Modified probability proportional to size sampling

Probability proportional to size (PPS) sampling is one of the most widely used designs for finite populations. We propose modifications to PPS designs with replacement and Rao–Hartley–Cochran design without replacement. These modifications consist of division of the population into two groups. Units in the first group are included in the sample with probability one. Under certain conditions, in both with and without replacement designs, the estimator of the population total based on the modified PPS sampling design is shown to be better than the corresponding estimator based on a PPS design. We illustrate our modification by an example and an application.     

A copula-based approach for estimating the survival functions of two alternating recurrent events

In this paper, we study the survival times of alternately occurring events. The dependence between the times to the two events is modelled through the Archimedean copula, while the dependence over the recurring cycles is modelled through a functional relationship of the distribution parameters. Taking account of appropriate censoring that may be present in the data, the model parameters are estimated using the maximum likelihood method. The standard errors of the estimators are then derived and confidence belts for the survival functions constructed. Methods for choosing the appropriate copula are also discussed. The results are illustrated through a clinical trial data on patients suffering from cystic fibrosis. A simulation study is also done to corroborate the results.     

USING L2 ESTIMATION FOR L1 ESTIMATORS: AN APPLICATION TO THE SINGLE-INDEX MODEL

The bootstrap method is used to compute the standard error of regression parameters when the data are non-Gaussian distributed. Simulation results with L₁ and L₂ norms for various degrees of “non-Gaussianess” are provided. The computationally efficient L₂ norm, based on the bootstrap method, provides a good approximation to the L₁ norm. The methodology is illustrated with daily security return data. The results show that decisions can be reversed when the ordinary least-squares estimate of standard errors is used with non-Gaussian data.     

Understanding Household Preferences for Hurricane Risk Mitigation Information: Evidence from Survey Responses

Risk information is critical to adopting mitigation measures, and seeking risk information is influenced by a variety of factors. An essential component of the recently adopted My Safe Florida Home (MSFH) program by the State of Florida is to provide homeowners with pertinent risk information to facilitate hurricane risk mitigation activities. We develop an analytical framework to understand household preferences for hurricane risk mitigation information through allowing an intensive home inspection. An empirical analysis is used to identify major drivers of household preferences to receive personalized information regarding recommended hurricane risk mitigation measures. A variety of empirical specifications show that households with home insurance, prior experience with damages, and with a higher sense of vulnerability to be affected by hurricanes are more likely to allow inspection to seek information. However, households with more members living in the home and households who live in manufactured/mobile homes are less likely to allow inspection. While findings imply MSFH program's ability to link incentives offered by private and public agencies in promoting mitigation, households that face a disproportionately higher level of risk can get priority to make the program more effective.     

Estimation of variance components in an unbalanced one-way classification

In the unbalanced one-way random effects model the weighted least squares approach with estimated weights is used to develop a relatively simple estimator of variance components. As the number of classes increases, the proposed estimator is seen not only to be best asymptotically normal but also to be asymptotically equivalent to the maximum likelihood estimator.     

Estimating the hazard functions of two alternating recurrent events in the presence of covariates

The motivation for this paper is a cystic fibrosis data which records a patient’s times to relapse and times to cure under several recurrences of the disease. The idea is to study the impact of covariates on the hazard rates of two alternately occurring events. The dependence between the times to the two events over the different cycles is modeled through an autoregressive-type setup. The partial likelihood function is then derived and the estimators obtained. The estimators are shown to be consistent and asymptotically normal. The technique is applied to study the motivating data. A simulation study is also conducted to corroborate the results.     

Fitting linear regression models to censored data by least squares and maximum likelihood methods

Several approaches have been suggested for fitting linear regression models to censored data. These include Cox's propor­tional hazard models based on quasi-likelihoods. Methods of fitting based on least squares and maximum likelihoods have also been proposed. The methods proposed so far all require special purpose optimization routines. We describe an approach here which requires only a modified standard least squares routine.

We present methods for fitting a linear regression model to censored data by least squares and method of maximum likelihood. In the least squares method, the censored values are replaced by their expectations, and the residual sum of squares is minimized. Several variants are suggested in the ways in which the expect­ation is calculated. A parametric (assuming a normal error model) and two non-parametric approaches are described. We also present a method for solving the maximum likelihood equations in the estimation of the regression parameters in the censored regression situation. It is shown that the solutions can be obtained by a recursive algorithm which needs only a least squares routine for optimization. The suggested procesures gain considerably in computational officiency. The Stanford Heart Transplant data is used to illustrate the various methods.