Yi-Ching Yao

Maximum likelihood estimation in hazard rate models with a change-point

The problem of estimation of parameters in hazard rate models with a change-point is considered. An interesting feature of this problem is that the likelihood function is unbounded. A maximum likelihood estimator of the change-point subject to a natural constraint is proposed, which is shown to be consistent.The limiting distributions are also derived.

On the asymptotic behavior of a class of nonparametric tests for a change-point problem

A class of linear rank statistics is considered for testing a sequence of independent random variables with common distribution against alternatives involving a change in distribution at an unknown time point. It is shown that, under the null hypothesis and suitably normalized, this class of statistics converges in distribution to the double exponential extreme value distribution.

Approximating the inverse of a symmetric positive definite matrix

Abstract It is shown for an n × n symmetric positive definite matrix T = ( t i , j with negative off-diagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order l/ n 2 , by a matrix S = ( s i , j ), where s i , j = δ i , j / t i , j + 1/ t.. , δ i , j being the Kronecker delta function, and t .. being the sum of the elements of T . An explicit bound on the approximation error is provided.

Some results on the Gittins index for a normal reward process

We consider the Gittins index for a normal distribution with unknown mean

On optimal nested group testing algorithms

\theta

A d -move local permutation routing for the d -cube

and known variance where

Comments on Bern's probabilistic results on rectilinear Steiner trees

\theta

SOME RESULTS ON THE BOMBER PROBLEM

has a normal prior. In addition to presenting some monotonicity properties of the Gittins index, we derive an approximation to the Gittins index by embedding the (discrete-time) normal setting into the continuous-time Wiener process setting in which the Gittins index is determined by the stopping boundary for an optimal stopping problem. By an application of Chernoffs continuity correction in optimal stopping, the approximation includes a correction term which accounts for the difference between the discrete and continuous-time stopping boundaries. Numerical results are also given to assess the performance of this simple approximation.

A note on testing for constant hazard against a change-point alternative

Abstract Group testing was first proposed for blood testing although it has many industrial applications as well. Most of the group testing literature has studied a naturally defined class of algorithms called nested algorithms. Optimal nested algorithms are usually defined by recursive equations which do not seem to have general closed-form solutions, and so are not in general well understood. One exception is a result that gives a necessary and sufficient condition for the individual testing algorithm to be optimal. The next simplest algorithm is the pairwise testing algorithm which tests a pair of items at a time except when a pair known to contain a defective is found, then a single item from that pair is tested. In this paper we present an explicit algorithm for optimally finding a single defective in a contaminated set and use this to derive a necessary and sufficient condition for the pairwise testing algorithm to be the optimal nested algorithm.

Markov chains on hypercubes: Spectral representations and several majorization relations

Abstract Optimal packet routing algorithms for all binary d -cubes of dimension d ⩽ 7 are presented. The algorithms given are synchronous, offer distributed control, and assume d -port, multiaccepting communication. While the previous best known packet routing algorithm [3]on the 7-cube takes 11 time-units, our algorithm has reduced the worst-case time complexity to the minimum possible of 7 units. We also give an optimal routing algorithm for the ternary 4-cube.