On generalized maximum likelihood estimation in the proportional hazards model with partially informative censoring

The generalized maximum likelihood estimator (GMLE) is derived and some of its variants are compared with the partial Abdushukurov-Cheng-Lin (PACL) and Kaplan-Meier (KM) estimators under the proportional hazards model with partially informative censoring. A comparison of small sample properties is conducted based on a simulation study. The results show that the GMLEs perform competitively with the PACL estimator.Acknowledgements.The authors are very much thankful to the referee for perceptive and illuminating comments. A substantial credit goes to the referee for an overall improvement of the paper.     

Nonparametric estimators of the bivariate survival function under random censoring

A large number of proposals for estimating the bivariate survival function under random censoring have been made. In this paper we discuss the most prominent estimators, where prominent is meant in the sense that they are best for practical use; Dabrowska's estimator, the Prentice–Cai estimator, Pruitt's modified EM-estimator, and the reduced data NPMLE of van der Laan. We show how these estimators are computed and present their intuitive background. The asymptotic results are summarized. Furthermore, we give a summary of the practical performance of the estimators under different levels of dependence and censoring based on extensive simulation results. This leads also to a practical advise.     

Estimating a generalized correlation coefficient for a generalized bivariate probit model

In this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. The estimator performs well in our simulation study.     

Right censoring in a discrete life model

Although there are many sophisticated models for estimation of failure rate based on censored data in continuous distributions, not much work has been done in the discrete case. We introduce a discrete model for life lengths and consider its properties. For this model, we derive the corresponding maximum likelihood estimators of the parameters under Type I and Type II right-censoring. Received May 2000     

Estimating overnight volatility of asset returns by using the generalized dynamic factor model approach

This paper proposes a new approach to estimate the overnight volatility of an individual stock return. Since markets generally do not trade during the overnight period, measures of realized volatility cannot be computed on a “high-frequency” basis. Some studies have resorted to using the square overnight return as a proxy for the overnight realized volatility, but this measure is typically very noisy. The new estimator of the overnight volatility proposed is obtained using the generalized dynamic factor model. The performance of the new proxy is examined using simulated data. This is found to perform better than the squared overnight return. Empirical analysis of the S&P100 constituents confirms the potential of this proxy.     

Strong consistency of the MLE under random censoring

LetX ₁, ...,X _n be an i.i.d. sample from some parametric family {_θ :θ (Θ} of densities. In the random censorship model one observesZ _i =min (X _i ,Y _i ) andδ _i =1_{ x _i ≤Y _i}, whereY _i is a censoring variable being independent ofX _i . In this paper we investigate the strong consistency ofθ _n maximizing the modified likelihood function based on (Z _i ,δ _i , 1≤i≤n. The main result constitutes an extension of Wald’s theorem for complete data to censored data. Work partially supported by the “Deutsche Forschungsgemeinschaft”.     

Estimating the shirking model with variable effort

We show in a theoretical efficiency wage model where firms differ in monitoring intensity that the impact of monitoring intensity on wages is ambiguous, a result that mirrors evidence from the empirical literature. We argue that to correctly specify the impact of monitoring on wages, the interaction between monitoring and effort needs to be modelled. Results using a worker, firm panel from Ghana which contains reasonable effort and monitoring proxies show that the return to effort is higher in poorly monitored sectors as the theory suggests.     

Asymptotically optimal nonparametric one- and two-way analysis of variance tests for the log linear model under censoring

We considerr ×c populations with failure ratesλ _ij(t) satisfying the condition

Estimating the autocorrelated error model with trended data

A Monte Carlo study of the small sample properties of various estimators of the linear regression model with first-order autocorrelated errors. When independent variables are trended, estimators using Ttransformed observations (Prais-Winsten) are much more efficient than those using T–1 (Cochrane–Orcutt). The best of the feasible estimators isiterated Prais-Winsten using a sum-of-squared-error minimizing estimate of the autocorrelation coefficient ?. None of the feasible estimators performs well in hypothesis testing; all seriously underestimate standard errors, making estimated coefficients appear to be much more significant than they actually are.     

Interval estimation for the two-parameter exponential distribution under progressive censoring

The interval estimation of the scale parameter and the joint confidence region of the parameters of two-parameter exponential distribution under Type II progressive censoring is proposed. In addition, the simulation study for the performance of all proposed pivotal quantities is done in this paper. The criteria of minimum confidence length and minimum confidence area are used to obtain the optimal estimation. The predictive intervals of the future observation and the future interarrival times based on the Type II progressive censored sample are also provided. One biometrical example is also given to illustrate the proposed methods.     

Polynomial spline estimation for generalized varying coefficient partially linear models with a diverging number of components

Generalized varying coefficient partially linear models are a flexible class of semiparametric models that deal with data with different types of responses. In this paper, we focus on polynomial spline estimator as a computationally easier alternative to the more commonly used local polynomial regression approach, since one can directly take advantage of many existing implementations for generalized linear models. Furthermore, motivated by the high dimensionality characteristics that accompany many modern data sets nowadays, we investigate its asymptotic properties when both the number of nonparametric and the number of parametric components grows with, but is still smaller than, the sample size. Simulations and a real data example are used to illustrate our proposal.     

Estimating a distribution function in the presence of auxiliary information

For estimating the distribution functionF of a population, the empirical or sample distribution functionF _n has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator for estimatingF in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality of . In this paper, we establish the weak convergence of to a Gaussian process and show that the asymptotic variance function of is uniformly smaller than that ofF _n . As an application of , we propose to employ the mean and varianceŜ _n ² of to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to assess the finite sample performance of the proposed estimators , andŜ _n ² .     

Asymptotic confidence intervals for the length of the shortt under random censoring

A short t of a one dimensional probability distribution is defined to be an interval which has at least probability t and minimal length. The length of a show and its obvious estimator are significant measures of scale of a distribution and the corresponding random sample, respectively. In this note a non-parametric asymptotic confidence interval for the length of the (uniqueness is assumed) short t is established in the random censorship from the right model. The estimator of the length of the short t is based on the product-limit (PL) estimator of the unknown distribution function. The proof of the result mainly follows from an appropriate combination of the Glivenko-Cantelli theorem and the functional central limit theorem for the PL estimator.     

Externalities in a life cycle model with endogenous survival

We study socially vs individually optimal life cycle allocations of consumption and health, when individual health care curbs own mortality but also has a spillover effect on other persons’ survival. Such spillovers arise, for instance, when health care activity at aggregate level triggers improvements in treatment through learning-by-doing (positive externality) or a deterioration in the quality of care through congestion (negative externality). We combine an age-structured optimal control model at population level with a conventional life cycle model to derive the social and private value of life. We then examine how individual incentives deviate from social incentives and how they can be aligned by way of a transfer scheme. The age-patterns of socially and individually optimal health expenditures and the transfer rate are derived. Numerical analysis illustrates the working of our model.     

Choice of a survival model for patients with a brain tumour

Tests of separate families of hypotheses are briefly described and applied to log-linear regression models. The procedure is used for the choice of a survival model for patients with a brain tumour.     

Estimating a semi-parametric duration model without specifying heterogeneity

This paper presents a new estimator for the mixed proportional hazard model that allows for a nonparametric baseline hazard and time-varying regressors. In particular, this paper allows for discrete measurement of the durations as happens often in practice. The integrated baseline hazard and all parameters are estimated at the regular rate, $\sqrt{N}$, where $N$ is the number of individuals. A hazard model is a natural framework for time-varying regressors. In particular, if a flow or a transition probability depends on a regressor that changes with time, a hazard model avoids the curse of dimensionality that would arise from interacting the regressors at each point in time with one another. This paper also presents a new test to detect unobserved heterogeneity.     

Estimating a tournament model of intra-firm wage differentials

We consider the estimation of a tournament model with moral hazard (based on Rosen (1986), AER)) when only aggregate data on intra-firm employment levels and salaries are available. Equilibrium restrictions of the model allow us to recover parameters of interest, including equilibrium effort levels in each hierarchical stage of the firm. We illustrate our estimation procedures using data from major retail chains in the US. We find that only a fraction of the wage differential directly compensates workers for higher effort levels, implying that a large portion of the differentials arises to maintain incentives at lower rungs of the retailers.     

Estimating the J function without edge correction

The interaction between points in a spatial point process can be measured by its empty space function F , its nearest-neighbour distance distribution function G , and by combinations such as the J function J = (1 G )/(1 F ). The estimation of these functions is hampered by edge effects: the uncorrected, empirical distributions of distances observed in a bounded sampling window W give severely biased estimates of F and G . However, in this paper we show that the corresponding uncorrected estimator of the function J = (1 G )/(1 F ) is approximately unbiased for the Poisson case, and is useful as a summary statistic. Specifically, consider the estimate _W of J computed from uncorrected estimates of F and G . The function J _W ( r ), estimated by _W , possesses similar properties to the J function, for example J _W ( r ) is identically 1 for Poisson processes. This enables direct interpretation of uncorrected estimates of J , something not possible with uncorrected estimates of either F , G or K . We propose a Monte Carlo test for complete spatial randomness based on testing whether J _W ( r ) 1. Computer simulations suggest this test is at least as powerful as tests based on edge corrected estimators of J .     

Asymptotics of likelihood ratio statistic for non-inferiority testing under exponential distribution with fixed censoring times

We discuss the problem of testing the non-inferiority of a new treatment compared with several standard ones in a survival model where the underlying distribution is exponential and censoring times are fixed. We derive the asymptotic distribution of the likelihood ratio statistic for k-samples. We construct a testing procedure with asymptotic size α based on the likelihood ratio statistic.