Some results on Tchebycheffian spline functions

AbstractThis report derives explicit solutions to problems involving Tchebycheffian spline functions. We use a reproducing kernel Hilbert space which depends on the smoothness criterion, but not on the form of the data, to solve explicitly Hermite-Birkhoff interpolation and smoothing problems. Sard's best approximation to linear functionals and smoothing with respect to linear inequality constraints are also discussed. Some of the results are used to show that spline interpolation and smoothing is equivalent to prediction and filtering on realizations of certain stochastic processes

Min and max scorings for two-sample ordinal data

Journal of the American Statistical Association, March 1992, Vol. 87, No. 417, Theory and MethodsTo analyze two-sample ordinal data, one must often assign some increasing numerical scores to the ordinal categories. The choice of appropriate scores in these types of analyses is often problematic. This article presents a new approach for reporting the results of such analyses. Using techniques of order-restricted inference, we obtain the minimum and maximum of standard two-sample test statistics over all possible assignments of increasing scores. If the range of the min and max values does not include the critical value for the test statistics, then we can immediately conclude that the result of the analysis remains the same no matter what choice of increasing scores is used. On the other hand, if the range includes a critical value, the choice of scores used in the analysis must be carefully justified. Numerous examples are given to clarify our approach

Some Results on Tchebychefian Spline Functions

This report derives explicit solutions to problems involving Tchebycheffian spline functions. We use a reproducing kernel Hilbert space which depends on the smoothness criterion, but not on the form of the data, to solve explicitly Hermite-Birkhoff interpolation and smoothing problems. Sard's best approximation to linear functionals and smoothing with respect to linear inequality constraints are also discussed. Some of the results are used to show that spline interpolation and smoothing is equivalent to prediction and filtering on realizations of certain stochastic processes

Applications Of Bayesian Statistics To Actuarial Graduation.

PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/184206/2/6606633.pd

A framework for positive dependence

Positive dependence, positive dependence ordering, positive dependence property, measure of positive dependence, Frechet bounds, positive quadrant dependence, measure of association, ordinal contingency table,

Duels with Continuous Firing

A game-theoretic model is proposed for the generalization of a discrete-fire silent duel to a silent duel with continuous firing. This zero-sum two-person game is solved in the symmetric case. It is shown that pure optimal strategies exist and hence also solve a noisy duel with continuous firing. A solution for the general nonsymmetric duel is conjectured.

Dependence structures in which uncorrelatedness implies independence

This paper considers dependence conditions under which the pairwise uncorrelatedness of the components of a random vector implies their independence. Some concepts of dependence between random vectors are developed, which together with uncorrelatedness implies the independence of the random vectors.association negative association linear positive dependence positively quadrant dependent setwise positively upper-set dependent