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Sieve maximum likelihood estimation in generalized linear models with an unknown link function

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Standard generalized linear models (GLMs) consist of three components: random component referring to a distribution of the response variable that belongs to the exponential family; systematic component referring to the linear predictor; and known link function specifying the relationship between the linear predictor and the mean of the distribution function. A flexible extension of the standard GLMs allows an unknown link function. Classical parametric likelihood approach is not applicable due to a large parameter space. To address this issue, sieve maximum likelihood estimation has been developed in literature in which the estimator of the unknown link function is assumed to lie in a sieve space. Various methods of sieves including the B‐spline and P‐spline based methods are introduced. The numerical implementation and theoretical properties of these methods are also discussed. WIREs Comput Stat 2018, 10:e1425. doi: 10.1002/wics.1425 This article is categorized under: Applications of Computational Statistics > Signal and Image Processing and Coding Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical Models > Generalized Linear Models Algorithms and Computational Methods > Maximum Likelihood Methods
Cubic B‐spline basis functions with nine interior knots evenly spaced from 0 to 1
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Scatter plot of the number of satellites against the estimated linear predictor (circles) and the estimated link function (solid curve)
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(a) Number of satellites by weight of female crab; (b) number of satellites by carapace width
[ Normal View | Magnified View ]

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Applications of Computational Statistics > Signal and Image Processing and Coding
Statistical Models > Generalized Linear Models
Algorithms and Computational Methods > Maximum Likelihood Methods
Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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