Multivariate generalizations of the Wald-Wolfowitz runs statistic and the Smirnov maximum deviation statistic for the two-sample problem are presented. They are based on the minimal spanning tree of the pooled sample points. Some null distribution results are derived, and a simulation study of power is reported. (To be published in Annals of Statistics) *Supported by Department of Energy **Supp...

By using the brute force algorithm, the application of the two-dimensional two-sample Kolmogorov–Smirnov test can be prohibitively computationally expensive. Thus a fast algorithm for computing the two-sample Kolmogorov–Smirnov test statistic is proposed to alleviate this problem. The newly proposed algorithm is O(n) times more efficient than the brute force algorithm, where n is the sum of the...

A theory of matrix-valued functions from the matricial Smirnov class Nn (D) is systematically developed. In particular, the maximum principle of V.I.Smirnov, inner-outer factorization, the Smirnov-Beurling characterization of outer functions and an analogue of Frostman’s theorem are presented for matrix-valued functions from the Smirnov class Nn (D). We also consider a family Fλ = F − λI of fun...

Hypothesis testing on point processes has several applications such as model fitting, plasticity detection, and non-stationarity detection. Standard tools for hypothesis testing include tests on mean firing rate and time varying rate function. However, these statistics do not fully describe a point process, and therefore, the conclusions drawn by these tests can be misleading. In this paper, we...

G08CDF also returns the standardized statistic Z 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n1 þ n2 n1n2 r D, where D may be Dn1;n2 , D þ n1;n2 or D n1;n2 depending on the choice of the alternative hypothesis. The distribution of this statistic converges asymptotically to a distribution given by Smirnov as n1 and n2 increase; see Feller (1948), Kendall and Stuart (1973), Kim and Jenri...

We consider the decision problem of making causal conclusions from observational data. Typically, using standard matched pairs techniques, there is a source of uncertainty that is not usually quantified, namely the uncertainty due to the choice of the experimenter: two different reasonable experimenters can easily have opposite results. In this work we present an alternative to the standard non...

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (i) definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (ii) generation of samples from uncertain analysis inputs, (iii) propagation of sampled inputs through an analysis, (iv) presentation of uncertainty analysis results, and (v) deter...

Introduction and Motivation: fMRI is a natural source of high-dimensional time series data. Recordings are typically acquired in several hour sessions, with processing and analysis done offline. Due to the short amount of recording time available from any session, there is an imbalance between the comparatively small number of time slices and the high dimensionality of the data at each slice. A...