In statistics, a sequence of estimators for parameter θ is said to be consistent (or asymptotically consistent) if this sequence converges in probability to θ. Intuitively, this means that estimators taken far enough in the sequence are more likely to be in the vicinity of the parameter being estimated, and in the limit they will be arbitrarily close to θ with probability one.

PropertyValue
dbpedia-owl:thumbnail
dbpprop:abstract
  • In statistics, a sequence of estimators for parameter θ is said to be consistent (or asymptotically consistent) if this sequence converges in probability to θ. Intuitively, this means that estimators taken far enough in the sequence are more likely to be in the vicinity of the parameter being estimated, and in the limit they will be arbitrarily close to θ with probability one. In practice one usually constructs a single estimator as a function of an available sample of size n, and then imagines being able to keep collecting data and expanding the sample ad infinitum. In this way one would obtain a sequence of estimators indexed by n and the notion of consistency will be understood as the sample size “tends to infinity”. If this sequence converges in probability to the true value of the parameter being estimated, we call it a consistent estimator; otherwise the estimator is said to be inconsistent. This interpretation of sample size “growing to infinity” is pervasive in modern statistics, although it is also criticized as being too unrealistic. Indeed, in those rare cases when additional data can be collected, the statistician is usually forced to use more refined models as more data becomes available, meaning that the “true” parameter θ does not remain fixed and in fact its dimension expands. Consistency with convergence in probability is sometimes referred to as weak consistency. The notion can be extended to other modes of convergence of random variables. In particular, a sequence is said to be strongly consistent if it converges almost surely to the true parameter.
dbpprop:hasPhotoCollection
rdfs:comment
  • In statistics, a sequence of estimators for parameter θ is said to be consistent (or asymptotically consistent) if this sequence converges in probability to θ. Intuitively, this means that estimators taken far enough in the sequence are more likely to be in the vicinity of the parameter being estimated, and in the limit they will be arbitrarily close to θ with probability one.
rdfs:label
  • Consistent estimator
owl:sameAs
skos:subject
foaf:depiction
foaf:page
is dbpprop:redirect of