Distributional inference

The making of statistical inferences in distributional form is conceptionally complicated because the epistemic 'probabilities' assigned are mixtures of fact and fiction. In this respect they are essentially different from 'physical' or 'frequency-theoretic' probabilities. The distributional form is so attractive and useful, however, that it should be pursued. Our approach is In line with Walds theory of statistical decision functions and with Lehmann's books about hypothesis testing and point estimation: loss functions are defined, risk functions are studied, unbiasedness and equivariance restrictions are made, etc. A central theme is that the loss function should be 'proper'. This fundamental concept has been explored by meteorologists, psychometrists, Bayesian statisticians, and others. The paper should be regarded as an attempt to reconcile various schools of statisticians. By accepting what we regard 88 good and useful in the various approaches we are trying to develop a nondogmatic approach

Model confidence sets for forecasting models

The paper introduces the model confidence set (MCS) and applies it to the selection of forecasting models. An MCS is a set of models that is constructed so that it will contain the “best” forecasting model, given a level of confidence. Thus, an MCS is analogous to a confidence interval for a parameter. The MCS acknowledges the limitations of the data so that uninformative data yield an MCS with many models, whereas informative data yield an MCS with only a few models. We revisit the empirical application in Stock and Watson (1999) and apply the MCS procedure to their set of inflation forecasts. In the first pre-1984 subsample we obtain an MCS that contains only a few models, notably versions of the Solow-Gordon Phillips curve. On the other hand, the second post-1984 subsample contains little information and results in a large MCS. Yet, the random walk forecast is not contained in the MCS for either of the samples. This outcome shows that the random walk forecast is inferior to inflation forecasts based on Phillips curve-like relationships.

Confidence Statements for Ordering Quantiles

This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and independence is its only requirement. All computations are performed using exact distributions with no need for any asymptotic considerations, and yet can be run using a fast quadratic-time dynamic programming idea. Computational performance is essential in high-dimensional domains, such as gene expression data. We describe the approach and discuss on the most important assumptions, building a parallel with assumptions and properties of widely used techniques for the same problem. Experiments using real data from biomedical studies are performed to empirically compare Quor and other methods in a classification task over a selection of high-dimensional data sets