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.     

Estimating the variance of a finite population under a superpopulation model

The problem of deriving optimum sampling strategies for estimating the variance of finite population has been considered under some super-population set up.     

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 a public school expenditure model under binding spending limitations

A model explaining desired expenditure on education is estimated for a sample of New Jersey school districts. Because the limit on annual increases in school spending is binding for a subsample of jurisdictions, the Tobit estimation procedure is used. We test for equality of the pre- and postlimitation structures and find substantial similarity. The cap on expenditure increases was part of a court-ordered reform of New Jersey school finance law. The results can be used to explain the failure of the existing school finance laws in lessening expenditure disparities at the lower end of the distribution.     

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

Smooth estimation of a monotone hazard and a monotone density under random censoring

We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n^2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).     

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.     

Estimating and testing a quantile regression model with interactive effects

This paper proposes a quantile regression estimator for a model with interactive effects potentially correlated with covariates. We provide conditions under which the estimator is asymptotically Gaussian and we investigate the finite sample performance of the method. An approach to testing the specification against a competing fixed effects specification is introduced. The paper presents an application to study the effect of class size and composition on educational attainment. The evidence suggests that while smaller classes are beneficial for low performers, larger classes are beneficial for high performers. The fixed effects specification is rejected in favor of the interactive effects specification.     

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 .     

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.     

An econometric procedure for estimation of a generalized systemic gravity model under incomplete information about the system

Gravity spatial interaction models have a long history and a wide scope of empirical applications, Alonso (1973) proposed a generalized model whose structure subsumes major versions of the gravity model in the literature as special cases. Little attention has been given to how the general model might be estimated, or if it is estimable at all. This paper develops an econometric procedure for situations where all places in a geographic system are not included in the observations. The general model and various constrained versions are empirically estimated on a sample of intermetropolitan migration data and compared.     

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.