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具有依赖结构的伯努利模型参数估计札记AI 解读

A generalization of a Bernoulli process which incorporates a dependence structure was given by Klotz (1972, 1973), in which he considered $X_1, X_2, \cdots, X_n$ as a stationary two-state Markov chain with state space $\{0, 1\}$. The parameters of the process are $p = P(X_i = 1)$ and $\lambda$, which measures the degree of persistence in the chain. Klotz was unable to solve the equations arising from the full likelihood for the M.L.E.'s of $p$ and $\lambda$, so proposed and…

利用近邻规则重建含噪马尔可夫链AI 解读

An observer desires to record a realization of a stationary two-state Markov chain X, but experimental conditions are such that he instead sees a realization of an error sequence Y. The objective is to reconstruct X. For a simple parameterization of both the Markov chain and the error sequence, a class of near-neighbor reconstruction rules is proposed and investigated. When the values of the parameters are unspecified, estimates are suggested and their asymptotic properties…

利用近邻规则重构含噪马尔可夫链AI 解读

An observer desires to record a realization of a stationary two-state Markov chain X, but experimental conditions are such that he instead sees a realization of an error sequence Y. The objective is to reconstruct X. For a simple parameterization of both the Markov chain and the error sequence, a class of near-neighbor reconstruction rules is proposed and investigated. When the values of the parameters are unspecified, estimates are suggested and their asymptotic properties…