Published in Mathematical Methods of Statistics
AbstractThis work studies the problem of binary classification with the F-score as the performance measure. We propose a post-processing algorithm for this problem which fits a threshold for any score base classifier to yield high F-score. The post-processing step involves only unlabeled data and can be performed in logarithmic time. We derive a ge...
Published in Mathematical Methods of Statistics
AbstractIn the regression model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y=b(X)+\sigma(X)\varepsilon$$\end{document}, where \documentclass[12pt]{minimal} \usepac...
Published in Mathematical Methods of Statistics
AbstractGiven observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing procedures using a projection approach. The structure of the optimal tests depends on regularity and ill-po...
Published in Mathematical Methods of Statistics
AbstractIn this note, we provide upper bounds on the expectation of the supremum of empirical processes indexed by Hölder classes of any smoothness and for any distribution supported on a bounded set in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...
Published in Mathematical Methods of Statistics
AbstractIn this paper, we consider the problem of estimating the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d$$\end{document}-th order derivative \documentclass[12...
Published in Mathematical Methods of Statistics
AbstractIn this paper, we develop Bayes and maximum a posteriori probability (MAP) approaches to monotonicity testing. In order to simplify this problem, we consider a simple white Gaussian noise model and with the help of the Haar transform we reduce it to the equivalent problem of testing positivity of the Haar coefficients. This approach permits...
Published in Mathematical Methods of Statistics
For a multinormal distribution with a p-dimensional mean vector θ and an arbitrary unknown dispersion matrix Σ, Rao ([8], [9]) proposed two tests for the problem of testing H0: θ1 = 0, θ2 = 0, Σ unspecified, versus H1: θ1 ≠ 0, θ2 = 0, Σ unspecified. These tests are known as Rao’s W-test and Rao’s U-test, respectively. In this paper, it is shown tha...
Published in Mathematical Methods of Statistics
In this paper we consider the problem of non-parametric relative regression for twice censored data. We introduce and study a new estimate of the regression function when it is appropriate to assess performance in terms of mean squared relative error of prediction. We establish the uniform consistency with rate over a compact set and asymptotic nor...
Published in Mathematical Methods of Statistics
The consistency of the Aalen—Johansen-derived estimator of state occupation probabilities in non-Markov multi-state settings is studied and established via a new route. This new route is based on interval functions and relies on a close connection between additive and multiplicative transforms of interval functions, which is established. Under cert...
Published in Mathematical Methods of Statistics
Van Zwet (1964) [16] introduced the convex transformation order between two distribution functions F and G, defined by F ≤cG if G−1 ∘ F is convex. A distribution which precedes G in this order should be seen as less right-skewed than G. Consequently, if F ≤cG, any reasonable measure of skewness should be smaller for F than for G. This property is t...
