We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their...

background breast cancer (bc) is the most common cancer in iranian women. studying the mortality statistics is important to monitor the effects of screening programs or the influence of earlier diagnosis on the burden of this chronic disease. misclassification is still a problem in the iranian death registry data and about 20% of death statistics are recorded in misclassified categories. object...

Across many forms of rent seeking contests, the impact of risk aversion on equilibrium play is indeterminate. We design an experiment to compare individuals’ decisions across three contests which are isomorphic under risk-neutrality, but are typically not isomorphic under other risk preferences. The pattern of individual play across our contests is not consistent with a Bayes-Nash equilibrium f...

It is worth keeping in mind the trade-off: Bayes estimators although easy to compute are somewhat subjective (in that they depend strongly on the prior π). Minimax estimators although more challenging to compute are not subjective, but do have the drawback that they are protecting against the worst-case which might lead to pessimistic conclusions, i.e. the minimax risk might be much higher than...

A k-nearest-neighbor classifier is approximated by a labeled cell classifier that recursively labels the nodes of a hierarchically organized reference sample (e.g., a k-d tree) if a local estimate of the conditional Bayes risk is sufficiently small. Simulations suggest that the labeled cell classifier is significantly faster than k-d tree implementations for problems with small Bayes risk; and ...

Of those things that can be estimated well in an inverse problem, which are best to estimate? Backus-Gilbert resolution theory answers a version of this question for linear (or linearized) inverse problems in Hilbert spaces with additive zero-mean errors with known, finite covariance, and no constraints on the unknown other than the data. This paper extends Backus-Gilbert resolution: it defines...

Vector Quantization (VQ) has its origins in signal processing where it is used for compact, accurate representation of input signals. However, since VQ induces a partitioning of the input space, it can also be used for statistical pattern recognition. In this paper we present a novel gradient descent VQ classi cation algorithm which minimizes the Bayes Risk, which we refer to as the Generalized...