Optimality of estimators for misspecified semi-Markov models

Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two models for the process are semiparametric, and the parameters can be estimated by conditional maximum likelihood estimators. The third model for the process is parametric, and the parameter can be estimated by an unconditional maximum likelihood estimator. We determine heuristically the asymptotic distributions of these estimators and show that they are asymptotically efficient. If the parametric models are not correct, the (conditional) maximum likelihood estimators estimate the parameter that maximizes the Kullback--Leibler information. We show that they remain asymptotically efficient in a nonparametric sense.Comment: To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm

Robust Trend Estimation for AR(1) Disturbances

We discuss the robust estimation of a linear trend if the noise follows an autoregressive process of first order. We find the ordinary repeated median to perform well except for negative correlations. In this case it can be improved by a Prais-Winsten transformation using a robust autocorrelation estimator. -- Wir behandeln die robuste Schätzung eines linearen Trends bei autoregressiven Fehlern erster Ordnung. Die Repeated Median Regression zeigt ein gutes Verhalten bei positiven Korrelationen. Bei negativen Korrelationen ist eine Verbesserung durch eine Prais-Winsten Transformation mittels eines robusten Korrelationsschätzers möglich.Robust Regression,Autocorrelations,Detrending,Cochrane-Orcutt Estimator,Prais-Winsten Estimator

Time distinctions in Kaingáng

The speakers of the Paraná dialect of Kaingáng, from whom the data of this study were gathered, have lived in close contact with the Brazilians since before the turn of the century. Although many members of this group are still monolingual and Kaingáng is spoken in all the homes, the influence of Portuguese is making an impact on the language. This can be seen not only in isolated loan words, but it is slowly changing the time dimension of the language and the thinking of the Indians. The change seems to have come about first through loan words, but it is now also affecting the semantic structure of the language and is beginning to affect the grammatical structure as well. The study here presented deals with this change as it can be seen in relation to time expressions such as yesterday – today – tomorrow; units of time such as day – month – year; kinship terms; and finally aspect particles. In considering the time expressions the meaning of various paradigms will be discussed. The paradigms are related to the time when events took place, to sequence of events, and to the point of the action. No Brazilian influence can be observed here. In the discussion of the units of time the semantic area of these units before and after Brazilian influence will be explored. Through Brazilian influence vocabulary has been developed with which it is possible to accurately pinpoint events in time which was not possible before this. The time distinctions within the kinship system will be discussed, and how they change with the influence of Brazilian terms. A whole new generation distinction is added in the modified kinship system. Similary several new aspect particles are being created through contractions, which now contain a time element. The whole development shows an emphasis on fine distinctions in time depth which came about through the contact with Portuguese and which can be observed in several points of the structure of Kaingáng

Spartan Daily, January 24, 1955

Volume 42, Issue 72https://scholarworks.sjsu.edu/spartandaily/12122/thumbnail.jp