The statue has its origins in 1878 when Walter M. Gibson, a member of the Hawaiian government at the time, wanted to commemorate the 100 year arrival of Captain Cook to the Hawaiian Islands. Gibson contacted Thomas R. Gould a Boston sculptor living abroad in Florence, Italy to create the statue. Even though photographs of Polynesians had been sent to him so that Gould could make an appropriate likeness, he seemed to ignore them. A Roman nose and more European features were adopted. This is most likely due to that fact that Gould was in Italy studying Roman sculpture.
The statue was too late for the 100th anniversary, but in 1883 the statue was placed aboard a ship and headed for Hawaii. Near the Falkland Islands the ship wrecked and the statue was thought lost. However, the Hawaiians had insured the statue for $12,000 and Gould rushed to complete a second.
Before the second statue could be sent the original had been recovered by some Falkland Islanders. They sold it to the Captain of the wrecked ship for $500, and the Captain then sold it to Gibson for $875. Now Hawaii had two statues. The original stands near the legendary king's birthplace in Kapaʻau in Kohala, on the island of Hawaiiʻi. The re-ordered one stands in front of Aliʻiolani Hale.
--- http://en.wikipedia.org/wiki/Kamehameha_Statue