Would it be possible to calculate the expected frequency of impact craters of all sizes on Earth Can the expected frequency of all sizes of impact craters on Earth be calculated based on the preservation of impact craters seen on the Moon? Taking into account the difference in gravity and atmosphere of the Earth and Moon, and assuming a similar age for both, it should be possible to come up with a reasonable estimate of how many meteorites, etc have hit the earth and their size distribution.
Yes. By looking at a nearby object that hasn't been subject to erosion and has been subject to the same position around the sun, you could estimate the distribution of impacts on the Earth in time and in size. The moon is excellent for this purpose.

Here's an article touching on the subject: http://adsabs.harvard.edu/full/1975LPSC....6.2597N