5,748 research outputs found
Generalized robust shrinkage estimator and its application to STAP detection problem
Recently, in the context of covariance matrix estimation, in order to improve
as well as to regularize the performance of the Tyler's estimator [1] also
called the Fixed-Point Estimator (FPE) [2], a "shrinkage" fixed-point estimator
has been introduced in [3]. First, this work extends the results of [3,4] by
giving the general solution of the "shrinkage" fixed-point algorithm. Secondly,
by analyzing this solution, called the generalized robust shrinkage estimator,
we prove that this solution converges to a unique solution when the shrinkage
parameter (losing factor) tends to 0. This solution is exactly the FPE
with the trace of its inverse equal to the dimension of the problem. This
general result allows one to give another interpretation of the FPE and more
generally, on the Maximum Likelihood approach for covariance matrix estimation
when constraints are added. Then, some simulations illustrate our theoretical
results as well as the way to choose an optimal shrinkage factor. Finally, this
work is applied to a Space-Time Adaptive Processing (STAP) detection problem on
real STAP data
Robust approximate Bayesian inference
We discuss an approach for deriving robust posterior distributions from
-estimating functions using Approximate Bayesian Computation (ABC) methods.
In particular, we use -estimating functions to construct suitable summary
statistics in ABC algorithms. The theoretical properties of the robust
posterior distributions are discussed. Special attention is given to the
application of the method to linear mixed models. Simulation results and an
application to a clinical study demonstrate the usefulness of the method. An R
implementation is also provided in the robustBLME package.Comment: This is a revised and personal manuscript version of the article that
has been accepted for publication by Journal of Statistical Planning and
Inferenc
Efficient Robust Estimation of Regression Models (Revision of DP 2006-08)
This paper introduces a new class of robust regression estimators. The proposed twostep least weighted squares (2S-LWS) estimator employs data-adaptive weights determined from the empirical distribution, quantile, or density functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However contrary to existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions; most importantly, the initial estimator does not need to be pn consistent. Moreover, we prove that 2S-LWS is asymptotically normal under B-mixing conditions and asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of 2S-LWS can reach 85–90% in samples of several tens of observations under various distributional models.asymptotic efficiency;breakdown point;least weighted squares
Nonparametric Frontier Estimation from Noisy Data
A new nonparametric estimator of production a frontier is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.
Nonparametric frontier estimation from noisy data
A new nonparametric estimator of production frontiers is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.production frontier, deconvolution, measurement error, efficiency analysis
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