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The quadratic exponential family
2011Various generalized estimating equations of order 2 (GEE2) to simultaneously estimate the mean and the association structure can be obtained from the pseudo maximum likelihood 2 (PML2) method. PML2 estimation has been introduced by Gourieroux et al. (1984b), and it is based on the quadratic exponential family.
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2009
Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible. Curved exponential families arise naturally with data from sequential experiments, considered in Section 5.2, and Section 5.3 considers ...
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Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible. Curved exponential families arise naturally with data from sequential experiments, considered in Section 5.2, and Section 5.3 considers ...
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On the linear exponential family
Mathematical Proceedings of the Cambridge Philosophical Society, 1968In this paper we give a characterization theorem for a subclass of the exponential family whose probability density function is given bywhere a(x) ≥ 0, f(ω) = ∫a(x) exp (ωx) dx and ωx is to be interpreted as a scalar product. The random variable X may be an s-vector. In that case ω will also be an s-vector.
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Nonlinear exponential families
1993The nonlinear regression model $$\begin{array}{*{20}{c}} {y = \eta \left( \vartheta \right) + \varepsilon ;\quad \left( {\vartheta \in \Theta } \right),} \\ {\varepsilon \sim N\left( {0,{{\sigma }^{2}}W} \right)} \\ \end{array}$$ considered in previous chapters, can be presented equivalently as a family of densities $$\left\{ {f(y\left ...
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The geometry of exponential families [PDF]
, 1993 Michael K. Murray, John W. Rice
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2011
Several estimating equations belonging to the class of generalized estimating equations for the mean structure, termed GEE1, can be derived as special cases of the pseudo maximum likelihood 1 (PML1) method. PML1 estima- tion is based on the linear exponential family, and this class of distributions is therefore discussed in this chapter. In Sect.
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Several estimating equations belonging to the class of generalized estimating equations for the mean structure, termed GEE1, can be derived as special cases of the pseudo maximum likelihood 1 (PML1) method. PML1 estima- tion is based on the linear exponential family, and this class of distributions is therefore discussed in this chapter. In Sect.
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Approximation by Exponential Families
1986In this chapter we give an extension of some of the results of Chapters 10 and 11, replacing the Gaussian shift families used there by other exponential families. The results obtained cover only a restricted domain. To go further, much additional work appears necessary.
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Genetic testing in prostate cancer management: Considerations informing primary care
Ca-A Cancer Journal for Clinicians, 2022Veda N Giri +2 more
exaly
Planning for post‐pandemic cancer care delivery: Recovery or opportunity for redesign?
Ca-A Cancer Journal for Clinicians, 2021Pelin Cinar +2 more
exaly