The best replacement for personal statement is statement of purpose.

The best alternatives to personal statement are rated as following:
★★★★★  statement of purpose
★★★★★  cover letter
★★★  letter of intent
★★  college essay
★★  essay
★  research statement
★  letter of interest
★  academic statement
★  motivation letter
★  common app essay
★  sop
★  autobiography
  diversity statement

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Speaking about personal statement, one probably shouldn't forget about cv.

Other search terms related to personal statement and their ratings are:
★★★★★ cv
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personal statement
statement of purpose
cover letter