Covariate-Adjusted Regression for Time Series

The main purpose of this article is to consider the covariate-adjusted regression (CAR) model for time series. The CAR model was initially proposed by Sentürk and Müller (2005 Sentürk , D. , Müller , H. G. ( 2005 ). Covariate-adjusted regression . Biometrika 92 : 75 – 89 .[Crossref], [Web of Science ®] , [Google Scholar]) for such situations where predictor and response variables are not directly observed, but are distorted by some common observable covariate. Despite CAR being originally designed for independent cross-sectional data, multiple works have extended this method to dependent data setting. In this article, the authors extend CAR to the distorted time series setting. This extension is meaningful in many fields such as econometrics, mathematical finance, and signal processing. The estimates of regression parameters are proposed by establishing connection with functional-coefficient time series model. The consistency and asymptotic normality of the proposed estimates are investigated under the α-mixing conditions. Real data and simulated examples are provided for illustration.     

Linear least squares estimates and nonlinear means

The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)^-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.     

A family of tests for exponentiality against IFR alternatives

In this paper we consider the problem of testing exponentiality against IFR alternatives. A measure of deviation from exponentiality is developed and a class of test statistics are constructed on the basis of this measure. It is shown that the test statistic is an L-statistic. The asymptotic as well as the exact distributions of the test statistics are obtained and the test statistics are proved to be consistent. The Pitman efficiency has also been studied.     

Adaptive penalized quantile regression for high dimensional data

We propose a new adaptive L₁ penalized quantile regression estimator for high-dimensional sparse regression models with heterogeneous error sequences. We show that under weaker conditions compared with alternative procedures, the adaptive L₁ quantile regression selects the true underlying model with probability converging to one, and the unique estimates of nonzero coefficients it provides have the same asymptotic normal distribution as the quantile estimator which uses only the covariates with non-zero impact on the response. Thus, the adaptive L₁ quantile regression enjoys oracle properties. We propose a completely data driven choice of the penalty level _λn${\lambda }_n$, which ensures good performance of the adaptive L₁ quantile regression. Extensive Monte Carlo simulation studies have been conducted to demonstrate the finite sample performance of the proposed method.     

Estimation in autoregressive models with surrogate data and validation data

Time-series data are often subject to measurement error, usually the result of needing to estimate the variable of interest. Generally, however, the relationship between the surrogate variables and the true variables can be rather complicated compared to the classical additive error structure usually assumed. In this article, we address the estimation of the parameters in autoregressive models in the presence of function measurement errors. We first develop a parameter estimation method with the help of validation data; this estimation method does not depend on functional form and the distribution of the measurement error. The proposed estimator is proved to be consistent. Moreover, the asymptotic representation and the asymptotic normality of the estimator are also derived, respectively. Simulation results indicate that the proposed method works well for practical situation.     

Some asymptotic distribution results in time-sequential estimation of the mean exponential survival time

The asymptotic distribution of the stopping time N in a time-sequential procedure for the estimation of the mean exponential survival time given by Gardiner, Susarla, and van Ryzin (1986) is obtained. The same techniques used to obtain this asymptotic distribution of N are used to obtain the asymptotic distribution of the statistic representing the time-on-test expended per unit item in the study.     

Self-consistent estimators of survival functions with doubly-censored data

The consistency and asymptotic normality of self-consistent estimators (SCE) of survival functions with doubly-censored data have been studied by many authors. However, to the best of our knowledge, expressions of the asymptotic variance of the SCE have not been derived in the literature. In this paper, under the assumption that the survival time and censoring time distributions are discrete with finitely many jump points, an expression and a consistent estimator of the asymptotic variance of the SCE are presented. A proof of the strong consistency of the SCE is also presented. Our simu¬lation studies indicate that the estimate of the asymptotic variance is very close to the true value even with moderate sample sizes and high censoring rates     

Asymptotic properties of the maximum-likelihood estimator in zero-inflated binomial regression

The zero-inflated binomial (ZIB) regression model was proposed to account for excess zeros in binomial regression. Since then, the model has been applied in various fields, such as ecology and epidemiology. In these applications, maximum-likelihood estimation (MLE) is used to derive parameter estimates. However, theoretical properties of the MLE in ZIB regression have not yet been rigorously established. The current paper fills this gap and thus provides a rigorous basis for applying the model. Consistency and asymptotic normality of the MLE in ZIB regression are proved. A consistent estimator of the asymptotic variance–covariance matrix of the MLE is also provided. Finite-sample behavior of the estimator is assessed via simulations. Finally, an analysis of a data set in the field of health economics illustrates the paper.     

Asymptotic Theory of Taguchi’s Natural Estimators of the Signal to Noise Ratio for Dynamic Robust Parameter Design

This article discusses the asymptotic theory of Taguchi’s natural estimators of the signal to noise ratio (SNR) for dynamic robust parameter design. Three asymptotic properties are shown. First, two natural estimators of the population SNR are asymptotically equivalent. Second, both of these estimators are consistent. Finally, both of these estimators are asymptotically normally distributed.     

Multivariate autoregressive extreme value process and its application for modeling the time series properties of the extreme daily asset prices

Abstract

In this article we suggest a new multivariate autoregressive process for modeling time-dependent extreme value distributed observations. The idea behind the approach is to transform the original observations to latent variables that are univariate normally distributed. Then the vector autoregressive DCC model is fitted to the multivariate latent process. The distributional properties of the suggested model are extensively studied. The process parameters are estimated by applying a two-stage estimation procedure. We derive a prediction interval for future values of the suggested process. The results are applied in an empirically study by modeling the behavior of extreme daily stock prices.     

Testing the proportional odds model for interval-censored data

This paper discusses the goodness-of-fit test for the proportional odds model for K-sample interval-censored failure time data, which frequently occur in, for example, periodic follow-up survival studies. The proportional odds model has a feature that allows the ratio of two hazard functions to be monotonic and converge to one and provides an important tool for the modeling of survival data. To test the model, a procedure is proposed, which is a generalization of the method given in Dauxois and Kirmani [Dauxois JY, Kirmani SNUA (2003) Biometrika 90:913–922]. The asymptotic distribution of the procedure is established and its properties are evaluated by simulation studies     

Asymptotics in the β-model for networks with a differentially private degree sequence

Abstract

The β-model is a natural model for characterizing the degree heterogeneity that widely exists in the network data. The estimators of the model parameters in the differentially private β-model with the denoised process have been shown to be consistent and asymptotically normal. In this paper, we show that the moment estimators of the parameters based on the differentially private degree sequence without the denoised process is consistent and asymptotically normal.