TY - JOUR
T1 - Random Sieve Likelihood and General Regression Models
AU - Shen, Xiaotong
AU - Shi, Jian
AU - Wong, Wing Hung
PY - 1999/9
Y1 - 1999/9
N2 - Consider a semiparametric regression model Y = f(θ, X, ϵ), where f is a known function, θ is an unknown vector, ϵ consists of a random error and possibly of some unobserved variables, and the distribution F(·) of (ϵ, X) is unspecified. This article introduces, in a general setting, new methodology for estimating θ and F(·). The proposed method constructs a profile likelihood defined on random-level sets (a random sieve). The proposed method is related to empirical likelihood but is more generally applicable. Four examples are discussed, including a quadratic model, high-dimensional semiparametric regression, a nonparametric random-effects model, and linear regression with right-censored data. Simulation results and asymptotic analysis support the utility and effectiveness of the proposed method.
AB - Consider a semiparametric regression model Y = f(θ, X, ϵ), where f is a known function, θ is an unknown vector, ϵ consists of a random error and possibly of some unobserved variables, and the distribution F(·) of (ϵ, X) is unspecified. This article introduces, in a general setting, new methodology for estimating θ and F(·). The proposed method constructs a profile likelihood defined on random-level sets (a random sieve). The proposed method is related to empirical likelihood but is more generally applicable. Four examples are discussed, including a quadratic model, high-dimensional semiparametric regression, a nonparametric random-effects model, and linear regression with right-censored data. Simulation results and asymptotic analysis support the utility and effectiveness of the proposed method.
KW - Empirical likelihood
KW - General regression model
KW - Profile likelihood
KW - Random sieve likelihood
UR - http://www.scopus.com/inward/record.url?scp=1542742691&partnerID=8YFLogxK
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U2 - 10.1080/01621459.1999.10474188
DO - 10.1080/01621459.1999.10474188
M3 - Article
AN - SCOPUS:1542742691
VL - 94
SP - 835
EP - 846
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
SN - 0162-1459
IS - 447
ER -