6 research outputs found
Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications
Inferring information from a set of acquired data is the main objective of
any signal processing (SP) method. In particular, the common problem of
estimating the value of a vector of parameters from a set of noisy measurements
is at the core of a plethora of scientific and technological advances in the
last decades; for example, wireless communications, radar and sonar,
biomedicine, image processing, and seismology, just to name a few. Developing
an estimation algorithm often begins by assuming a statistical model for the
measured data, i.e. a probability density function (pdf) which if correct,
fully characterizes the behaviour of the collected data/measurements.
Experience with real data, however, often exposes the limitations of any
assumed data model since modelling errors at some level are always present.
Consequently, the true data model and the model assumed to derive the
estimation algorithm could differ. When this happens, the model is said to be
mismatched or misspecified. Therefore, understanding the possible performance
loss or regret that an estimation algorithm could experience under model
misspecification is of crucial importance for any SP practitioner. Further,
understanding the limits on the performance of any estimator subject to model
misspecification is of practical interest. Motivated by the widespread and
practical need to assess the performance of a mismatched estimator, the goal of
this paper is to help to bring attention to the main theoretical findings on
estimation theory, and in particular on lower bounds under model
misspecification, that have been published in the statistical and econometrical
literature in the last fifty years. Secondly, some applications are discussed
to illustrate the broad range of areas and problems to which this framework
extends, and consequently the numerous opportunities available for SP
researchers.Comment: To appear in the IEEE Signal Processing Magazin
Slepian-Bangs formula and Cramér Rao bound for circular and non-circular complex elliptical symmetric distributions
International audienceThis letter is mainly dedicated to an extension of the Slepian-Bangs formula to non-circular complex elliptical symmetric (NC-CES) distributions, which is derived from a new stochastic representation theorem. This formula includes the non-circular complex Gaussian and the circular CES (C-CES) distributions. Some general relations between the Cramér Rao bound (CRB) under CES and Gaussian distributions are deduced. It is proved in particular that the Gaussian distribution does not always lead to the largest stochastic CRB (SCRB) as many authors tend to believe it. Finally a particular attention is paid to the noisy mixture where closed-form expressions for the SCRBs of the parameters of interest are derived
A Lower Bound on the Mean Square Estimation Error Under Model Mismatching
In this paper, a covariance inequality for the Mean Square Error (MSE) of any estimator of a real deterministic parameter vector under misspecified models is derived. In addition, a closed form expression of the lower bound (called the Huber bound (HB)) on the MSE of the Mismatched Maximum Likelihood estimator (MML) is proposed and its relation with the Huber “sandwich” covariance matrix is investigated. A toy example is also provided to clarify the theoretical findings. Furthermore, the application of the proposed framework to the estimation of the scatter matrix in the Complex Elliptically Symmetric (CES) distributions is discussed. In particular, the performance of the MML estimator is compared, under mismatched conditions, with the derived HB and with the Cramér-Rao Lower Bound (CRLB) in some relevant study case
Innovations in Quantitative Risk Management
Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science
Innovations in Quantitative Risk Management
Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science
STK /WST 795 Research Reports
These documents contain the honours research reports for each year for the Department of Statistics.Honours Research Reports - University of Pretoria 20XXStatisticsBSs (Hons) Mathematical Statistics, BCom (Hons) Statistics, BCom (Hons) Mathematical StatisticsUnrestricte