Data and models are two sources of information in a statistical analysis. Data carry noise but are “unbiased,” whereas models, effectively a set of constraints, help to reduce noise but are responsible for “biases.” Representing the two extremes on the spectrum of “bias-variance” trade-off are standard parametric models and constraint-free nonparametric “models” such as the empirical distribution for a probability density. In between the two extremes, there exist scores of nonparametric or semiparametric models, of which most are also known as smoothing methods. A family of such nonparametric models in a variety of stochastic settings can be derived through the penalized likelihood method, forming the subject of this book.
KeywordsSmoothing Parameter Side Condition Smoothing Spline Multivariate Function Multivariate Statistical Model
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