Generalised K-S confidence regions: some exact results

One-sided confidence regions for continuous cumulative distribution function are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. Significance levels necessary for implementation are given. Some other K-S type distances useful in constructing a confidence region with nonconstant width are also included.     

Double shrinkage estimators for large sparse covariance matrices

Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft thresholding, and generalized thresholding were therefore developed to this end. However, these estimators do not always yield well-conditioned covariance estimates. To have sparse and well-conditioned estimates, we propose doubly shrinkage estimators: shrinking small covariances towards zero and then shrinking covariance matrix towards a diagonal matrix. Additionally, a richness index is defined to evaluate how rich a covariance matrix is. According to our simulations, the richness index serves as a good indicator to choose relevant covariance estimator.     

Rank repeated measures analysis of covariance

When analyzing a response variable at the presence of both factors and covariates, with potentially correlated responses and violated assumptions of the normal residual or the linear relationship between the response and the covariates, rank-based tests can be an option for inferential procedures instead of the parametric repeated measures analysis of covariance (ANCOVA) models. This article derives a rank-based method for multi-way ANCOVA models with correlated responses. The generalized estimating equations (GEE) technique is employed to construct the proposed rank tests. Asymptotic properties of the proposed tests are derived. Simulation studies confirmed the performance of the proposed tests.     

A stochastic procedure to solve linear ill-posed problems

In this work, we propose a stochastic procedure of Robbins–Monro type to resolve linear inverse problems in Hilbert space. We study the probability of large deviation between the exact solution and the approximated one and build a confidence domain for the approximated solution while precising the rate of convergence. To check the validity of our work, we give a simulation application into a deconvolution problem.     

Asymptotic expansions for sequential confidence levels in inverse linear regression

Non-linear renewal theory is used to derive second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter xin the inverse linear regression model. These expansions are obtained for a two-stage sequential procedure, proposed by Perng and Tong (1974) for the construction of a confidence interval for x.     

Exponential Inequalities in Stochastic Inverse Problems Using an Iterative Method

We consider an iterative method in order to solve linear inverse problems. We establish exponential inequalities for the probability of the distance between the approximated solution and the exact one for a calibration problem. The approximate is given by an iterative method with Gaussian errors. We treat an operator equation of the form Ax = u, where A is a compact operator.     

Effect of a new selection procedure on adaptive estimation

Adaptive estimation of parameters of some failure time distributionsis considered. A new procedure named the F-procedure has beendeveloped for selecting an appropriate model out of two possible models by Pandey et.al. (1991). Applying this F-procedure adaptive estimatorsof parameters of exponential, Wei bull, inverse Gaussian (IG) and Wald failure time distributions have been proposed in this paper. Comparison of these estimators has been undertaken with MLE's of the respective parameters and with some previous adaptiveestimators by simulation of samples using the Monte Carlo method.Adaptive estimation of parameters of some failure time distributions is considered. A new procedure named the F-procedure has been developedfor selecting an appropriate model out of two possible models by Pandey et.al. (1991). Applying this F-procedure adaptive estimators of parameters of exponential, Wei bull, inverse Gaussian (IG) and Wald failure time distributions have been proposed in this paper. Comparison of these estimators has been undertaken with MLE's of the respective parameters and with some previous adaptive estimators by simulation of samples using the Monte Carlo method.     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.     

Application of the Bootstrap Approach to the Choice of Dimension and the α Parameter in the SIRα Method

To reduce the dimensionality of regression problems, sliced inverse regression approaches make it possible to determine linear combinations of a set of explanatory variables X related to the response variable Y in general semiparametric regression context. From a practical point of view, the determination of a suitable dimension (number of the linear combination of X) is important. In the literature, statistical tests based on the nullity of some eigenvalues have been proposed. Another approach is to consider the quality of the estimation of the effective dimension reduction (EDR) space. The square trace correlation between the true EDR space and its estimate can be used as goodness of estimation. In this article, we focus on the SIR_α method and propose a naïve bootstrap estimation of the square trace correlation criterion. Moreover, this criterion could also select the α parameter in the SIR_α method. We indicate how it can be used in practice. A simulation study is performed to illustrate the behavior of this approach.     

A note on approximate confidence limits for the negative binomial model

Four methods of approximating confidence limits for the single negative binomial parameter, P, are outlined and an empirical study is presented. Some remarks on prediction intervals are also included.