The parents are listed on familysearch.org in 1910 as family number 153, but on a different page from the children, listed as dau's in family number 153.
The NH death record lists Annie died in Elmira, NY.No spouse or parents noted. death date: 22 Oct 1921Elimira, NY interment: New Ipswich, Hillsborough, NH
1910 census name: Harre Nelson birthplace: Finland relationship to head of household: Self residence: New Ipswich, Hillsborough, New Hampshire marital status: Married race : White gender: Male immigration year: 1902 father's birthplace: Finland mother's birthplace: Finland
family number: 153 page number: 4
self Harre Nelson M 31y Finland wife Hilma S NelsonF 31yFinland
family number: 153page number: 7
dauAnnie NelsonF 9y Finland dauJennie Nelson F 7y New Hampshire dauHilma Nelson F 5y New Hampshire dauMaimi Nelson F y 11m New Hampshire