Statistical Methodology最新文献

A new statistical approach for on-line change detection in uncertain dynamic system is proposed. In change detection problem, the distribution of a sequence of observations can change at some unknown instant. The goal is to detect this change, for example a parameter change, as quickly as possible with a minimal risk of false detection. In this paper, the observations come from an uncertain system modeled by an autoregressive model containing an unknown functional component. The popular Page’s CUSUM rule is not applicable anymore since it requires the full knowledge of the model. A new detection CUSUM-like scheme is proposed, which is based on the nonparametric estimation of the unknown component from a learning sample. Moreover, the estimation procedure can be updated on-line which ensures a better detection, especially at the beginning of the monitoring procedure. Simulation trials were performed on a model describing a water treatment process and show the interest of this new procedure with respect to the classic CUSUM rule.

Kernel-based association test (KAT) is a widely used tool in genetics association analysis. The performance of such a test depends on the choice of kernel. In this paper, we study the statistical power of a KAT using a Gaussian kernel. We explicitly develop a notion of analytical power function in this family of tests. We propose a novel approach to select the kernel so as to maximize the analytical power function of the test at a given test level (an upper bound on the probability of making a type I error). We assess some theoretical properties of our optimal estimator, and compare its performance with some similar existing alternatives using simulation studies. Neuroimaging data from an Alzheimer’s disease study is also used to illustrate the proposed kernel selection methodology.

This paper considers a particular generalized inverse trinomial distribution which may be regarded as the convolution of binomial and negative distributions for the statistical analysis of count data. This distribution has the flexibility to cater for under-, equi- and over-dispersion in the data. Some basic and probabilistic properties and tail approximation of the distribution have been derived. Conditions for the numerical stability of the two-term probability recurrence formula have also been examined to facilitate computation. For the purpose of statistical analysis, test of hypothesis for equi-dispersion by the score and likelihood ratio tests and simulation study of their power, parameter estimation by maximum likelihood and a probability generating function based methods have been considered. The versatility of the distribution is illustrated by its application to real biological data sets which exhibit under and over dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM-Poisson distributions.

In this paper, we present a non-parametric continuous density Hidden Markov mixture model (CDHMMix model) with unknown number of mixtures for blind segmentation or clustering of sequences. In our presented model, the emission distributions of HMMs are chosen to be Gaussian with full, diagonal, or tridiagonal covariance matrices. We apply a Bayesian approach to train our presented model and drive the inference of our model using the Monte Carlo Markov Chain (MCMC) method. For the multivariate Gaussian emission a method that maintains the tridiagonal structure of the covariance is introduced. Moreover, we present a new sampling method for hidden state sequences of HMMs based on the Viterbi algorithm that increases the mixing rate.

Two theoretical approaches are usually employed for the fitting of ordinal data: the underlying variables approach (UV) and the item response theory (IRT). In the UV approach, limited information methods [generalized least squares (GLS) and weighted least squares (WLS)] are employed. In the IRT approach, fitting is carried out with full information methods [Proportional Odds Model (POM), and the Normal Ogive (NOR)]. The four estimation methods (GLS, WLS, POM and NOR) are compared in this article at the same time, using a simulation study and analyzing the goodness-of-fit indices obtained. The parameters used in the Monte Carlo simulation arise from the application of a political action scale whose two-factor structure is well known. The results show that the estimation method employed affects the goodness-of-fit to the model. In our case, the IRT approach shows a better fitting than UV, especially with the POM method.

Rényi (1961) proposed the Rényi entropy. Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Nanda et al. (2014) obtained a quantile version of the Rényi residual entropy, the Rényi residual quantile entropy (RRQE). Based on the RRQE function, they defined a new stochastic order, the Rényi quantile entropy (RQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the RQE order are investigated, closure and reversed closure properties are obtained, meanwhile, some illustrative examples are shown. As applications of a main result, the preservation of the RQE order in several stochastic models are discussed.

We propose a new variable selection and estimation technique for high dimensional single index models with unknown monotone smooth link function. Among many predictors, typically, only a small fraction of them have significant impact on prediction. In such a situation, more interpretable models with better prediction accuracy can be obtained by variable selection. In this article, we propose a new penalized forward selection technique which can reduce high dimensional optimization problems to several one dimensional optimization problems by choosing the best predictor and then iterating the selection steps until convergence. The advantage of optimizing in one dimension is that the location of optimum solution can be obtained with an intelligent search by exploiting smoothness of the criterion function. Moreover, these one dimensional optimization problems can be solved in parallel to reduce computing time nearly to the level of the one-predictor problem. Numerical comparison with the LASSO and the shrinkage sliced inverse regression shows very promising performance of our proposed method.

This research is motivated from the analysis of a real gene expression data that aims to identify a subset of “interesting” or “significant” genes for further studies. When we blindly applied the standard false discovery rate (FDR) methods, our biology collaborators were suspicious or confused, as the selected list of significant genes was highly unbalanced: there were ten times more under-expressed genes than the over-expressed genes. Their concerns led us to realize that the observed two-sample $t$-statistics were highly skewed and asymmetric, and thus the standard FDR methods might be inappropriate. To tackle this case, we propose a symmetric directional FDR control method that categorizes the genes into “over-expressed” and “under-expressed” genes, pairs “over-expressed” and “under-expressed” genes, defines the $p$-values for gene pairs via column permutations, and then applies the standard FDR method to select “significant” gene pairs instead of “significant” individual genes. We compare our proposed symmetric directional FDR method with the standard FDR method by applying them to simulated data and several well-known real data sets.

The present paper deals with a nonparametric $M$-estimation for right censored regression model with stationary ergodic data. Defined as an implicit function, a kernel-type estimator of a family of robust regression is considered when the covariate takes its values in $R^d$ ($d\ge 1$) and the data are sampled from a stationary ergodic process. The strong consistency (with rate) and the asymptotic distribution of the estimator are established under mild assumptions. Moreover, a usable confidence interval is provided which does not depend on any unknown quantity. Our results hold without any mixing condition and do not require the existence of marginal densities. A comparison study based on simulated data is also provided.

In many situations, multiple copies of a software are tested in parallel with different test cases as input, and the detected errors from a particular round of testing are debugged together. In this article, we discuss a discrete time model of software reliability for such a scenario of periodic debugging. We propose likelihood based inference of the model parameters, including the initial number of errors, under the assumption that all errors are equally likely to be detected. The proposed method is used to estimate the reliability of the software. We establish asymptotic normality of the estimated model parameters. The performance of the proposed method is evaluated through a simulation study and its use is illustrated through the analysis of a dataset obtained from testing of a real-time flight control software. We also consider a more general model, in which different errors have different probabilities of detection.