1. The Chapman Robbins bound also holds under much weaker regularity conditions . 2. This makes the regularity conditions unnecessary as Baire measures are automatically regular. 3. Then, if regularity conditions are satisfied, 4. Which expresses the strong regularity condition . 5. Under mild regularity conditions this process converges on maximum likelihood ( or maximum posterior ) values for parameters. 6. For the variations and restricted by the constraints ( assuming the constraints satisfy some regularity conditions ) is generally 7. Note that a limit distribution need not exist : this requires regularity conditions on the tail of the distribution. 8. As a consequence, the rate of convergence of the Gauss Newton algorithm can be quadratic under certain regularity conditions . 9. It has been shown that under certain regularity conditions , learnable classes and uniformly Glivenko-Cantelli classes are equivalent. 10. The method can converge much faster though, with an order which approaches 2 provided that f satisfies the regularity conditions described below.
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