Selecting tuning parameters in minimum distance estimators

Many minimum distance estimators have the potential to provide parameter estimates which are both robust and efficient and yet, despite these highly desirable theoretical properties, they are rarely used in practice. This is because the performance of these estimators is rarely guaranteed per se but obtained by placing a suitable value on some tuning parameter. Hence there is a risk involved in implementing these methods because if the value chosen for the tuning parameter is inappropriate for the data to which the method is applied, the resulting estimators may not have the desired theoretical properties and could even perform less well than one of the simpler, more widely used alternatives. There are currently no data-based methods available for deciding what value one should place on these tuning parameters hence the primary aim of this research is to develop an objective way of selecting values for the tuning parameters in minimum distance estimators so that the full potential of these estimators might be realised. This new method was initially developed to optimise the performance of the density power divergence estimator, which was proposed by Basu, Harris, Hjort and Jones [3]. The results were very promising so the method was then applied to two other minimum distance estimators and the results compared

Model selection in High-Dimensions: A Quadratic-risk based approach

In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a nonnegative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a quick-to-compute approximation for the risk function. Its derivation is analogous to the Akaike Information Criterion (AIC), but unlike AIC, the quadratic risk is a global comparison tool. The method does not require resampling, a great advantage when point estimators are expensive to compute. The method is illustrated using the problem of selecting the number of components in a mixture model, where it is shown that, by using an appropriate kernel, the method is computationally straightforward in arbitrarily high data dimensions. In this same context it is shown that the method has some clear advantages over AIC and BIC.Comment: Updated with reviewer suggestion

The Kentucky Noisy Monte Carlo Algorithm for Wilson Dynamical Fermions

We develop an implementation for a recently proposed Noisy Monte Carlo approach to the simulation of lattice QCD with dynamical fermions by incorporating the full fermion determinant directly. Our algorithm uses a quenched gauge field update with a shifted gauge coupling to minimize fluctuations in the trace log of the Wilson Dirac matrix. The details of tuning the gauge coupling shift as well as results for the distribution of noisy estimators in our implementation are given. We present data for some basic observables from the noisy method, as well as acceptance rate information and discuss potential autocorrelation and sign violation effects. Both the results and the efficiency of the algorithm are compared against those of Hybrid Monte Carlo. PACS Numbers: 12.38.Gc, 11.15.Ha, 02.70.Uu Keywords: Noisy Monte Carlo, Lattice QCD, Determinant, Finite Density, QCDSPComment: 30 pages, 6 figure

Efficient and robust estimation for financial returns: an approach based on q-entropy

We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvàt-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-off between robustness and effciency. The method is applied to expected return and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical results on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.q-entropy; robust estimation; power-divergence; financial returns