Strong representations for LAD estimators in linear models

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

Consider the standard linear model yi=ziβ+ei, i=1, 2,..., n, where zi denotes the ith row of an n x p design matrix, β∈ℝp is an unknown parameter to be estimated and ei are independent random variables with a common distribution function F. The least absolute deviation (LAD) estimate {Mathematical expression} of β is defined as any solution of the minimization problem {Mathematical expression} In this paper Bahadur type representations are obtained for {Mathematical expression} under very mild conditions on F near zero and on zi, i=1,..., n. These results are extended to the case, when {ei} is a mixing sequence. In particular the results are applicable when the residuals ei form a simple autoregressive process.

Original languageEnglish (US)
Pages (from-to)547-558
Number of pages12
JournalProbability Theory and Related Fields
Volume83
Issue number4
DOIs
StatePublished - Dec 1 1989

Fingerprint

Least Absolute Deviation
Linear Model
Estimator
Mixing Sequence
Representation Type
Autoregressive Process
Independent Random Variables
Unknown Parameters
Minimization Problem
Standard Model
Distribution Function
Denote
Zero
Estimate
Deviation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{b265be17a8304748801c0ae916c5e31a,
title = "Strong representations for LAD estimators in linear models",
abstract = "Consider the standard linear model yi=ziβ+ei, i=1, 2,..., n, where zi denotes the ith row of an n x p design matrix, β∈ℝp is an unknown parameter to be estimated and ei are independent random variables with a common distribution function F. The least absolute deviation (LAD) estimate {Mathematical expression} of β is defined as any solution of the minimization problem {Mathematical expression} In this paper Bahadur type representations are obtained for {Mathematical expression} under very mild conditions on F near zero and on zi, i=1,..., n. These results are extended to the case, when {ei} is a mixing sequence. In particular the results are applicable when the residuals ei form a simple autoregressive process.",
author = "Babu, {Gutti Jogesh}",
year = "1989",
month = "12",
day = "1",
doi = "10.1007/BF01845702",
language = "English (US)",
volume = "83",
pages = "547--558",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "4",

}

Strong representations for LAD estimators in linear models. / Babu, Gutti Jogesh.

In: Probability Theory and Related Fields, Vol. 83, No. 4, 01.12.1989, p. 547-558.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Strong representations for LAD estimators in linear models

AU - Babu, Gutti Jogesh

PY - 1989/12/1

Y1 - 1989/12/1

N2 - Consider the standard linear model yi=ziβ+ei, i=1, 2,..., n, where zi denotes the ith row of an n x p design matrix, β∈ℝp is an unknown parameter to be estimated and ei are independent random variables with a common distribution function F. The least absolute deviation (LAD) estimate {Mathematical expression} of β is defined as any solution of the minimization problem {Mathematical expression} In this paper Bahadur type representations are obtained for {Mathematical expression} under very mild conditions on F near zero and on zi, i=1,..., n. These results are extended to the case, when {ei} is a mixing sequence. In particular the results are applicable when the residuals ei form a simple autoregressive process.

AB - Consider the standard linear model yi=ziβ+ei, i=1, 2,..., n, where zi denotes the ith row of an n x p design matrix, β∈ℝp is an unknown parameter to be estimated and ei are independent random variables with a common distribution function F. The least absolute deviation (LAD) estimate {Mathematical expression} of β is defined as any solution of the minimization problem {Mathematical expression} In this paper Bahadur type representations are obtained for {Mathematical expression} under very mild conditions on F near zero and on zi, i=1,..., n. These results are extended to the case, when {ei} is a mixing sequence. In particular the results are applicable when the residuals ei form a simple autoregressive process.

UR - http://www.scopus.com/inward/record.url?scp=0000318629&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000318629&partnerID=8YFLogxK

U2 - 10.1007/BF01845702

DO - 10.1007/BF01845702

M3 - Article

AN - SCOPUS:0000318629

VL - 83

SP - 547

EP - 558

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -