Convexity of probit weights

Martin Schumann, Gautam Tripathi*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We demonstrate that the probit weight function is U-shaped on R, i.e., it is strictly decreasing on (-infinity, 0), strictly increasing on [0, infinity), and strictly convex on R. Knowledge of the shape of the probit weight function can be useful in several contexts. For instance, it can resolve any confusion that may arise from a result in the classic paper of Sampford (1953). The shape of the probit weight function can also be used to justify why the computation of the probit maximum likelihood estimator (MLE) - in fact, in general, the computation of all two-step estimators whenever the first step involves estimating a probit model - may fail in the presence of outliers or unbounded parameter spaces. (C) 2018 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)81-85
Number of pages5
JournalStatistics & Probability Letters
Publication statusPublished - Dec 2018
Externally publishedYes


  • Convexity
  • Probit model
  • Shape
  • Weight function

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