Paper Info
Title
Density estimation by stochastic complexity
Abstract
The results by P. Hall and E.J. Hannan (1988) on optimization of histogram density estimators with equal bin widths by minimization of the stochastic complexity are extended and sharpened in two separate ways. As the first contribution, two generalized histogram estimators are constructed. The first has unequal bin widths which, together with the number of the bins, are determined by minimization of the stochastic complexity using dynamic programming. The other estimator consists of a mixture of equal bin width estimators, each of which is defined by the associated stochastic complexity. As the main contribution in the present work, two theorems are proved, which together extend the universal coding theorems to a large class of data generating densities. The first gives an asymptotic upper bound for the code redundancy in the order of magnitude, achieved with a special predictive type of histogram estimator, which sharpens a related bound. The second theorem states that this bound cannot be improved upon by any code whatsoever.<>
Year
DOI
Venue
1992
10.1109/18.119689
IEEE Transactions on Information Theory - Part 2
Keywords
Field
DocType
dynamic programming,encoding,estimation theory,information theory,minimisation,stochastic processes,asymptotic upper bound,code redundancy,data generating densities,density estimation,dynamic programming,equal bin widths,generalized histogram estimators,minimization,minimum description length principle,stochastic complexity,unequal bin widths,universal coding theorems
Information theory,Density estimation,Discrete mathematics,Histogram,Combinatorics,Bin,Upper and lower bounds,Stochastic process,Estimation theory,Mathematics,Estimator
Journal
Volume
Issue
ISSN
38
2
0018-9448
Citations 
PageRank 
References 
43
17.08
6
Authors
3
Name
Order
Citations
PageRank
Jorma Rissanen11665798.14
T P Speed28422.85
Bin Yu31984241.03