-аппроксимация функции правдоподобия
Náhodové diferenciální rovnice
Natural a-Quantiles and Conditional a-Quantlies.
N-dimensional measures of dependence.
In recent joint papers with B. Schweizer, we used the notion of a copula to introduce a family of symmetric, nonparametric measures of dependence of two random variables. Here, we present n-dimensional extensions of these measures and of Spearman's ro. We study them vis-a-vis appropriate higher dimensional analogues of Rényi's axioms for measures of dependence, determine relations among them, and in some cases establish reduction formulae for their computation.
Nearest neighbor classification in infinite dimension
Let X be a random element in a metric space (F,d), and let Y be a random variable with value 0 or 1. Y is called the class, or the label, of X. Let (Xi,Yi)1 ≤ i ≤ n be an observed i.i.d. sample having the same law as (X,Y). The problem of classification is to predict the label of a new random element X. The k-nearest neighbor classifier is the simple following rule: look at the k nearest neighbors of X in the trial sample and choose 0 or 1 for its label according to the majority vote. When , Stone...
Near-exact distributions for the generalized Wilks Lambda statistic
Two near-exact distributions for the generalized Wilks Lambda statistic, used to test the independence of several sets of variables with a multivariate normal distribution, are developed for the case where two or more of these sets have an odd number of variables. Using the concept of near-exact distribution and based on a factorization of the exact characteristic function we obtain two approximations, which are very close to the exact distribution but far more manageable. These near-exact distributions...
Necessary and sufficient condition for the existence of a Fréchet mean on the circle
Let ( S 1 , d S 1 ) be the unit circle in ℝ2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure μto admit a well defined Fréchet mean on ( S 1 , d S 1 ). We derive a new sufficient condition of existenceP(α, ϕ) with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.
Necessary and Sufficient Conditions for Consistency of Generalized M-Estimates.
Necessary conditions for the bootstrap of the mean of a triangular array
Negative dependence structures through stochastic ordering.
Several new multivariate negative dependence concepts such as negative upper orthant dependent in sequence, negatively associated in sequence, right tail negatively decreasing in sequence and upper (lower) negatively decreasing in sequence through stochastic ordering are introduced. These concepts conform with the basic idea that if a set of random variables is split into two sets, then one is increasing whenever the other is decreasing. Our concepts are easily verifiable and enjoy many closure...
Několik úvah v souvislosti s projektem mezinárodní srovnávací studie vzdělávání učitelů matematiky
International projects TIMSS, PISA and similar deal with testing pupils' knowledge, among others in mathematics. The public notices their results especially in terms of ranking countries according to their success in these tests. It turns out, however, that the dependence of success in tests on the county, from which pupils come, cannot be proved. Rather, there is a dependence on competence of these pupils' teachers. This competence, however, is difficult to test - both in the Czech Republic and...
Některé analogie necentrálního -testu
Některé modifikace intervalového odhadu a volba počtu pozorování ve speciálním případě binomické náhodné proměnné
Nested Balanced N-Ary Designs.
Nestejné počty pozorování při srovnávání několika skupin s jednou kontrolní
Neural network realizations of Bayes decision rules for exponentially distributed data
For general Bayes decision rules there are considered perceptron approximations based on sufficient statistics inputs. A particular attention is paid to Bayes discrimination and classification. In the case of exponentially distributed data with known model it is shown that a perceptron with one hidden layer is sufficient and the learning is restricted to synaptic weights of the output neuron. If only the dimension of the exponential model is known, then the number of hidden layers will increase...
Neural networks using Bayesian training
Bayesian probability theory provides a framework for data modeling. In this framework it is possible to find models that are well-matched to the data, and to use these models to make nearly optimal predictions. In connection to neural networks and especially to neural network learning, the theory is interpreted as an inference of the most probable parameters for the model and the given training data. This article describes an application of Neural Networks using the Bayesian training to the problem...
Neuromorphic features of probabilistic neural networks
We summarize the main results on probabilistic neural networks recently published in a series of papers. Considering the framework of statistical pattern recognition we assume approximation of class-conditional distributions by finite mixtures of product components. The probabilistic neurons correspond to mixture components and can be interpreted in neurophysiological terms. In this way we can find possible theoretical background of the functional properties of neurons. For example, the general...
New approximate solutions per unit of time for periodically checked systems with different lifetime distributions.
New copulas based on general partitions-of-unity and their applications to risk management
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows, in contrast to finite partition-of-unity copulas, for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.