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On the Stochastic Matrix in a Genetic Model of Moran
On the stochastic matrix in a genetic model of Moran
Problems in the Probability Theory of Storage Systems
Sufficiency Conditions in Regular Markov Chains and Certain Random Walks
SUFFICIENCY CONDITIONS IN REGULAR MARKOV CHAINS AND CERTAIN RANDOM WALKS
正则马尔可夫链及某些随机游走中的充分性条件
For positively regular Markov chains with a finite number of states, transition probabilities of the form are known to admit a sufficient estimator of θ in realizations of the chain starting with a fixed state and consisting of a fixed number of transitions. This paper considers whether transition probabilities of the same form will admit a sufficient estimator of θ in other finite regular, but not positively regular, Markov chains. For chains with an irreducible subset of…
Some Theorems and Sufficiency Conditions for the Maximum-Likelihood Estimator of an Unknown Parameter in a Simple Markov Chain
SOME THEOREMS AND SUFFICIENCY CONDITIONS FOR THE MAXIMUM-LIKELIHOOD ESTIMATOR OF AN UNKNOWN PARAMETER IN A SIMPLE MARKOV CHAIN
简单马尔可夫链未知参数最大似然估计的定理与充分性条件
The paper begins with proofs of the usual theorems for the optimum properties of the maximum-likelihood estimator of an unknown parameter θ which defines the transition probabilities pij(θ) of a simple ergodic Markov chain. By an ergodic chain is meant one for which, not only is the final chain stationary, but also all possible initial states remain permanently available; these conditions are sufficient to prove that the maximum-likelihood estimator is consistent, and…