Weak convergence of linear rank statistics

Weak Convergence of Generalized U - Statistics

Empirical performance maximization for linear rank statistics

The ROC curve is known to be the golden standard for measuring performance of a test/scoring statistic regarding its capacity of discrimination between two populations in a wide variety of applications, ranging from anomaly detection in signal processing to information retrieval, through medical diagnosis. Most practical performance measures used in scoring applications such as the AUC, the loc...

Linear Convergence in the Approximation of Rank-one Convex Envelopes

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope f of a given function f : Rn×m → R, i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington. Mathematics Subject Classification. 65K10, 74G15, 74G65, 74N99. Received: May 27...

Weak Convergence of the Serial Linear Rank Statistic with Unbounded Scores and Regression Constants under Mixing Conditions

Hare1 and Puri (1990) established the weak convergence of a class of the serial linear rank statistics with bounded score functions and regression constants when the random variables are q-mixing or strong mixing. This paper extends these results to the case when the score functions as well as the regression constants are not necessarily bounded. AMS Subject Classifications: Primary 60B10, 60F05.

Order-Restricted Inference with Linear Rank Statistics in Microarray Data

The classification of subjects with unknown distribution in a small sample size often involves order-restricted constraints in multivariate parameter setups. Those problems make the optimality of a conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Multivariate linear...