Showing papers on "Weak consistency published in 1980"
TL;DR: In this article, strong consistency of estimates of the maximum lags of an autoregressive moving average process is established under general conditions, and a theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of overestimation of a maximum lag is evaluated.
Abstract: Under general conditions strong consistency of certain estimates of the maximum lags of an autoregressive moving average process is established. A theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of over-estimation of a maximum lag is evaluated.
513 citations
01 Dec 1980
TL;DR: In this article, a truncated maximum likelihood estimation scheme is proposed for consistent estimation of the transition probabilities in a linear discrete-time system with interrupted observations, where the interrupted observation mechanism is expressed in terms of a two-state Markov chain.
Abstract: A linear discrete-time system with interrupted observations is considered. The interrupted observation mechanism is expressed in terms of a two-state Markov chain. The transition probability matrix of the Markov chain is unknown and is assumed to belong to a compact set. A novel scheme, called truncated maximum likelihood estimation, is proposed for consistent estimation of the transition probabilities. Conditions for weak consistency are investigated.
2 citations
01 Dec 1980
TL;DR: In this paper, the asymptotic behavior of Bayes optimal adaptive state estimation schemes (also called the partitioned adaptive estimation algorithms) for continuous-time linear dynamic Gauss-Markov systems with unknown parameters is investigated.
Abstract: The asymptotic behavior of Bayes optimal adaptive state estimation schemes (also called the partitioned adaptive estimation algorithms) for continuous-time linear dynamic Gauss-Markov systems with unknown parameters is investigated. The unknown system parameters are assumed to belong to a finite set. The results are developed through weak consistency of the maximum likelihood and the maximum a posteriori probability estimates of the unknown parameters.
2 citations
TL;DR: In this paper, it was shown that proofs in the higher-order predicate calculus of M.W. Bunder can be normalised in a particular way, and it is then possible to show that the false proposition EHI is not provable using a normalised proof.
Abstract: In this paper it is shown that proofs in the higher order predicate calculus of M.W. Bunder, A one axiom set theory can be normalised in a particular way. At the same time the weak consistency result, that certain terms without normal forms are not provable, results. It is then possible to show that the false proposition EHI is not provable using a normalised proof. As negation (Λ) is defined by λχ ( χ⊃ EHI) this proves that for no term X , both X and Λ X are provable. The only nonconstructive steps used in the proof are an implicit use of the axiom of infinity in some lemmas and the use of the law of excluded middle in the form “A term has a normal from or it has not”. The property of having normal form is known to be undecidable.
1 citations