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Variance estimation and influence fu...

Massie, Tristan Shaw.

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Variance estimation and influence functions for threshold models.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Variance estimation and influence functions for threshold models./
作者:	Massie, Tristan Shaw.
面頁冊數:	121 p.
附註:	Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4443.
Contained By:	Dissertation Abstracts International63-10B.
標題:	Biology, Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3066362
ISBN:	0493856420

Variance estimation and influence functions for threshold models.
Massie, Tristan Shaw.

Variance estimation and influence functions for threshold models. - 121 p.

Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4443.

Thesis (Ph.D.)--Virginia Commonwealth University, 2002.

A threshold model is a segmented regression model which implies a constant response below a certain level of the covariate, known as the threshold, and a non-constant response above the threshold. Segmented regression models require special treatment because the likelihood function is not smooth and, hence, the assumptions of classical maximum likelihood theory are not satisfied. A large sample theory was developed which circumvented this problem but simulation studies revealed that the theory may be inadequate for small to moderate sample sizes. In particular, the empirical variances of the parameter estimates are substantially larger than those predicted by the large sample theory. This dissertation investigates two potential solutions to the problem: an influence function approach to variance estimation and the use of a smooth model, which approximates the threshold model. The smooth model is a Fourier type expansion of the threshold model in terms of orthogonal polynomials. It depends on the same parameters as the threshold model and the integral of the squared differences between the two models over the experimental region is small so that the models are, in a sense, close. Simulation studies indicate that the influence approach does not improve agreement between empirical and theoretical variances, but the polynomial approximation approach does for a range of polynomial degrees. The various methods were applied to data from a study of Status Epilepticus, the occurrence of a prolonged seizure, because a threshold model seems to be appropriate for the relationship between age and the log odds of death.

ISBN: 0493856420Subjects--Topical Terms:

1018416
Biology, Biostatistics.

Variance estimation and influence functions for threshold models.
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500 $a Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4443.
500 $a Director: Daijin Ko.
502 $a Thesis (Ph.D.)--Virginia Commonwealth University, 2002.
520 $a A threshold model is a segmented regression model which implies a constant response below a certain level of the covariate, known as the threshold, and a non-constant response above the threshold. Segmented regression models require special treatment because the likelihood function is not smooth and, hence, the assumptions of classical maximum likelihood theory are not satisfied. A large sample theory was developed which circumvented this problem but simulation studies revealed that the theory may be inadequate for small to moderate sample sizes. In particular, the empirical variances of the parameter estimates are substantially larger than those predicted by the large sample theory. This dissertation investigates two potential solutions to the problem: an influence function approach to variance estimation and the use of a smooth model, which approximates the threshold model. The smooth model is a Fourier type expansion of the threshold model in terms of orthogonal polynomials. It depends on the same parameters as the threshold model and the integral of the squared differences between the two models over the experimental region is small so that the models are, in a sense, close. Simulation studies indicate that the influence approach does not improve agreement between empirical and theoretical variances, but the polynomial approximation approach does for a range of polynomial degrees. The various methods were applied to data from a study of Status Epilepticus, the occurrence of a prolonged seizure, because a threshold model seems to be appropriate for the relationship between age and the log odds of death.
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