Model semiparametric

D Verotta, LB Sheiner, WF Ebling, DR Stanski. A semiparametric approach to physiological flow models. J Pharmacokin Biopharm 17 463-491, 1989. 

Compare the fully parametric and semiparametric approaches to estimation of a discrete choice model such as the multinomial logit model discussed in Chapter 21. What are the benefits and costs of the semiparametric approach ... 

A fully parametric model/estimator provides consistent, efficient, and comparatively precise results. The semiparametric model/estimator, by comparison, is relatively less precise in general terms. But, the payoff to this imprecision is that the semiparametric formulation is more likely to be robust to failures of the assumptions of the parametric model. Consider, for example, the binary probit model of Chapter 21, which makes a strong assumption of normality and homoscedasticity. If the assumptions are coirect, the probit estimator is the most efficient use of the data. However, if the normality assumption or the homoscedasticity assumption are incorrect, then the probit estimator becomes inconsistent in an unknown fashion. Lewbel s semiparametric estimator for the binary choice model, in contrast, is not very precise in comparison to the probit model. But, it will remain consistent if the normality assumption is violated, and it is even robust to certain kinds of heteroscedasticity. 

Yi, B. (2002). Nonparametric, parametric and semiparametric models for screening and decoding pools of chemical compounds. Unpublished PhD dissertation. North Carolina State University, Department of Statistics. 

Others have modeled the biophase using systems (24,25), semiparametric models (50), and nonparametric (15) models to account for the temporal displacement of the effect curve relative to Q,. The two other elements, biosensor and transduction kinetics, in PD modehng can also be employed to account for effect curve temporal displacement. These other two areas are covered in other chapters of this book. 

Shamlaye, and T.W. Clarkson. 1998. Semiparametric modeling of age at achieving developmental milestones after prenatal exposure to methylmercury in the Seychelles child development study. Environ. Health Perspect. 106(9) 559-564. 

Harrell F (1999) Semiparametric Modeling of Health Care Cost and Resource Utilization. Available at http //biostat.mc.vanderbilt.edu/twiki/pub/Main/FHHandouts/slide.pdfAccessed 5 April 2007. 

In terms of models, they fall into three categories parametric, nonparametric, and semiparametric. A parametric model only contains a finite number of parameters. One of the simplest examples of a parametric statistical model is the following ... 

The reason that model 2 is a nonparametric model is because F is unknown so the value of F at every real number, x, represents an unknown parameter. Models that are neither parametic nor nonparametric are said to be semiparametric. An example of a semiparametric model is the following ... 

Model 3 is semiparametric because it contains a parameter of interest (m) as well as the infinite-dimensional parameter F x) for every value of x. 

Intuitively, parametric models tend to yield estimates that are less variable than nonparametric and semiparametric models. However, parametric models are more sensitive to model misspecification. What model misspecification means is that if the distribution of the data does not match the model assumed, then the answers gotten from the model will tend to be quite wrong or, in statistical jargon, biased. By contrast, nonparametric and semiparametric models tend to make fewer... 

The advantage of parametric models is that estimates obtained from such models will tend to have lower variability than those obtained from semiparametric and nonparametric models. 

The advantage of semiparametric and nonparametric models is that they have more robustness than parametric models. If the true data model does not match the model being fit by the investigator, then estimates from the semiparametric and nonparametric models will have less associated bias than that from a parametric model. 

Bickel, P.J., C.A.J. Klaassen, Y. Ritov, and J. Wellner. Efficient and Adaptive Estimation for Semiparametric Models. Springer-Verlag, New York, 1997. 

Robins, J.M. and A. Rotnitzky. Comment on the Bickel and Kwon article, "Inference for semiparametric models Some questions and an answer". Stat Sinica, ll(4) 920-936,2001. 

Scharfstein, D.O., A. Rotnitzky, and J.M. Robins. Adjusting for nonignorable dropout using semiparametric nonresponse models (with discussion and rejoinder). 7 Am Stat Assoc, 94 1096-1146,1999. 

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