In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a conventional differential inequality studied in the literature, but also handles non-differentiable or disco...

The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in interval (0, 1), such as rates, proportions, percentages fractions. Generally, parameters of BRM are estimated by method maximum likelihood estimation (MLE). However, MLE does not offer accurate reliable estimates explanatory variables correlated. To solve this problem, ridge Liu est...

We present a multi-task learning approach to jointly estimate the means of multiple independent distributions from samples. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the individual task’s sample averages. We derive the optimal amount of regularization for the two task case for the minimum risk estimator and a minimax estimator, and show that the optima...

Abstract: The problem of estimating the centre of symmetry of an unknown periodic function observed in Gaussian white noise is considered. Using the penalized blockwise James-Stein method, a smoothing filter allowing to define the penalized profile likelihood is proposed. The estimator of the centre of symmetry is then the maximizer of this penalized profile likelihood. This estimator is shown ...

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of the features. We capture both properties with an empirical Bayes estimator that shrinks coefficients monotonically with respect to their anticipated importa...

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James–Stein estimator is such an estimator, having a property called min...

Nearly all estimators in statistical prediction come with an associated tuning parameter, in one way or another. Common practice, given data, is to choose the tuning parameter value that minimizes a constructed estimate of the prediction error of the estimator; we focus on Stein’s unbiased risk estimator, or SURE (Stein, 1981; Efron, 1986), which forms an unbiased estimate of the prediction err...

Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of covariates. In a linear regression model with homoscedastic Normal noise, I consider shrinkage estimation of the nuisance parameters associated with control...

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James–Stein estimator is such an estimator, having a property called min...

We study orthogonal decomposition of symmetric statistics based on samples drawn without replacement from finite populations. Under very mild smoothness conditions the first k terms of the decomposition provide stochastic expansion with remainder O(N−k/2). Assuming that the linear part of the decomposition is nondegenerate we establish one term Edgeworth expansion of the distribution function o...