1 Summary of Lecture 12 In the last lecture we derived a risk (MSE) bound for regression problems; i.e., select an f ∈ F so that E[(f(X)− Y )]− E[(f∗(X)− Y )] is small, where f∗(x) = E[Y |X = x]. The result is summarized below. Theorem 1 (Complexity Regularization with Squared Error Loss) Let X = R, Y = [−b/2, b/2], {Xi, Yi}i=1 iid, PXY unknown, F = {collection of candidate functions}, f : R → ...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...

Based on progressively Type-II censored samples, the maximum likelihood and Bayes estimators for the scale parameter, reliability and cumulative hazard functions are derived. The Bayes estimators are studied under symmetric (squared error) loss function and asymmetric (LINEX and general entropy) loss functions. Tow techniques are used for computing the Bayes estimates; standard Bayes and import...

An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss. AMS(2000) Subject Classification: Primary 62C15; Secondary 62F10

An admissible estimator of the eigenvalues of the variance-covariance matrix is given for multivariate normal distributions with respect to the scale-invariant squared error loss. AMS(2000) Subject Classification: Primary 62C15; Secondary 62F10

A simple geometric representation of Bayes and unbiased rules for squared error loss is provided. Some orthogonality relationships between them and the functions they are estimating are proved. Bayes estimators are shown to be behave asymptotically like unbiased estimators.