Recognition of ring pairs in the data analysis of Cherenkov detectors

We present a new algorithm for the identification of ring pairs in Cherenkov detectors. The approach combines linear regression methods for the construction of an appropriate reference quantity, methods from statistics for the evaluation of hypotheses and Monte Carlo simulation runs for the tuning of threshold levels.     

A result on hypothesis testing for a multivariate normal distribution when some observations are missing

Let U_i = (X_i, Y_i), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μ_x, μ_y) and covariance matrix

. Let X_i, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H₀ : μ = 0 vs. H₁ : μ ≠ 0. We prove that Hotelling's T² test, which uses (X_i, Y_i), i = 1, 2,…, n (and discards X_i, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T²-test cannot be beaten. A similar result is also proved for the problem of testing μ_x ? μ_y = 0. A Bayes test and other competitors which are similar tests are discussed.     

Tychonoff expansions by independent families

A method for Tychonoff expansions using independent families is introduced. Using this method we prove that every countable Tychonoff space which admits a partition into infinitely many open-hereditarily irresolvable dense subspaces has a Tychonoff expansion that is -resolvable but not strongly extraresolvable. We also show that, under Luzin's Hypothesis ( ), there exists an -resolvable Tychonoff space of size which is not maximally resolvable.

     

The Design and Analysis of Benchmark Experiments

The assessment of the performance of learners by means of benchmark experiments is an established exercise. In practice, benchmark studies are a tool to compare the performance of several competing algorithms for a certain learning problem. Cross-validation or resampling techniques are commonly used to derive point estimates of the performances which are compared to identify algorithms with good properties. For several benchmarking problems, test procedures taking the variability of those point estimates into account have been suggested. Most of the recently proposed inference procedures are based on special variance estimators for the cross-validated performance. We introduce a theoretical framework for inference problems in benchmark experiments and show that standard statistical test procedures can be used to test for differences in the performances. The theory is based on well-defined distributions of performance measures which can be compared with established tests. To demonstrate the usefulness in practice, the theoretical results are applied to regression and classification benchmark studies based on artificial and real world data.     

Bootstrap tests for unit roots in seasonal autoregressive models

This paper proposes bootstrap tests for the presence of unit roots in a seasonal autoregressive model. The asymptotic validity of the proposed bootstrap scheme is established, and Monte Carlo experiments are used to investigate the small-sample performance of the tests.     

On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

Testing procedures for detection of linear dependencies in efficiency models

The validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of (or uncorrelated with) technical efficiency, however few studies have attempted to test these assumptions. In a recent paper, Wilson (2003) investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes. In this study we discuss the implications of these assumptions in three situations: (i) bootstrapping non-parametric efficiency models; (ii) estimating stochastic frontier models and (iii) obtaining aggregate measures of industry efficiency. We propose a semi-parametric Hausmann-type asymptotic test for linear independence (uncorrelation), and use a Monte Carlo experiment to show that it has good size and power properties in finite samples. We also describe how the test can be generalized in order to detect higher order dependencies, such as heteroscedasticity, so that the test can be used to test for (full) independence when the efficiency distribution has a finite number of moments. Finally, an empirical illustration is provided using data on US electric power generation.     

A compact F-space not co-absolute with βN−N

We show that if every Parovi?enko space of weight $\text{c}$ is co-absolute with $\text{β}\text{N}\text{?}\text{N}$, then .     

First countable, countably compact spaces and the continuum hypothesis

We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah's iteration theorems appearing in Chapters V and VIII of Proper and improper forcing (1998), as well as Eisworth and Roitman's (1999) iteration theorem. We close the paper with a ZFC example (constructed using Shelah's club-guessing sequences) that shows similar results do not hold for closed pre-images of .