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...

The question of recovering a multiband signal from noisy observations motivates a model in which the multivariate data points consist of an unknown deterministic trend Ξ observed with multivariate Gaussian errors. A cognate random trend model suggests affine shrinkage estimators Ξ̂A and Ξ̂B for Ξ, which are related to an extended Efron-Morris estimator. When represented canonically, Ξ̂A performs c...

In non-parametric function estimation, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. Here we propose two methods of constructing an average coverage confidence interval built from block shrinkage estimation methods. One is based on the James-Stein shrin...

In this paper, a modified estimation algorithm has been developed refers to covariance shaping least square estimation based on the quantum mechanical concepts and constraints. The algorithm has been applied to the speech signal and the performance is estimated using probability theories. The same models can be applied with additive white Gaussian Noise which estimates the bias in the parameter...

In this paper, a modified estimation algorithm has been developed refers to Covariance Shaping Least Square (CSLS) estimation based on the quantum mechanical concepts and constraints. The algorithm has been applied to Auto Regressive Moving Average (ARMA models with various parameter values. The same models can be applied with Colored Noise which estimates the bias in the parameter and the vali...

An unknown signal plus white noise is observed at n discrete time points. Within a large convex class of linear estimators of , we choose the estimator b that minimizes estimated quadratic risk. By construction, b is nonlinear. This estimation is done after orthogonal transformation of the data to a reasonable coordinate system. The procedure adaptively tapers the coeecients of the transformed ...

The question of recovering a multiband signal from noisy observations motivates a model in which the multivariate data points consist of an unknown deter-ministic trend observed with multivariate Gaussian errors. A cognate random trend model suggests aane shrinkage estimators ^ A and ^ B for , which are related to an extended Efron-Morris estimator. When represented canonically, ^ A performs co...

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...

This paper revisits the methodology of Stein (1975, 1986) for estimating a covariance matrix in the setting where the number of variables can be of the same magnitude as the sample size. Stein proposed to keep the eigenvectors of the sample covariance matrix but to shrink the eigenvalues. By minimizing an unbiased estimator of risk, Stein derived an ‘optimal’ shrinkage transformation. Unfortuna...