Data Analysis and Graphics

  • Two Way Plots Two-way tables record the response in a system to two stimuli, each varying over a finite set. Examples are ubiquitous and include traditional multivariate data, the simultaneous observation of several time series, and the measurement of a quality outcome under conditions described by two variables. Two-way plots offer a graphical means to show the values in the table such that the row and column structure is preserved.

  • HR-Distributions Any continuous distribution can be realized via a continuous transformation Y=h(Z) of a Gaussian random variable Z. For a given h-function, the variable Y is easy to simulate and the quantiles of Y are also very easy to compute. The distribution and density of Y, however, require knowledge of the inverse of h. H-distributions are obtained by considering h(z) = z exp(hz^2/2) for h >= 0, which means that for h > 0 they have heavier tails than the Gaussian. HR-distributions generalize this choice to h(z) = z exp(hz^2/(2+r z^2)) for r > 0 and h > -2r, and contain both heavy-tailed and lighter-tailed laws.

  • Data Description A certain degree of simplification is useful when presenting data. This can take the form of smoothing, of reducing the dimension, etc. No successful and widely-adopted theoretical framework for data description exists, even though the questions posed by such procedures are of great practical interest and even though data description is in many ways different from estimation. Describing global properties of descriptive procedures has been the main thrust of our work.