Discrete regularized discriminant analysis

A method of regularized discriminant analysis for discrete data, denoted DRDA, is proposed. This method is related to the regularized discriminant analysis conceived by Friedman (1989) in a Gaussian framework for continuous data. Here, we are concerned with discrete data and consider the classification problem using the multionomial distribution. DRDA has been conceived in the small-sample, high-dimensional setting. This method has a median position between multinomial discrimination, the first-order independence model and kernel discrimination. DRDA is characterized by two parameters, the values of which are calculated by minimizing a sample-based estimate of future misclassification risk by cross-validation. The first parameter is acomplexity parameter which provides class-conditional probabilities as a convex combination of those derived from the full multinomial model and the first-order independence model. The second parameter is asmoothing parameter associated with the discrete kernel of Aitchison and Aitken (1976). The optimal complexity parameter is calculated first, then, holding this parameter fixed, the optimal smoothing parameter is determined. A modified approach, in which the smoothing parameter is chosen first, is discussed. The efficiency of the method is examined with other classical methods through application to data.     

Kernel Estimation of the Spectral Density of Stationary Random Closed Sets

A non‐parametric kernel estimator of the spectral density of stationary random closed sets is studied. Conditions are derived under which this estimator is asymptotically unbiased and mean‐square consistent. For the planar Boolean model with isotropic compact and convex grains, an averaged version of the kernel estimator is compared with the theoretical spectral density.     

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.     

Non-parametric Tests for the Comparison of Point Processes Based on Incomplete Data

We consider the comparison of point processes in a discrete observation situation in which each subject is observed only at discrete time points and no history information between observation times is available. A class of non-parametric test statistics for the comparison of point processes based on this kind of data is presented and their asymptotic distributions are derived. The proposed tests are generalizations of the corresponding tests for continuous observations. Some results from a simulation study for evaluating the proposed tests are presented and an illustrative example from a clinical trial is discussed.     

Unmasking the Trend Sought by Jonckheere-Type Tests for Right-Censored Data

Medical and epidemiological studies often involve groups of subjects associated with increasing levels of exposure to a risk factor. Survival of the groups is expected to follow the same order as the level of exposure. Formal tests for this trend fall into the regression framework if one knows what function of exposure to use as a covariate. When unknown, a linear function of exposure level is often used. Jonckheere-type tests for trend have generated continued interest largely because they do not require specification of a covariate. This paper shows that the Jonckheere-type test statistics are special cases of a generalized linear rank statistic with time-dependent covariates which unfortunately depend on the initial group sizes and censoring distributions. Using asymptotic relative efficiency calculations, the Jonckheere tests are compared to standard linear rank tests based on a linear covariate over a spectrum of shapes for the true trend.     

A note on calibration weightings for stratified double sampling with equal probability

This study proposes a more efficient calibration estimator for estimating population mean in stratified double sampling using new calibration weights. The variance of the proposed calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed calibration estimator and existing calibration estimators in stratified double sampling. Analytical results showed that the proposed calibration estimator is more efficient than existing members of its class in stratified double sampling. Analysis and evaluation are presented.     

Life here beyond now: Chronotopes of the ideal life among Iranian transnationals

I address how U.S.‐based Iranian transnationals’ migration paths affect their (re)‐construction of chronotopes of the ideal life. Adopting an ethnographically grounded, discourse‐analytic approach, I illustrate how participants with student visas and U.S. Green Cards position themselves differently relative to images of success here [in the U.S.] and lack of success there [in Iran]. I argue that the chronotopes of success here and lack of success there (re)‐constructed by non‐resident Iranian students are prompted by a large‐scale cultural chronotope which pertains to their aspiration to stay in the U.S. This chronotope of ‘life beyond’ is less about a ‘remove from homeland’ and more about an ideal future in the host country. Migrants’ desires and anxieties, I argue, can determine what receives topical prominence in migration chronotopes – as in the case of Iranian educational migrants whose future positionings make temporality topically more prominent than spatiality.

     

Ensemble Approaches to Estimating the Population Mean with Missing Response

We propose new ensemble approaches to estimate the population mean for missing response data with fully observed auxiliary variables. We first compress the working models according to their categories through a weighted average, where the weights are proportional to the square of the least‐squares coefficients of model refitting. Based on the compressed values, we develop two ensemble frameworks, under which one is to adjust weights in the inverse probability weighting procedure and the other is built upon an additive structure by reformulating the augmented inverse probability weighting function. The asymptotic normality property is established for the proposed estimators through the theory of estimating functions with plugged‐in nuisance parameter estimates. Simulation studies show that the new proposals have substantial advantages over existing ones for small sample sizes, and an acquired immune deficiency syndrome data example is used for illustration.     

Kullback-Leibler divergence to evaluate posterior sensitivity to different priors for autoregressive time series models

In this paper we use the Kullback-Leibler divergence to measure the distance between the posteriors of the autoregressive (AR) model coefficients, aiming to evaluate mathematically the sensitivity of the coefficients posterior to different types of priors, i.e. Jeffreys’, g, and natural conjugate priors. In addition, we evaluate the impact of the posteriors distance in Bayesian estimates of mean and variance of the model coefficients by generating a large number of Monte Carlo simulations from the posteriors. Simulation study results show that the coefficients posterior is sensitive to prior distributions, and the posteriors distance has more influence on Bayesian estimates of variance than those of mean of the model coefficients. Same results are obtained from the application to real-world time series datasets.