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EFFICIENT SMALL-SAMPLE INFERENCE IN THE NON-LINEAR CALIBRATION PROBLEM

Title
EFFICIENT SMALL-SAMPLE INFERENCE IN THE NON-LINEAR CALIBRATION PROBLEM
Authors
조은영
Issue Date
1995
Department/Major
대학원 통계학과
Keywords
EFFICIENTSMALL-SAMPLEINFERENCENON-LINEARCALIBRATION PROBLEM
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
In this thesis, we consider the problem of efficient estimator in the univariate non-linear calibration model : y_(i) = f(χ_(i) ; β)+δε_(i) , i = l ,…, n, y = f(χ ; β)+δε , where f(·;β) represents an arbitrary monotonic non-linear function of χ in the region of interest, (y_(1), …, y_(n), y) an observation vector, {χ_(i)} fixed design vector, B =(β_(i), …, β_(k)) vector of regression parameters, χ unknown true value of interest and {ε_(i)}, ε are mutually uncorrelated measurement errors with zero mean and unit variance but otherwise unknown distributions. On the basis of simple small-sample asymptotics, we derive a lower bound for the low-noise Asymptotic Mean Square Errors (AMSE) of the arbitrary regular consistent estimators of χ irrespective of the type of measurement errors. We also give the sufficient condition for the existence of efficient estimator of χ, and we show that both the classical and inverse estimators have the smallest low-noise AMSE. Finally we illustrate the applicability and the utility of the main optimality results by the real data example and the simulation study. ;본 논문에서는 단변량 비선형 검량모형(univariate nonlinear calibration model)에서 간단한 소표본 근사에 기초를 두어 분산이 작을 때의 일치추정량(regular-consistent estimator)의 점근 평균 제곱오차(low-noise Asymptotic Mean Square Error)의 하한(lower bound)을 유도하였다. 이 하한은 추정 오차의 분포 형태에 무관하였다. 또한 고전적 추정치(classical estimator)와 역추정치(inverse estimator)의 효율성에 대한 충분조건을 구하였고 그 두 추정치가 최소의 점근 평균 제곱 오차를 가지는 것을 보였다. 그리고 실제 자료와 모의실험을 통해 주요 최적 결과의 타당성과 유용성을 보였다.
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