TY - JOUR
T1 - An upper bound for functions of estimators in high dimensions
AU - Caner, Mehmet
AU - Han, Xu
PY - 2021
Y1 - 2021
N2 - We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge faster, slower, or at the same rate as estimators depending on the behavior of the partial derivative of the function. We illustrate this via three examples. The first two examples use the upper bound for testing in high dimensions, and third example derives the estimated out-of-sample variance of large portfolios. All our results allow for a larger number of parameters, p, than the sample size, n.
AB - We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge faster, slower, or at the same rate as estimators depending on the behavior of the partial derivative of the function. We illustrate this via three examples. The first two examples use the upper bound for testing in high dimensions, and third example derives the estimated out-of-sample variance of large portfolios. All our results allow for a larger number of parameters, p, than the sample size, n.
KW - Lasso
KW - many assets
KW - many restrictions
KW - Lasso
KW - many assets
KW - many restrictions
KW - Lasso
KW - many assets
KW - many restrictions
UR - http://www.scopus.com/inward/record.url?scp=85089918631&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85089918631&origin=recordpage
U2 - 10.1080/07474938.2020.1808370
DO - 10.1080/07474938.2020.1808370
M3 - 21_Publication in refereed journal
VL - 40
SP - 1
EP - 13
JO - Econometric Reviews
JF - Econometric Reviews
SN - 0747-4938
IS - 1
ER -