Inference for the Extended Bifurcating Autoregressive Model for Cell Lineage Studies

Huggins & Basawa (1999) proposed several extensions of the bifurcating autoregressive model used to model cell lineage trees. These models overcame limitations in the original bifurcating autoregressive mode by allowing larger correlations between cousin cells and other cells in the same generation. Huggins & Basawa only considered maximum likelihood inference based on independent trees. This paper examines the asymptotic properties of maximum likelihood estimators based on a single large tree.     

Inference with Bivariate Truncated Data

Inthis paper we build on previous work for estimation of the bivariatedistribution of the time variables T ₁ and T ₂when they are observable only on the condition that one of thetime variables, say T ₁, is greater than (left-truncation)or less than (right truncation) some observed time variable C ₁.In this paper, we introduce several results based on the InfluenceCurve (which we derive in this paper) of the NPMLE of the distributionF of (T ₁,T ₂) developed by van derLaan (van der Laan, 1996). Specifically we will: prove that theNPMLE is asymptotically equivalent to an estimator developedby Gürler (Gürler, 1997), derive the asymptotic distributionof the NPMLE based on its Influence Curve, present tests to determinethe amount of dependence between T ₁ and T ₂,present the results of simulation studies that compare the NPMLEand Gürler's estimator and evaluate the performance of boththe above mentioned tests and confidence intervals of Fbased on the asymptotic distribution of the NPMLE, and finallywe will apply the methods in a data analysis in which we alsopoint out practical issues that arise in the implementation ofthe estimator.     

Estimation of the Association for Bivariate Interval-censored Failure Time Data

Abstract.  Multivariate failure time data frequently occur in medical studies and the dependence or association among survival variables is often of interest ( Biometrics , 51 , 1995, 1384; Stat. Med. , 18 , 1999, 3101; Biometrika , 87 , 2000, 879; J. Roy. Statist. Soc. Ser. B , 65 , 2003, 257). We study the problem of estimating the association between two related survival variables when they follow a copula model and only bivariate interval-censored failure time data are available. For the problem, a two-stage estimation procedure is proposed and the asymptotic properties of the proposed estimator are established. Simulation studies are conducted to assess the finite sample properties of the presented estimate and the results suggest that the method works well for practical situations. An example from an acquired immunodeficiency syndrome clinical trial is discussed.     

Empirical Likelihood-based Inference for Stationary-ergodicity of the Generalized Random Coefficient Autoregressive Model

In this article, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. When the order of the model is 1, we derive an empirical likelihood ratio test statistic to test the stationary-ergodicity. Some simulation studies are also conducted to investigate the finite sample performances of the proposed test.     

Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing

We consider an extension of the recursive bivariate probit model for estimating the effect of a binary variable on a binary outcome in the presence of unobserved confounders, nonlinear covariate effects and overdispersion. Specifically, the model consists of a system of two binary outcomes with a binary endogenous regressor which includes smooth functions of covariates, hence allowing for flexible functional dependence of the responses on the continuous regressors, and arbitrary random intercepts to deal with overdispersion arising from correlated observations on clusters or from the omission of non‐confounding covariates. We fit the model by maximizing a penalized likelihood using an Expectation‐Maximisation algorithm. The issues of automatic multiple smoothing parameter selection and inference are also addressed. The empirical properties of the proposed algorithm are examined in a simulation study. The method is then illustrated using data from a survey on health, aging and wealth.     

存在自相关时检验和估计方法的改进——基于自回归分布滞后模型的自相关检验和参数估计

存在自相关时的自相关检验和参数估计是基础计量经济学的一个重要内容,并且存在自相关时的原模型已转化为自回归分布滞后模型。讨论存在自相关时的自相关检验和参数估计问题,提出了一种基于自回归分布滞后模型的自相关检验法,并同时给出了相应的参数估计。     

An Adjustment to Improve the Bivariate Survivor Function Repaired NPMLE

We recently proposed a representation of the bivariate survivor function as a mapping of the hazard function for truncated failure time variates. The representation led to a class of estimators that includes van der Laan’s repaired nonparametric maximum likelihood estimator (NPMLE) as an important special case. We proposed a Greenwood-like variance estimator for the repaired NPMLE but found somewhat poor agreement between the empirical variance estimates and these analytic estimates for the sample sizes and bandwidths considered in our simulation study. The simulation results also confirmed those of others in showing slightly inferior performance for the repaired NPMLE compared to other competing estimators as well as a sensitivity to bandwidth choice in moderate sized samples. Despite its attractive asymptotic properties, the repaired NPMLE has drawbacks that hinder its practical application. This paper presents a modification of the repaired NPMLE that improves its performance in moderate sized samples and renders it less sensitive to the choice of bandwidth. Along with this modified estimator, more extensive simulation studies of the repaired NPMLE and Greenwood-like variance estimates are presented. The methods are then applied to a real data example. This revised version was published online in September 2005 with a correction to the second author's name.     

Bivariate generalized gamma distributions of Kibble's type

In this paper, a new type of bivariate generalized gamma (BGG) distribution derived from the bivariate gamma distribution of Kibble [Two-variate gamma-type distribution. Sankh?a 1941;5:137–150] by means of a power transformation is presented. The explicit expressions of statistical properties of the BGG distribution are presented. The estimation of marginal and dependence parameters using the method of moments and the method of inference functions for margins are discussed, and their performance through a Monte Carlo simulation study is assessed. Finally, an example is given to illustrate the applicability of the distributions introduced here.     

Inference for proportional hazard model with propensity score

Since the publication of the seminal paper by Cox (1972), proportional hazard model has become very popular in regression analysis for right censored data. In observational studies, treatment assignment may depend on observed covariates. If these confounding variables are not accounted for properly, the inference based on the Cox proportional hazard model may perform poorly. As shown in Rosenbaum and Rubin (1983), under the strongly ignorable treatment assignment assumption, conditioning on the propensity score yields valid causal effect estimates. Therefore we incorporate the propensity score into the Cox model for causal inference with survival data. We derive the asymptotic property of the maximum partial likelihood estimator when the model is correctly specified. Simulation results show that our method performs quite well for observational data. The approach is applied to a real dataset on the time of readmission of trauma patients. We also derive the asymptotic property of the maximum partial likelihood estimator with a robust variance estimator, when the model is incorrectly specified.     

Bivariate Constant-Stress Accelerated Degradation Model and Inference

To assess the reliability of highly reliable products that have two or more performance characteristics (PCs) in an accurate manner, relations between the PCs should be taken duly into account. If they are not independent, it would then become important to describe the dependence of the PCs. For many products, the constant-stress degradation test cannot provide sufficient data for reliability evaluation and for this reason, accelerated degradation test is usually performed. In this article, we assume that a product has two PCs and that the PCs are governed by a Wiener process with a time scale transformation, and the relationship between the PCs is described by the Frank copula function. The copula parameter is dependent on stress and assumed to be a function of stress level that can be described by a logistic function. Based on these assumptions, a bivariate constant-stress accelerated degradation model is proposed here. The direct likelihood estimation of parameters of such a model becomes analytically intractable, and so the Bayesian Markov chain Monte Carlo (MCMC) method is developed here for this model for obtaining the maximum likelihood estimates (MLEs) efficiently. For an illustration of the proposed model and the method of inference, a simulated example is presented along with the associated computational results.     

Weighted L1-estimates for the First-order Bifurcating Autoregressive Model

We developed robust estimators that minimize a weighted L₁ norm for the first-order bifurcating autoregressive model. When all of the weights are fixed, our estimate is an L₁ estimate that is robust against outlying points in the response space and more efficient than the least squares estimate for heavy-tailed error distributions. When the weights are random and depend on the points in the factor space, the weighted L₁ estimate is robust against outlying points in the factor space. Simulated and artificial examples are presented. The behavior of the proposed estimate is modeled through a Monte Carlo study.     

Statistical Inference on the Parametric Component in Partially Linear Spatial Autoregressive Models

A statistical test procedure is proposed to check whether the parameters in the parametric component of the partially linear spatial autoregressive models satisfy certain linear constraint conditions, in which a residual-based bootstrap procedure is suggested to derive the p-value of the test. Some simulations are conducted to assess the performance of the test and the results show that the bootstrap approximation to the null distribution of the test statistic is valid and the test is of satisfactory power. Furthermore, a real-world example is given to demonstrate the application of the proposed test.     

A comparison of estimation procedures for the parameters of the star model

A simulation experiment compares the accuracy and precision of three alternate estimation techniques for the parameters of the STARMA model. Maximum likelihood estimation, in most ways the "best" estimation procedure, involves a large amount of computational effort so that two approximate techniques, exact least squares and conditional maximum likelihood, are often proposed for series of moderate lengths. This simulation experiment compares the accuracy of these three estimation procedures for simulated series of various lengths, and discusses the appropriateness of the three procedures as a function of the length of the observed series.     

Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions

In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non‐parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper.     

Empirical Likelihood for Threshold Autoregressive Models

This article develops empirical likelihood for threshold autoregressive models. We propose general estimating equations based on moment constraint. Under some suitable conditions, we show the empirical likelihood estimators for parameter are asymptotically normally distributed, and the proposed log empirical likelihood ratio statistic asymptotically follows a standard chi-squared distribution.     

Doubly Robust Inference for the Distribution Function in the Presence of Missing Survey Data

Item non‐response in surveys occurs when some, but not all, variables are missing. Unadjusted estimators tend to exhibit some bias, called the non‐response bias, if the respondents differ from the non‐respondents with respect to the study variables. In this paper, we focus on item non‐response, which is usually treated by some form of single imputation. We examine the properties of doubly robust imputation procedures, which are those that lead to an estimator that remains consistent if either the outcome variable or the non‐response mechanism is adequately modelled. We establish the double robustness property of the imputed estimator of the finite population distribution function under random hot‐deck imputation within classes. We also discuss the links between our approach and that of Chambers and Dunstan. The results of a simulation study support our findings.     

Statistical Inference for Curved Fibrous Objects in 3D – Based on Multiple Short Observations of Multivariate Autoregressive Processes

This paper deals with statistical inference on the parameters of a stochastic model, describing curved fibrous objects in three dimensions, that is based on multivariate autoregressive processes. The model is fitted to experimental data consisting of a large number of short independently sampled trajectories of multivariate autoregressive processes. We discuss relevant statistical properties (e.g. asymptotic behaviour as the number of trajectories tends to infinity) of the maximum likelihood (ML) estimators for such processes. Numerical studies are also performed to analyse some of the more intractable properties of the ML estimators. Finally the whole methodology, i.e., the fibre model and its statistical inference, is applied to appropriately describe the tracking of fibres in real materials.     

Robust regression for estimating the Burr XII parameters with outliers

The Burr XII distribution offers a more flexible alternative to the lognormal, log-logistic and Weibull distributions. Outliers can occur during reliability life testing. Thus, we need an efficient method to estimate the parameters of the Burr XII distribution for censored data with outliers. The objective of this paper is to present a robust regression (RR) method called M-estimator to estimate the parameters of a two-parameter Burr XII distribution based on the probability plotting procedure for both the complete and multiply-censored data with outliers. The simulation results show that the RR method outperforms the unweighted least squares and maximum likelihood methods in most cases in terms of bias and errors in the root mean square.