On the distribution of crossings in a generalized random walk

This paper deals with the derivation of the probability distribution of the rank order statistic N¹_μ,n(r), the number of crossings of heightr(≥0) in a generalized random walk with steps 1 and ?μ by using the modified Dwass technique.     

Profile analysis of several groups

In this paper, profile analysis of several groups is considered. The maximum likelihood estimate, along with its covariance matrix, is given for the “level differences” between the grops. Likelihood ratio test procedures, with their distributions, are given for the three hypothesis known in the literature as “parallelism”, “level hypothesis” and “ no condition variation”. In the literature, even for the two groups case, some procedures are not likelihood procedures.     

Economical process adjustment with measurement error

Srivastava and Wu (1997) considered a random walk model with sampling interval and measurement error which was assumed to be white noise. In this paper, we consider the situation in which the measurement error is also a random walk. It is assumed that there is a sampling cost and an adjustment cost. The cost of deviating from the target value is assumed to be proportional to the square of the deviations. The long-run average cost rate is evaluated exactly in terms of the first four moments of a randomly stopped random walk. Using approximations of those moments, optimum, values of the control parameters are given.     

Optimal linear projections for enhancing desired data statistics

Problems involving high-dimensional data, such as pattern recognition, image analysis, and gene clustering, often require a preliminary step of dimension reduction before or during statistical analysis. If one restricts to a linear technique for dimension reduction, the remaining issue is the choice of the projection. This choice can be dictated by desire to maximize certain statistical criteria, including variance, kurtosis, sparseness, and entropy, of the projected data. Motivations for such criteria comes from past empirical studies of statistics of natural and urban images. We present a geometric framework for finding projections that are optimal for obtaining certain desired statistical properties. Our approach is to define an objective function on spaces of orthogonal linear projections—Stiefel and Grassmann manifolds, and to use gradient techniques to optimize that function. This construction uses the geometries of these manifolds to perform the optimization. Experimental results are presented to demonstrate these ideas for natural and facial images.     

Optimization in statistics: an overview

This note presents a brief overview of the applications of optimization techniques in statistics. Optimizing techniques are broadly classified as classical, variational, numerical, and mathematical programming. A brief discussion of their applications to statistics is given, and a few references are provided for illustrative purposes.     

Some approaches to statistical analysis of a weather modification experiment

Data from a weather modification experiment are examined and a number of statistical analyses reported. The validity of earlier inferences is studied as are the utilities of various statistical methods. The experiment is described. The original analysis of North American Weather Consultants, who conducted the experiment, is reviewed. Data summarization is reported. A major approach to analysis is through the use of cloud-physics covari-ates in regression analyses. Finally, a multivariate analysis is discussed. It appears that the covariates may have been affected by treatment (cloud seeding) and that their use is invalid, not only reducing error variances but removing treatment effect. Some recommendations for improved design of similar future experiments are given in a concluding section, including preliminary trial use of blocking by storms.