1. A.B. Nobel, G. Morvai, and S. Kulkarni, "Density estimation from an individual numerical sequence", IEEE Transactions on Information Theory, vol. 44, pp.537-541, 1998.

Summary: This paper studies the L1-consistent estimation of an unknown univariate density f from an individual (non-random) sequence taking values in R. It is shown that consistent estimation is possible assuming only that (i) the limiting relative frequency of each bounded interval is equal to the integral of f over that interval, and (ii) that there is a known upper bound on the variation of f on each interval [-i,i] for i > 0. It is also shown that no estimation scheme gives consistent estimates of every density f of bounded variation from sequences satisfying (i).

2. G. Morvai, S. Kulkarni, and A.B. Nobel, "Regression estimation from an individual stable sequence", Statistics, vol. 33, pp.99-118, 1999.

Summary: The paper considers estimation of an unknown univariate regression function g from an individual bivariate sequence whose limiting sample averages are governed by g. A scheme for estimating g from such a sequence is described, and conditions for its L2-consistency are established.

3. A.B. Nobel, "First order predictive sequences and induced transformations", Department of Statistics Technical Report #2367, University of North Carolina, Chapel Hill, 1999.

Summary: Recent work on chaos and non linear dynamics has established the importance of deterministic systems that exhibit random behavior. Repeated measurements of a system made at discrete time instants can be represented by a sequence of elements from the state space S of the system. The paper gives general conditions under which such a sequence induces a measure preserving transformation of S. It is argued that such sequences, and the systems from which they arise, be classified as deterministic. The results of the paper generalize earlier work on D-sequences by Maharam and others, but are established by different methods.