Non-asymptotic calibration and resolution
Theoretical Computer Science
The complexity of forecast testing
ACM SIGecom Exchanges
On calibration error of randomized forecasting algorithms
Theoretical Computer Science
Strategic Manipulation of Empirical Tests
Mathematics of Operations Research
Calibration and internal no-regret with random signals
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
On sequences with non-learnable subsequences
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
A Geometric Proof of Calibration
Mathematics of Operations Research
On universal algorithms for adaptive forecasting
Problems of Information Transmission
On-Line regression competitive with reproducing kernel hilbert spaces
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Efficient testing of forecasts
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Each period an outcome (out of finitely many possibilities) is observed. For simplicity assume two possible outcomes, a and b. Each period, a forecaster announces the probability of a occurring next period based on the past.Consider an arbitrary subsequence of periods (e.g., odd periods, even periods, all periods in which b is observed, etc.). Given an integer n, divide any such subsequence into associated sub-subsequences in which the forecast for a is between [i/n, i+ 1/n), i ∈ {0, 1,...,n}.We compare the forecasts and the outcomes (realized next period) separately in each of these subsubsequences. Given any countable partition of [0, 1] and any countable collection of subsequences, we construct a forecasting scheme such that for all infinite strings of data, the long-run average forecast for a matches the long-run frequency of realized a's.