The best replacement for maximum likelihood is least squares.

The best alternatives to maximum likelihood are rated as following:
★★★★★  least squares
★★★★  bayesian
★★★  maximum a posteriori
★★★  ols
★★★  maximum parsimony
★★  method of moments
★★  bayesian inference
★★  neighbor joining
★  maximum entropy
★  restricted maximum likelihood
★  ordinary least squares
★  principal axis factoring
★  expectation maximization
  generalized least squares
  principal component analysis
  principal components
  likely hood

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maximum likelihood
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