The performance of Neyman-Pearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the statespace structure of the signal and observation model, a closed-form expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that...

Jerzy Neyman’s life history and some of his contributions to applied statistics are reviewed. In a 1960 article he wrote: “Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research which, if treated realistically, does not involve operations on stochastic processes. The time has arrived for the theory of stochastic processes to become an item of us...

In many binary classification applications, such as disease diagnosis and spam detection, practitioners commonly face the need to limit type I error (i.e., the conditional probability of misclassifying a class 0 observation as class 1) so that it remains below a desired threshold. To address this need, the Neyman-Pearson (NP) classification paradigm is a natural choice; it minimizes type II err...

We propose two test statistics for use in inverse regression problems Y = Kθ + , where K is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations Y for the function θ are available. Both test statistics have a counterpart in classical hypothesis testing, where they are called the order selection test and the data-driven Neyman smooth test. We als...

Distributed spectrum sensing (DSS) is of great importance in Cognitive Radio, especially under fading or shadowing effects. In order to evaluate the performance of a distributed system, it is commonly compared with the centralized system as an upper performance bound. Now the question is whether or not one can obtain a distributed strategy serving as an upper bound to benchmark any distributed ...

In his 1923 landmark article, Neyman introduced randomization-based inference to estimate average treatment effects from experiments under the completely randomized design. Under this framework, Neyman considered the statistical estimation of the sample average treatment effect and derived the variance of the standard estimator using the treatment assignment mechanism as the sole basis of infer...

The CPIT transformations do not, in general, give the same set of transformed values for different orderings of the observations in a sample. When these transformations are followed by a test of uniformity to give an overall goodness-of-fit test, it is possible to obtain different results for different orderings of a sample. We consider here the probability that two goodness-of-fit tests based ...

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Professor Brillinger is to be congratulated on this paper which is both a contribution to the history of statistics and an introduction to statistical modeling using stochastic processes, a topic that continues to be of great relevance in theory and applications. It is interesting to see how many ideas have been formulated already at an early stage. In particular, I like the idea of “synthetic ...