I had a look at the attestation papers and didn't think the NOK last name was Arnett. Looked more like Hinett to me so went looking for directories for North Bay.
http://northbayhistory.homestead.comAnnie Hinett (wid Chas), 186 John
then I went to
http://automatedgenealogy.comOntario/Nippissing/1911 census
Mrs Annie Hinett, head, widow, b. July 1869, age 41, England, immigrated 1882
all children born in Ontario
Daughters Flossie, Blanche, Lillian, Hazel and Stella
Son Victor
She doesn't have any boarders in 1911 but that could have changed or she may have been related to Frank in some way.
I still haven't found him on the census but depending on what work he was doing and if he was moving around following the work he may have been missed on the census or mistranscribed.