It is argued that a main aim of statistics is to produce statistical procedures which in this article are defined as algorithms with inputs and outputs. The structure and properties of such procedures are investigated with special reference to topological and testing considerations. Procedures...

For a stationary Gaussian process either almost all sample paths are almost everywhere differentiable or almost all sample paths are almost nowhere differentiable. In this paper it is shown by means of an example involving a random lacunary trigonometric series that "almost everywhere...

Stochastic models approximate data and are not true representations of the same. Statistical procedure make use of approximate stochastic models to facilitate the analysis of data.

The standard model for the analysis of variance is over-parameterized. The resulting identifiability problem is typically solved by placing linear constraints on the parameters. In the case of the interactions, these require that the marginal sums be zero. Although seemingly neutral, these...

We consider data consisting of photon counts of diffracted X-rays as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself...

The concept of breakdown point was introduced by Hodges (1967) and Hampel (1968, 1971) and still plays an important though at times a controversial role in robust statistics. It has proved most successful in the context of location, scale and regression problems. In this paper we argue that this...