Arthur's parents' names should be on his 1943 death cert.
However, he could have been the s/o Samuel and Rachel FERGUSON. In 1900, the family lived in Jackson, Wood, OH:
head, Samuel, 55, b Feb 1845, md 30 yrs, OH OH OH, farmer
wife, Rachel S., 51, b May 1849, 8 chn, 7 living, OH PA DE
son, Joseph D., 26, b Sep 1873, OH, farmer
son, Lincoln, 24, b Jul 1875, OH, farmer
son, Arthur, 19, b Jul 1881, OH
dau, Stella, 13, b Jun 1886, OH
dau, Sarah A., 11, b Jul 1889, OH
Rachel's other 2 living children could have been Mary E. and Eliza J. Both are in the 1880 Jackson, Wood, OH census; Mary was 8 and Eliza was 1.