Calibration with many checking rules

Alvaro Sandroni*, Rann Smorodinsky, Rakesh V. Vohra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)141-153
Number of pages13
JournalMathematics of Operations Research
Issue number1
StatePublished - Feb 2003


  • Calibration
  • Forecast
  • Probabilistic forecast

ASJC Scopus subject areas

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


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