Weak Convergence of Sequential Linear Rank Statistics

Weak Convergence of Generalized U - Statistics

Weak Sequential Convergence in L , ( p , X )

We provide some new results on the weak convergence of sequences or nets lying in L,((T, & r), X) = L,(p, X), 1 <p < co, i.e., the space of equivalence classes of X-valued (X is a Banach space) Bochner integrable functions on the finite measure space ( r, z, I”). Our theorems generalize in several directions recent resuls on weak sequential convergence in L,(p, X) obtained by M. A. Khan and M. ...

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.