation comes without any tuning parameter and may hence be preferred due to
its simplicity
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
Application of parameter estimation to aircraft stability and control: The output-error approach
The practical application of parameter estimation methodology to the problem of estimating aircraft stability and control derivatives from flight test data is examined. The primary purpose of the document is to present a comprehensive and unified picture of the entire parameter estimation process and its integration into a flight test program. The document concentrates on the output-error method to provide a focus for detailed examination and to allow us to give specific examples of situations that have arisen. The document first derives the aircraft equations of motion in a form suitable for application to estimation of stability and control derivatives. It then discusses the issues that arise in adapting the equations to the limitations of analysis programs, using a specific program for an example. The roles and issues relating to mass distribution data, preflight predictions, maneuver design, flight scheduling, instrumentation sensors, data acquisition systems, and data processing are then addressed. Finally, the document discusses evaluation and the use of the analysis results
Two-Channel Speech Enhancement and Implementation Considerations: Noise Reduction and Speech Quality
- …