Ranking paired contestants

The ranking of paired contestants (players) after a series of contests is difficult when every player does not play every other player. In the 1975 JASA Mark Thompson presented a maximum likelihood solution based on the assumption that the probability of any one player defeating any other is a function only of the difference in their ranks. Here the linear approximation to that likelihood is shown to lead to a nonparametric measure of the efficacy of the ranking, called the net difference in ranks (NDR) , which is the sum of the differences in ranks of the paired players in the observed contests that agree with the ranking minus the sum of the differences in ranks in the observed contests that disagree with the ranking (upsets) . The subject is part of a large literature that has been consolidated by H.A. David in The Method of Paired Comparisons (1963, 1988). The method was introduced by the psychophysicist Fechner in 1860 and has been widely applied to sensory testing,     

Convergence Rate of Wavelet Expansions of Gaussian Random Processes

This article characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.     

Some concepts of mult1variate dependence

Several types of positive dependence are shown to be equiv-alent to the concept of a distribution with a density which is TP₂ in pairs. Among these is the concept of m^?-positive depend-ence of Alam and Wallenius. Using this result, all relationships among many of the most important concepts of positive dependence are determined. Furthermore, an application of the equivalences of these types of positive dependence yields a results of Ahmed, Langberg, Leon and Proschan.     

Nonparametric tests for scale shift at an unknown time point

A class of linear rank tests is suggested for testing a shift in scale at an unknown time point in a sequence of independent observations. The tests,based on inverse normal scores and on ordered exponential scores,are shown to be asymptotically as efficient as their distribution-oriented competitors. Critical values and powers for these two rank tests are also discussed.     

The effects of correlation among observations on the consistency property of sample variance

It is well known that even when the sample observations are correlated and not normal the sample variance, S² converges in probability to E(S²). But the required sample size for S² to be a consistent estimator of E(S²) is an open question. Some light is shed on this question in this paper. In particular the relation between the rate of convergence and the correlation property of the observations is explored. It is shown that the retardation to the rate of convergence is not appreciable if the correlation is moderate but it can be severe for extreme correlations.     

A survey of statistical methods on remote sensing in russian literature from 1976 to 1985

In this article we review the major areas of remote sensing in the Russian literature for the period 1976 to 1985 that use statistical methods to analyze the observed data. For each of the areas, the problems that have been studied and the statistical techniques that have been used are briefly described     

A Corrected Plug-in Method for Quantile Interval Construction Through a Transformed Regression

We propose a corrected plug-in method for constructing confidence intervals of the conditional quantiles of an original response variable through a transformed regression with heteroscedastic errors. The interval is easy to compute. Factors affecting the magnitude of the correction are examined analytically through the special case of Box–Cox regression. Monte Carlo simulations show that the new method works well in general and is superior over the commonly used delta method and the quantile regression method. An empirical application is presented.     

On a bayesian approach for the shiftpoint problem

Using a direct resampling process, a Bayesian approach is developed for the analysis of the shiftpoint problem. In many problems it is straight forward to isolate the marginal posterior distribution of the shift-point parameter and the conditional distribution of some of the parameters given the shift point and the other remaining parameters. When this is possible, a direct sampling approach is easily implemented whereby standard random number generators can be used to generate samples from the joint posterior distribution of aii the parameters in the model. This technique is illustrated with examples involving one shift for Poisson processes and regression models.     

Asymptotic robustness of least median of squares for autoregressions with additive outliers

This paper considers the robustness properties in the time series context of the least median of squares (LMS) estimator. The influence function of the LMS estimator is derived under additive outlier contamination. This influence function is redescending and bounded for fixed values of the AR parameters. The gross-error sensitivity, however, is an unbounded function of the AR parameters. In order to asses the global robustness behavior of the LMS estimator, we consider several notions of breakdown. The breakdown points of the LMS estimator depend on the value of the underlying AR parameter. Generally, the breakdown point is below one half for high values of the AR parameter. The bias curves of the LMS estimator reveal, however, that the magnitude of outliers has to be considerable in order to cause breakdown.     

The non-null distributions in anoya

Under the traditional assumptions, any entry in ANOVA interpreted to include all Linear model analyses] is equivalent in disiributien to a quadratic form Q=[μ₁+σ₁Z₁]²+…+ [μ_ν+σ_νZ_ν]²]wherein Z₁..Z_ν are independent standard normal variables. Test statisics in ANOVE are distributed as ratio R of two depenbent such quadretic forms. The non-null distribution of R is a mixture of null distributions; the mixing variable is an easy generalitatlon of the Poisson variable. Fast algorithms yield the power function in both fixed and random effects models in AVOVA to user-specified accuracy.