Gusztáv MORVAI and Benjamin WEISS: Order Estimation of Markov Chains
ثبت نشده
چکیده
We describe estimators χ n (X 0 , X 1 ,. .. , X n), which when applied to an unknown stationary process taking values from a countable alphabet X , converge almost surely to k in case the process is a k-th order Markov chain and to infinity otherwise.
منابع مشابه
On classifying processes
We prove several results concerning classifications, based on successive observations (X 1 ,. .. , X n) of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov chains.
متن کاملLimitations on intermittent forecasting
Bailey showed that the general pointwise forecasting for stationary and ergodic time series has a negative solution. However, it is known that for Markov chains the problem can be solved. Morvai showed that there is a stopping time sequence {λ n } such that P (X λn+1 =) such that the difference between the conditional probability and the estimate vanishes along these stoppping times for all sta...
متن کاملEvaluation of First and Second Markov Chains Sensitivity and Specificity as Statistical Approach for Prediction of Sequences of Genes in Virus Double Strand DNA Genomes
Growing amount of information on biological sequences has made application of statistical approaches necessary for modeling and estimation of their functions. In this paper, sensitivity and specificity of the first and second Markov chains for prediction of genes was evaluated using the complete double stranded DNA virus. There were two approaches for prediction of each Markov Model parameter,...
متن کاملEmpirical 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...
متن کاملPrediction for discrete time series
Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X . Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times λn along which we will be able to estimate the conditional probability P (Xλn+1 = x|X0, . . . , Xλn) from data segment (X0, . . . , Xλn) in a pointwise consistent way for a restricted ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007