35,664 research outputs found
Lecture notes on ridge regression
The linear regression model cannot be fitted to high-dimensional data, as the
high-dimensionality brings about empirical non-identifiability. Penalized
regression overcomes this non-identifiability by augmentation of the loss
function by a penalty (i.e. a function of regression coefficients). The ridge
penalty is the sum of squared regression coefficients, giving rise to ridge
regression. Here many aspect of ridge regression are reviewed e.g. moments,
mean squared error, its equivalence to constrained estimation, and its relation
to Bayesian regression. Finally, its behaviour and use are illustrated in
simulation and on omics data. Subsequently, ridge regression is generalized to
allow for a more general penalty. The ridge penalization framework is then
translated to logistic regression and its properties are shown to carry over.
To contrast ridge penalized estimation, the final chapter introduces its lasso
counterpart
Reliable inference for complex models by discriminative composite likelihood estimation
Composite likelihood estimation has an important role in the analysis of
multivariate data for which the full likelihood function is intractable. An
important issue in composite likelihood inference is the choice of the weights
associated with lower-dimensional data sub-sets, since the presence of
incompatible sub-models can deteriorate the accuracy of the resulting
estimator. In this paper, we introduce a new approach for simultaneous
parameter estimation by tilting, or re-weighting, each sub-likelihood component
called discriminative composite likelihood estimation (D-McLE). The
data-adaptive weights maximize the composite likelihood function, subject to
moving a given distance from uniform weights; then, the resulting weights can
be used to rank lower-dimensional likelihoods in terms of their influence in
the composite likelihood function. Our analytical findings and numerical
examples support the stability of the resulting estimator compared to
estimators constructed using standard composition strategies based on uniform
weights. The properties of the new method are illustrated through simulated
data and real spatial data on multivariate precipitation extremes.Comment: 29 pages, 4 figure
The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach
Robust inference based on the minimization of statistical divergences has
proved to be a useful alternative to the classical maximum likelihood based
techniques. Recently Ghosh et al. (2013) proposed a general class of divergence
measures for robust statistical inference, named the S-Divergence Family. Ghosh
(2014) discussed its asymptotic properties for the discrete model of densities.
In the present paper, we develop the asymptotic properties of the proposed
minimum S-Divergence estimators under continuous models. Here we use the
Basu-Lindsay approach (1994) of smoothing the model densities that, unlike
previous approaches, avoids much of the complications of the kernel bandwidth
selection. Illustrations are presented to support the performance of the
resulting estimators both in terms of efficiency and robustness through
extensive simulation studies and real data examples.Comment: Pre-Print, 34 page
- …