左模张量积的同态及其基础环的转移

本文在[1]的基础上，讨论了两个左模张量积的同态，左模和左模张量积的基础环的转移，逆转移。并给出了基础环逆转移的一个同构定理。     

On stochastic processes for quantitative trait locus mapping under selective genotyping

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0, T] representing a chromosome. The originality of this study is that we are under selective genotyping: only the individuals with extreme phenotypes are genotyped. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0, T] and under local alternatives with a QTL at t^☆ on [0, T]. We show that the LRT process is asymptotically the square of a ‘non-linear interpolated and normalized Gaussian process’. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that we have to genotype symmetrically and that the threshold is exactly the same as in the situation where all the individuals are genotyped.     

Empirical likelihood for single index model with missing covariates at random

In this paper, we investigate the empirical-likelihood-based inference for the construction of confidence intervals and regions of the parameters of interest in single index models with missing covariates at random. An augmented inverse probability weighted-type empirical likelihood ratio for the parameters of interest is defined such that this ratio is asymptotically standard chi-squared. Our approach is to directly calibrate the empirical log-likelihood ratio, and does not need multiplication by an adjustment factor for the original ratio. Our bias-corrected empirical likelihood is self-scale invariant and no plug-in estimator for the limiting variance is needed. Some simulation studies are carried out to assess the performance of our proposed method.     

A software reliability model using mean residual quantile function

In this paper, we propose a class of distributions with the inverse linear mean residual quantile function. The distributional properties of the family of distributions are studied. We then discuss the reliability characteristics of the family of distributions. Some characterizations of the class of distributions are also discussed. The parameters of the class of distributions are estimated using the method of L-moments. The proposed class of distributions is applied to a real data set.     

Variable selection via a multi-stage strategy

Variable selection for nonlinear regression is a complex problem, made even more difficult when there are a large number of potential covariates and a limited number of datapoints. We propose herein a multi-stage method that combines state-of-the-art techniques at each stage to best discover the relevant variables. At the first stage, an extension of the Bayesian Additive Regression tree is adopted to reduce the total number of variables to around 30. At the second stage, sensitivity analysis in the treed Gaussian process is adopted to further reduce the total number of variables. Two stopping rules are designed and sequential design is adopted to make best use of previous information. We demonstrate our approach on two simulated examples and one real data set.     

Nonparametric regression in a statistical modified Helmholtz equation using the Fourier spectral regularization

In this paper, we deal with the Cauchy problem for the modified Helmholtz equation. We consider two models of data: the bounded variance model and the i.i.d. model. The trigonometric estimators of nonparametric regression is applied to solve the problem. In addition, the general forms of regularization parameter corresponding to the pointwise mean squared error and the mean integrated squared error are discussed in detail. The minimax rate convergence corresponding to the bounded variance model is also presented. In the i.i.d. model, we construct the asymptotic confidence interval for the solution of the problem. Finally, we give some numerical experiments and discuss the obtained results.     

Adaptive Bayesian Procedures Using Random Series Priors

We consider a general class of prior distributions for nonparametric Bayesian estimation which uses finite random series with a random number of terms. A prior is constructed through distributions on the number of basis functions and the associated coefficients. We derive a general result on adaptive posterior contraction rates for all smoothness levels of the target function in the true model by constructing an appropriate ‘sieve’ and applying the general theory of posterior contraction rates. We apply this general result on several statistical problems such as density estimation, various nonparametric regressions, classification, spectral density estimation and functional regression. The prior can be viewed as an alternative to the commonly used Gaussian process prior, but properties of the posterior distribution can be analysed by relatively simpler techniques. An interesting approximation property of B‐spline basis expansion established in this paper allows a canonical choice of prior on coefficients in a random series and allows a simple computational approach without using Markov chain Monte Carlo methods. A simulation study is conducted to show that the accuracy of the Bayesian estimators based on the random series prior and the Gaussian process prior are comparable. We apply the method on Tecator data using functional regression models.     

Brownian Bridge and Other Path-dependent Gaussian Processes Vectorial Simulation

The iterative simulation of the Brownian bridge is well known. In this article, we present a vectorial simulation alternative based on Gaussian processes for machine learning regression that is suitable for interpreted programming languages implementations. We extend the vectorial simulation of path-dependent trajectories to other Gaussian processes, namely, sequences of Brownian bridges, geometric Brownian motion, fractional Brownian motion, and Ornstein–Ulenbeck mean reversion process.