Some new developments in Markov chains

Some New Developments in Small Area Estimation

Small area estimation has received a lot of attention in recent years due to growing demand for reliable small area statistics. Traditional area-specific estimators may not provide adequate precision because sample sizes in small areas are seldom large enough. This makes it necessary to employ indirect estimators based on linking models. Basic area level and unit level models have been extensiv...

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Some Inequalities for Reversible Markov Chains

Graph Reconstruction - Some New Developments

The reconstruction conjecture claims that every graph on at least three vertices is uniquely determined by its collection of vertex deleted subgraphs. Even though it is one of the foremost unsolved problems in Graph Theory, work on it has slowed down, may be due to the general feeling that existing techniques are not likely to lead to a complete solution. Here we give the results that have appe...

A new machine replacement policy based on number of defective items and Markov chains

  A novel optimal single machine replacement policy using a single as well as a two-stage decision making process is proposed based on the quality of items produced. In a stage of this policy, if the number of defective items in a sample of produced items is more than an upper threshold, the machine is replaced. However, the machine is not replaced if the number of defective items is less than ...