Finding cost basis from stock before 2011

Hi - 

 

I'm trying to find a good way to estimate the cost basis of a mutual fund which paid capital gains and dividends yearly. I have the cost basis after Jan of 2011. However, I have about 15 line items which likely were before that date with no cost basis and no purchase date.  I have been unable to get any further information from the holding investment bank. 

 

Any thoughts on ways I can estimate the cost basis so it is not zero?