On a class of statistics of polynomial samples
-
B. I. Selivanov
Abstract
We consider M ≥ 1 independent samples each of which is a realisation of some polynomial scheme. The number of outcomes N and the number of samples M are fixed, the sample sizes grow without bound. We study the asymptotic properties of statistics of the form g(
), where g(
) is a differentiable function of MN real-valued variables, is the vector of relative frequencies of outcomes in samples. Statistics of such a kind are playing an important part in the applied statistical analysis.
In this research we expand the capabilities of the well-known δ-method (the linearisation method) in the case of polynomial samples. We prove the asymptotic normality and convergence in distribution of the statistics g() to quadratic forms of normal random variables (both for the fixed probabilities of outcomes in the case of the null hypothesis and for the case of contigual alternatives to it). We give conditions for both types of convergence.
© de Gruyter 2009
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Articles in the same Issue
- Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric
- New methods of investigation of perfectly balanced Boolean functions
- On completeness and A-completeness of S-sets of determinate functions containing all one-place determinate S-functions
- On repetition-free Boolean functions over pre-elementary monotone bases
- Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions
- Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials
- On a class of statistics of polynomial samples
- Score lists in [h-k]-bipartite hypertournaments
- On one statistical model of steganography
