Autocovariance Estimation in Regression with a Discontinuous Signal and m‐Dependent Errors: A Difference‐Based Approach

We discuss a class of difference‐based estimators for the autocovariance in nonparametric regression when the signal is discontinuous and the errors form a stationary m‐dependent process. These estimators circumvent the particularly challenging task of pre‐estimating such an unknown regression function. We provide finite‐sample expressions of their mean squared errors for piecewise constant signals and Gaussian errors. Based on this, we derive biased‐optimized estimates that do not depend on the unknown autocovariance structure. Notably, for positively correlated errors, that part of the variance of our estimators that depend on the signal is minimal as well. Further, we provide sufficient conditions for ‐consistency; this result is extended to piecewise Hölder regression with non‐Gaussian errors. We combine our biased‐optimized autocovariance estimates with a projection‐based approach and derive covariance matrix estimates, a method that is of independent interest. An R package, several simulations and an application to biophysical measurements complement this paper.     

A nonparametric approach to detecting the difference of survival medians

Some nonparametric methods have been proposed to compare survival medians. Most of them are based on the asymptotic null distribution to estimate the p-value. However, for small to moderate sample sizes, those tests may have inflated Type I error rate, which makes their application limited. In this article, we proposed a new nonparametric test that uses bootstrap to estimate the sample mean and variance of the median. Through comprehensive simulation, we show that the proposed approach can control Type I error rates well. A real data application is used to illustrate the use of the new test.     

A Bayesian semiparametric accelerated failure time model for arbitrarily censored data with covariates subject to measurement error

A flexible Bayesian semiparametric accelerated failure time (AFT) model is proposed for analyzing arbitrarily censored survival data with covariates subject to measurement error. Specifically, the baseline error distribution in the AFT model is nonparametrically modeled as a Dirichlet process mixture of normals. Classical measurement error models are imposed for covariates subject to measurement error. An efficient and easy-to-implement Gibbs sampler, based on the stick-breaking formulation of the Dirichlet process combined with the techniques of retrospective and slice sampling, is developed for the posterior calculation. An extensive simulation study is conducted to illustrate the advantages of our approach.     

Restricted ridge estimator in the logistic regression model

It is known that when the multicollinearity exists in the logistic regression model, variance of maximum likelihood estimator is unstable. As a remedy, Schaefer et al. presented a ridge estimator in the logistic regression model. Making use of the ridge estimator, when some linear restrictions are also present, we introduce a restricted ridge estimator in the logistic regression model. Statistical properties of this newly defined estimator will be studied and comparisons are done in the simulation study in the sense of mean squared error criterion. A real-data example and a simulation study are introduced to discuss the performance of this estimator.     

Adaptive procedure for generalized familywise error rate control

This article considers multiple hypotheses testing with the generalized familywise error rate k-FWER control, which is the probability of at least k false rejections. We first assume the p-values corresponding to the true null hypotheses are independent, and propose adaptive generalized Bonferroni procedure with k-FWER control based on the estimation of the number of true null hypotheses. Then, we assume the p-values are dependent, satisfying block dependence, and propose adaptive procedure with k-FWER control. Extensive simulations compare the performance of the adaptive procedures with different estimators.     

A comparison of stepwise common singular spectrum analysis and horizontal multi-channel singular spectrum analysis

The problem of forecasting a time series by using information provided by a second time series is considered. Two multivariate extensions of Singular Spectrum Analysis (SSA) are compared in terms of forecast error: Horizontal Multi-channel SSA and Stepwise Common SSA. Different signal structures, defined in terms of trend, period, amplitude and phase, are investigated. In broad terms we find that neither Horizontal Multichannel SSA nor Stepwise Common SSA is best in all cases. Horizontal MSSA is outperformed particularly in cases where different trends are considered.     

Assessing Type I error and power of multistate Markov models for panel data—A simulation study

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the Type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the Type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.     

Jackknife empirical likelihood for the error variance in linear models

Variance estimation is a fundamental yet important problem in statistical modelling. In this paper, we propose jackknife empirical likelihood (JEL) methods for the error variance in a linear regression model. We prove that the JEL ratio converges to the standard chi-squared distribution. The asymptotic chi-squared properties for the adjusted JEL and extended JEL estimators are also established. Extensive simulation studies to compare the new JEL methods with the standard method in terms of coverage probability and interval length are conducted, and the simulation results show that our proposed JEL methods perform better than the standard method. We also illustrate the proposed methods using two real data sets.     

Estimation for varying coefficient partially nonlinear models with distorted measurement errors

In this paper, we propose a new varying coefficient partially nonlinear model where both the response and predictors are not directly observed, but are observed by unknown distorting functions of a commonly observable covariate. Because of the complexity of the model, existing estimation methods cannot be directly employed. For this, we propose using an efficient nonparametric regression to estimate the unknown distortion functions concerning the covariates and response on the distorting variable, and further, we obtain the profile nonlinear least squares estimators for the parameters and the coefficient functions using the calibrated variables. Furthermore, we establish the asymptotic properties of the resulting estimators. To illustrate our proposed methodology, we carry out some simulated and real examples.