The laws of the iterated logarithm of some estimates in partly linear models

Jiti Gao

doi:10.1016/0167-7152(94)00217-V

The laws of the iterated logarithm of some estimates in partly linear models

Jiti Gao

Econometrics & Business Statistics

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

36 Citations (Scopus)

Abstract

Consider the regression model Y_i = x_i′β + g(t_i) + e_i, 1 ≤ i ≤ n, where x_i = (x_i1, x_i2, ..., x_ip)′ and t_i (t_i ε{lunate} [0, 1]) are known and nonrandom design points, β = (β₁, ..., β_p)′ (p ≥ 1) is an unknown parameter, g(·) is an unknown function, and e_i are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of β and an estimator of σ² = Ee₁² < ∞ are investigated.

Original language	English
Pages (from-to)	153-162
Number of pages	10
Journal	Statistics and Probability Letters
Volume	25
Issue number	2
DOIs	https://doi.org/10.1016/0167-7152(94)00217-V
Publication status	Published - 1 Nov 1995

Keywords

Least-square estimator
Partly linear model
The law of iterated logarithm

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10.1016/0167-7152(94)00217-V

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abstract = "Consider the regression model Yi = xi′β + g(ti) + ei, 1 ≤ i ≤ n, where xi = (xi1, xi2, ..., xip)′ and ti (ti ε\{lunate\} [0, 1]) are known and nonrandom design points, β = (β1, ..., βp)′ (p ≥ 1) is an unknown parameter, g(·) is an unknown function, and ei are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of β and an estimator of σ2 = Ee12 < ∞ are investigated.",

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N2 - Consider the regression model Yi = xi′β + g(ti) + ei, 1 ≤ i ≤ n, where xi = (xi1, xi2, ..., xip)′ and ti (ti ε{lunate} [0, 1]) are known and nonrandom design points, β = (β1, ..., βp)′ (p ≥ 1) is an unknown parameter, g(·) is an unknown function, and ei are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of β and an estimator of σ2 = Ee12 < ∞ are investigated.

AB - Consider the regression model Yi = xi′β + g(ti) + ei, 1 ≤ i ≤ n, where xi = (xi1, xi2, ..., xip)′ and ti (ti ε{lunate} [0, 1]) are known and nonrandom design points, β = (β1, ..., βp)′ (p ≥ 1) is an unknown parameter, g(·) is an unknown function, and ei are i.i.d. random errors. Based on g estimated by nonparametric kernel estimation, the laws of the iterated logarithm of the least-square estimator of β and an estimator of σ2 = Ee12 < ∞ are investigated.

KW - Least-square estimator

KW - Partly linear model

KW - The law of iterated logarithm

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SP - 153

EP - 162

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

The laws of the iterated logarithm of some estimates in partly linear models

Abstract

Keywords

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