Nonparametric Statistical Data Modeling.
STATE UNIV OF NEW YORK AT BUFFALO AMHERST STATISTICAL SCIENCE DIV
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It is the aim of this paper to introduce new types of keys for exploratory data analysis of continuous data based on estimating the quantile function and density quantile function. The distinction between exploratory and confirmatory data analysis can be regarded as a distinction between confirmatory non-parametric statistical data analysis or modeling, and confirmatory parametric statistical data analysis. Quantile, quantile-density, density-quantile, and score functions are defined in Section 2, and their fundamental inter-relations are discussed. Transformations to observed data which have specified distributions are studied in Section 3, and formulas are given for their derivatives. Auto-regressive representations of density-quantile functions are introduced in Section 4. Sample quantile functions and their linear functionals are defined in Section 5. Goodness of Fit Tests for location and scale parameter models are introduced in Section 6. Estimators of density-quantile functions are discussed in Section 7. Section 8 considers two examples -- Rayleigh data and Buffalo snowfall. Section 9 discusses theoretical examples of density-quantile functions, and their classification according to tail behavior. Location and scale parameter estimation is discussed in Section 10. Section 11 lists some open research problems for extensions.
- Statistics and Probability