A mental health trial is analyzed using a dose-response model, in which the number of sessions attended by the patients is deemed indicative of the dose of psychotherapeutic treatment. Here, the parameter of interest is the difference in causal treatment effects between the subpopulations that take part in different numbers of therapy sessions. For this data set, interactions between random tre...

Pre-test estimator has been studied to estimate the mean of a normal distribution when non-sample prior information is avaliable. Our aim is to consider pre-test estimator of the mean in thepresence of outliers. A well known procedure to define pre-test estimator of the mean is using thesample mean. However, the sample mean is not a robust location parameter. In order to overcom...

Many multivariate Gaussian models can conveniently be split into independent, block-wise problems. Common settings where this situation arises are balanced ANOVA models, balanced longitudinal models, and certain block-wise shrinkage estimators in nonparametric regression estimation involving orthogonal bases such as Fourier or wavelet bases. It is well known that the standard, least squares est...

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...

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press a...

A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference step of modern kernel methods that rely on embedding probability distributions in RKHSs. Given a finite sample, an empirical average has been used commonly as...

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...