A new First-Order mixture integer-valued threshold autoregressive process based on binomial thinning and negative binomial thinning

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset.Comment: 34 pages;5 figure

Approximating Partial Likelihood Estimators via Optimal Subsampling

With the growing availability of large-scale biomedical data, it is often time-consuming or infeasible to directly perform traditional statistical analysis with relatively limited computing resources at hand. We propose a fast and stable subsampling method to effectively approximate the full data maximum partial likelihood estimator in Cox's model, which reduces the computational burden when analyzing massive survival data. We establish consistency and asymptotic normality of a general subsample-based estimator. The optimal subsampling probabilities with explicit expressions are determined via minimizing the trace of the asymptotic variance-covariance matrix for a linearly transformed parameter estimator. We propose a two-step subsampling algorithm for practical implementation, which has a significant reduction in computing time compared to the full data method. The asymptotic properties of the resulting two-step subsample-based estimator is established. In addition, a subsampling-based Breslow-type estimator for the cumulative baseline hazard function and a subsample estimated survival function are presented. Extensive experiments are conducted to assess the proposed subsampling strategy. Finally, we provide an illustrative example about large-scale lymphoma cancer dataset from the Surveillance, Epidemiology,and End Results Program

The strong law under a semiparametric model for truncated and censored data

In this paper we study integrals for any nonnegative measurable functions with respect to semiparametric estimators of the survival function and the cumulative hazard function based on left truncated and right censored data. The strong law of large numbers for these integrals is given. The results are useful in establishing strong consistency of many estimators under the semiparametric model for truncated and censored data.Truncated and censored data Product-limit estimator Semiparametric estimation Strong law of large numbers Reverse supermartingale

Bandwidth choice for hazard rate estimators from left truncated and right censored data

In this paper, two types of kernel based estimators of hazard rate under left truncation and right censorship are considered. An asymptotic representation of the integrated squared error for both estimators is obtained. Also it is shown that the bandwidth selected by the data-based method of least squares cross-validation is asymptotically optimal in a compelling sense.Left truncation right censorship Hazard rate estimation Asymptotic representation Cross-validation Optimal bandwidth

Sequential confidence bands for densities under truncated and censored data

In this paper an asymptotic distribution is obtained for the maximal deviation between the kernel density estimator and the density when the data are subject to random left truncation and right censorship. Based on this result we propose a fully sequential procedure for constructing a fixed-width confidence band for the density on a finite interval and show that the procedure has the desired coverage probability asymptotically as the width of the band approaches zero.Truncated censored data Density estimation Maximal deviation Asymptotic distribution Confidence band Sequential estimation

Inference in the additive risk model with time-varying covariates subject to measurement errors

For the additive risk model with time-varying covariates which are subject to measurement errors, we study the estimation of both regression parameters and cumulative baseline hazard function. We first develop a procedure to estimate the regression parameters by correcting the bias of the naive estimator, and provide the large-sample properties of the bias-adjusted estimators. The procedure can be repeated to further improve the accuracy of the estimator. We then construct a corresponding estimator for the cumulative baseline hazard function and derive its asymptotic properties. Based on these results, confidence bands are constructed for the cumulative hazard function as well as the survival function. Monte Carlo studies are conducted to evaluate the performance of these estimators.8 page(s

Regression analysis of multivariate recurrent event data with time-varying covariate effects

Recurrent event data occur in many fields and many approaches have been proposed for their analyses (Andersen et al. (1993) [1]; Cook and Lawless (2007) [3]). However, most of the available methods allow only time-independent covariate effects, and sometimes this may not be true. In this paper, we consider regression analysis of multivariate recurrent event data in which some covariate effects may be time-dependent. For the problem, we employ the marginal modeling approach and, especially, estimating equation-based inference procedures are developed. Both asymptotic and finite-sample properties of the proposed estimates are established and an illustrative example is provided.Event history study Marginal models Recurrent event data Time-varying coefficients

A Class of Box-Cox transformation models for recurrent event data

In this article, we propose a class of Box-Cox transformation models for recurrent event data, which includes the proportional means models as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the proposed models, we apply a profile pseudo-partial likelihood method to estimate the model parameters via estimating equation approaches and establish large sample properties of the estimators and examine its performance in moderate-sized samples through simulation studies. In addition, some graphical and numerical procedures are presented for model checking. An example of application on a set of multiple-infection data taken from a clinic study on chronic granulomatous disease (CGD) is also illustrated.22 page(s