The phrase "extinction method" refers to a way of getting rid of a behavior or habit by no longer rewarding it. It is like making the behavior "extinct" because it no longer gets any positive outcomes. Full definition
Is the controversial extinction method of sleep training harder on older kids than young babies? (romper.com)
Most parents, however, don't use extinction methods. (romper.com)
Most interventions have included parent education about normal sleep and sleep cycles, advice to maximise environmental differences between day and night, and strategies to encourage infant self - settling.7 - 10 Strategies included range from the graduated extinction method described above to encouraging parents to stretch night time feed intervals (in the hope that the infant will self - settle) and encouraging the use of parent - independent sleep cues. (child-encyclopedia.com)