Any discrimination rule can have an arbitrarily bad probability of error for finite sample size
Related Experiment Video
Updated: May 29, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
Published on: May 10, 2019
1School of Computer Science, McGill University, Montreal, P.Q., Canada.
Abstract:
Consider the basic discrimination problem based on a sample of size n drawn from the distribution of (X, Y) on the Borel sets of Rdx {O, 1}. If 0 < R*< is a given number, and 'n - 0 is an arbitrary positive sequence, then for any discrimination rule one can find a distribution for (X, Y), not depending upon n, with Bayes probability of error R* such that the probability of error (Rn) of the discrimination rule is larger than R* + 'On for infinitely many n. We give a formal proof of this result, which is a generalization of a result by Cover [1].
Related Concept Videos
Bias
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...
Random Error
Contaminants and Errors
Another key consideration is determining the appropriate number of samples required to...
Errors In Hypothesis Tests
Systematic Error: Methodological and Sampling Errors
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
Accuracy and Errors in Hypothesis Testing
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
