Likelihood, Replicability and Robbins' Confidence Sequences

Empirical Likelihood Confidence Band

OF DISSERTATION Empirical Likelihood Confidence Band The confidence band represents an important measure of uncertainty associated with a functional estimator and empirical likelihood method has been proved to be a viable approach to constructing confidence bands in many cases. Using the empirical likelihood ratio principle, this dissertation developed simultaneous confidence bands for many fun...

Empirical likelihood based confidence intervals for copulas

Copula as an effective way of modeling dependence has become more or less a standard tool in risk management, and a wide range of applications of copula models appear in the literature of economics, econometrics, insurance, finance, etc. How to estimate and test a copula plays an important role in practice, and both parametric and nonparametric methods have been studied in the literature. In th...

Nonaliquots and Robbins Numbers∗

Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of m ≤ x for which the equation m = σ(n)−n has no solution. We also show that the set of positive integers m not of the form (p − 1)/2 − φ(p − 1) for some prime number p has a positive lower asymptotic density. ∗MSC numbers: 11A25; 11A41, 11N64

Variations on KamLAND: likelihood analysis and frequentist confidence regions

In this letter the robustness of the first results from the KamLAND reactor neutrino experiment with respect to variations in the statistical analysis is considered. It is shown that an event-by-event based likelihood analysis provides a more powerful tool to extract information from the currently available data sample than a leastsquares method based on energy binned data. Furthermore, a frequ...

Variations on KamLAND: likelihood analysis and frequentist confidence regions