Change-Point Estimation in Long Memory Nonparametric Models with Applications

We consider the estimation of a change point or discontinuity in a regression function for random design model with long memory errors. We provide several change-point estimators and investigate the consistency of the estimators. Using the fractional ARIMA process as an example of long memory process, we report a small Monte Carlo experiment to compare the performance of the estimators in finite samples. We finish by applying the method to a climatological data example.     

Identification of average marginal effects under misspecification when covariates are normal

A previously known result in the econometrics literature is that when covariates of an underlying data generating process are jointly normally distributed, estimates from a nonlinear model that is misspecified as linear can be interpreted as average marginal effects. This has been shown for models with exogenous covariates and separability between covariates and errors. In this paper, we extend this identification result to a variety of more general cases, in particular for combinations of separable and nonseparable models under both exogeneity and endogeneity. So long as the underlying model belongs to one of these large classes of data generating processes, our results show that nothing else must be known about the true DGP—beyond normality of observable data, a testable assumption—in order for linear estimators to be interpretable as average marginal effects. We use simulation to explore the performance of these estimators using a misspecified linear model and show they perform well when the data are normal but can perform poorly when this is not the case.     

SEMIPARAMETRIC ADDITIVE RISKS REGRESSION FOR TWO-STAGE DESIGN SURVIVAL STUDIES

In this article we study a semiparametric additive risks model (McKeague and Sasieni (1994)) for two-stage design survival data where accurate information is available only on second stage subjects, a subset of the first stage study. We derive two-stage estimators by combining data from both stages. Large sample inferences are developed. As a by-product, we also obtain asymptotic properties of the single stage estimators of McKeague and Sasieni (1994) when the semiparametric additive risks model is misspecified. The proposed two-stage estimators are shown to be asymptotically more efficient than the second stage estimators. They also demonstrate smaller bias and variance for finite samples. The developed methods are illustrated using small intestine cancer data from the SEER (Surveillance, Epidemiology, and End Results) Program.     

A robust pairwise likelihood method for incomplete longitudinal binary data arising in clusters

Clustered longitudinal data feature cross‐sectional associations within clusters, serial dependence within subjects, and associations between responses at different time points from different subjects within the same cluster. Generalized estimating equations are often used for inference with data of this sort since they do not require full specification of the response model. When data are incomplete, however, they require data to be missing completely at random unless inverse probability weights are introduced based on a model for the missing data process. The authors propose a robust approach for incomplete clustered longitudinal data using composite likelihood. Specifically, pairwise likelihood methods are described for conducting robust estimation with minimal model assumptions made. The authors also show that the resulting estimates remain valid for a wide variety of missing data problems including missing at random mechanisms and so in such cases there is no need to model the missing data process. In addition to describing the asymptotic properties of the resulting estimators, it is shown that the method performs well empirically through simulation studies for complete and incomplete data. Pairwise likelihood estimators are also compared with estimators obtained from inverse probability weighted alternating logistic regression. An application to data from the Waterloo Smoking Prevention Project is provided for illustration. The Canadian Journal of Statistics 39: 34–51; 2011 © 2010 Statistical Society of Canada     

Pseudomartingale estimating equations for modulated renewal process models

Summary.  We adapt martingale estimating equations based on gap time information to a general intensity model for a single realization of a modulated renewal process. The consistency and asymptotic normality of the estimators is proved under ergodicity conditions. Previous work has considered either parametric likelihood analysis or semiparametric multiplicative models using partial likelihood. The framework is generally applicable to semiparametric and parametric models, including additive and multiplicative specifications, and periodic models. It facilitates a semiparametric extension of a popular parametric earthquake model. Simulations and empirical analyses of Taiwanese earthquake sequences illustrate the methodology's practical utility.     

Estimating multivariate autoregressive moving average models by fitting long autoregressions

Some simple methods for the estimation of mixed multivariate autoregressive moving average time series models are introduced. The methods require the fitting of a long autoregression to the data and the computation of consistent initial estimates for the parameters of the model. After these preliminaries the estimators of the paper are obtained by applying weighted least squares to a multivariate auxiliary regression model. Two types of weight matrices are considered. Both of them yield estimators which are strongly consistent and asymptotically normally distributed. The first estimators are also asymptotically efficient while the second ones are not fully efficient but computationally simple. A simulation study is performed to illustrate the behaviour of the estimators in finite samples.     

Location and scale parameter estimation from randomly censored data

The problem of location and scale parameter estimation from randomly censored data is analyzed through use of a regression model for the Kaplan-Meier quantlle process. Continuous time regression techniques are employed to construct estimators that are both asymptotically normal and efficient. Estimators with a particularly simple form are obtained for the Koziol-Green model for random censorship. In the event of no censoring the regression model, and resulting estimators, reduce to those proposed by Parzen (1979 a, b).     

Estimation for Location-Scale Models with Censored Data

This article considers a class of estimators for the location and scale parameters in the location-scale model based on ‘synthetic data’ when the observations are randomly censored on the right. The asymptotic normality of the estimators is established using counting process and martingale techniques when the censoring distribution is known and unknown, respectively. In the case when the censoring distribution is known, we show that the asymptotic variances of this class of estimators depend on the data transformation and have a lower bound which is not achievable by this class of estimators. However, in the case that the censoring distribution is unknown and estimated by the Kaplan–Meier estimator, this class of estimators has the same asymptotic variance and attains the lower bound for variance for the case of known censoring distribution. This is different from censored regression analysis, where asymptotic variances depend on the data transformation. Our method has three valuable advantages over the method of maximum likelihood estimation. First, our estimators are available in a closed form and do not require an iterative algorithm. Second, simulation studies show that our estimators being moment-based are comparable to maximum likelihood estimators and outperform them when sample size is small and censoring rate is high. Third, our estimators are more robust to model misspecification than maximum likelihood estimators. Therefore, our method can serve as a competitive alternative to the method of maximum likelihood in estimation for location-scale models with censored data. A numerical example is presented to illustrate the proposed method.     

Semiparametric multiparameter regression survival modeling

We consider a log-linear model for survival data, where both the location and scale parameters depend on covariates, and the baseline hazard function is completely unspecified. This model provides the flexibility needed to capture many interesting features of survival data at a relatively low cost in model complexity. Estimation procedures are developed, and asymptotic properties of the resulting estimators are derived using empirical process theory. Finally, a resampling procedure is developed to estimate the limiting variances of the estimators. The finite sample properties of the estimators are investigated by way of a simulation study, and a practical application to lung cancer data is illustrated.     

基于ARFIMA(p, d, q)过程的半参数估计量分布特征及其有偏性研究7737976300

 本文运用蒙特卡罗模拟的方法对小样本下长记忆性的三种半参数估计量的分布特征尤其是有偏性问题进行了深入分析,结果发现,当长记忆和短记忆同时存在时,在大多数情况下,各参数估计量仍然服从正态分布,因此在小样本下仍可以构造t统计量判别参数的显著性,但由于受到短期参数的影响,估计量的分布是有偏的,因此导致参数的估计和检验出现偏差。而当真实数据过程接近非平稳或过度差分时,半参数估计量的分布也会发生改变。     

Semi parametric estimation of employment duration models

Semi parametric methods provide estimates of finite parameter vectors without requiring that the complete data generation process be assumed in a finite-dimensional family. By avoiding bias from incorrect specification, such estimators gain robustness, although usually at the cost of decreased precision. The most familiar semi parametric method in econometrics is ordi¬nary least squares, which estimates the parameters of a linear regression model without requiring that the distribution of the disturbances be in a finite-parameter family. The recent literature in econometric theory has extended semi parametric methods to a variety of non-linear models, including models appropriate for analysis of censored duration data. Horowitz and Newman make perhaps the first empirical application of these methods, to data on employment duration. Their analysis provides insights into the practical problems of implementing these methods, and limited information on performance. Their data set, containing 226 male controls from the Denver income maintenance experiment in 1971-74, does not show any significant covariates (except race), even when a fully parametric model is assumed. Consequently, the authors are unable to reject the fully parametric model in a test against the alternative semi parametric estimators. This provides some negative, but tenuous, evidence that in practical applications the reduction in bias using semi parametric estimators is insufficient to offset loss in precision. Larger samples, and data sets with strongly significant covariates, will need to be interval, and if the observation period is long enough will eventually be more loyal on average for those starting employment spells near the end of the observation period.     

Semiparametric regression for restricted mean residual life under right censoring

A mean residual life function (MRLF) is the remaining life expectancy of a subject who has survived to a certain time point. In the presence of covariates, regression models are needed to study the association between the MRLFs and covariates. If the survival time tends to be too long or the tail is not observed, the restricted mean residual life must be considered. In this paper, we propose the proportional restricted mean residual life model for fitting survival data under right censoring. For inference on the model parameters, martingale estimating equations are developed, and the asymptotic properties of the proposed estimators are established. In addition, a class of goodness-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and the approach is applied to a set of real life data collected from a randomized clinical trial.     

Parameter estimation for fractional Poisson processes

The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data with long memory is to make the standard Poisson model more flexible by permitting non-exponential, heavy-tailed distributions of interarrival times and different scaling properties. We establish the asymptotic normality of our estimators for the two parameters appearing in our fPp model. This fact permits construction of the corresponding confidence intervals. The properties of the estimators are then tested using simulated data.     

Penalized least squares for single index models

The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squares method to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously. When the dimension of parameters in the single index model is a fixed constant, under some regularity conditions, we demonstrate that the proposed estimators for parameters have the so-called oracle property, and furthermore we establish the asymptotic normality and develop a sandwich formula to estimate the standard deviations of the proposed estimators. Simulation studies and a real data analysis are presented to illustrate the proposed methods.     

Correlated and misclassified binary observations in complex surveys

Misclassifications in binary responses have long been a common problem in medical and health surveys. One way to handle misclassifications in clustered or longitudinal data is to incorporate the misclassification model through the generalized estimating equation (GEE) approach. However, existing methods are developed under a non-survey setting and cannot be used directly for complex survey data. We propose a pseudo-GEE method for the analysis of binary survey responses with misclassifications. We focus on cluster sampling and develop analysis strategies for analyzing binary survey responses with different forms of additional information for the misclassification process. The proposed methodology has several attractive features, including simultaneous inferences for both the response model and the association parameters. Finite sample performance of the proposed estimators is evaluated through simulation studies and an application using a real dataset from the Canadian Longitudinal Study on Aging.     

Estimating Long and Short Run Effects in Static Panel Models

Abstract

This paper assesses the biases of four different estimators with respect to the short run and the long run parameters if a static panel model is used, although the data generating process is a dynamic error components model. We analytically derive the associated biases and provide a discussion of the determinants thereof. Our analytical and numerical results as well as Monte Carlo simulations illustrate that the asymptotic bias of both the within and the between parameter with respect to the short run and long run impact can be substantial, depending on the memory of the data generating process, the length of the time series and the importance of the cross-sectional variation in the explanatory variables.     

Inverse probability weighted estimators for single-index models with missing covariates

Abstract

In this article, we consider the inverse probability weighted estimators for a single-index model with missing covariates when the selection probabilities are known or unknown. It is shown that the estimator for the index parameter by using estimated selection probabilities has a smaller asymptotic variance than that with true selection probabilities, thus is more efficient. Therefore, the important Horvitz-Thompson property is verified for the index parameter in single index model. However, this difference disappears for the estimators of the link function. Some numerical examples and a real data application are also conducted to illustrate the performances of the estimators.     

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates,with application to analysis of biomarker correlates in vaccine trials

This article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.     

Estimation in multitype epidemics

A multitype epidemic model is analysed assuming proportionate mixing between types. Estimation procedures for the susceptibilities and infectivities are derived for three sets of data: complete data, meaning that the whole epidemic process is observed continuously; the removal processes are observed continuously; only the final state is observed. Under the assumption of a major outbreak in a population of size n it is shown that, for all three data sets, the susceptibility estimators are always efficient, i.e. consistent with a √ n rate of convergence. The infectivity estimators are 'in most cases' respectively efficient, efficient and unidentifiable. However, if some susceptibilities are equal then the corresponding infectivity estimators are respectively barely consistent (√log( n ) rate of convergence), not consistent and unidentifiable. The estimators are applied to simulated data.     

Model averaging for multivariate multiple regression models

The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.