Statistical estimation with bounded memory

Leonid Kontorovich

doi:10.1007/s11222-011-9293-5

Statistical estimation with bounded memory

Leonid Kontorovich

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We investigate bounded-memory estimators of statistical functionals. It is shown that, for nondegenerate functionals and stochastic processes, it is impossible to achieve consistent estimation with bounded memory. In the positive direction, we show that O(log(1/ε)) states suffice to achieve ε-consistent estimation for a natural class of functionals. A canonical optimal construction is conjectured for arbitrary statistical functionals.

Original language	English
Pages (from-to)	1155-1164
Number of pages	10
Journal	Statistics and Computing
Volume	22
Issue number	5
DOIs	https://doi.org/10.1007/s11222-011-9293-5
State	Published - 1 Sep 2012

Keywords

Automaton
Bounded memory
DFA
Regular approximation
Statistical estimation

ASJC Scopus subject areas

Theoretical Computer Science
Statistics and Probability
Statistics, Probability and Uncertainty
Computational Theory and Mathematics

Access to Document

10.1007/s11222-011-9293-5

Cite this

@article{a7e4cc906989472fbd399fedb1308cc7,

title = "Statistical estimation with bounded memory",

abstract = "We investigate bounded-memory estimators of statistical functionals. It is shown that, for nondegenerate functionals and stochastic processes, it is impossible to achieve consistent estimation with bounded memory. In the positive direction, we show that O(log(1/ε)) states suffice to achieve ε-consistent estimation for a natural class of functionals. A canonical optimal construction is conjectured for arbitrary statistical functionals.",

keywords = "Automaton, Bounded memory, DFA, Regular approximation, Statistical estimation",

author = "Leonid Kontorovich",

note = "Funding Information: Supported in part by the Israel Science Foundation.",

year = "2012",

month = sep,

day = "1",

doi = "10.1007/s11222-011-9293-5",

language = "English",

volume = "22",

pages = "1155--1164",

journal = "Statistics and Computing",

issn = "0960-3174",

publisher = "Springer Netherlands",

number = "5",

}

TY - JOUR

T1 - Statistical estimation with bounded memory

AU - Kontorovich, Leonid

N1 - Funding Information: Supported in part by the Israel Science Foundation.

PY - 2012/9/1

Y1 - 2012/9/1

N2 - We investigate bounded-memory estimators of statistical functionals. It is shown that, for nondegenerate functionals and stochastic processes, it is impossible to achieve consistent estimation with bounded memory. In the positive direction, we show that O(log(1/ε)) states suffice to achieve ε-consistent estimation for a natural class of functionals. A canonical optimal construction is conjectured for arbitrary statistical functionals.

AB - We investigate bounded-memory estimators of statistical functionals. It is shown that, for nondegenerate functionals and stochastic processes, it is impossible to achieve consistent estimation with bounded memory. In the positive direction, we show that O(log(1/ε)) states suffice to achieve ε-consistent estimation for a natural class of functionals. A canonical optimal construction is conjectured for arbitrary statistical functionals.

KW - Automaton

KW - Bounded memory

KW - DFA

KW - Regular approximation

KW - Statistical estimation

UR - http://www.scopus.com/inward/record.url?scp=84863547116&partnerID=8YFLogxK

U2 - 10.1007/s11222-011-9293-5

DO - 10.1007/s11222-011-9293-5

M3 - Article

AN - SCOPUS:84863547116

SN - 0960-3174

VL - 22

SP - 1155

EP - 1164

JO - Statistics and Computing

JF - Statistics and Computing

IS - 5

ER -

Statistical estimation with bounded memory

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this