Improved combinations of parametric and nonparametric Regression estimators

This paper provides a systematic and unified treatment of the developments in the area of kernel estimation in econometrics and statistics. Both the estimation and hypothesis testing issues are discussed for the nonparametric and semiparametric regression models. A discussion on the choice of windowwidth is also presented.

Factors affecting the technical efficiency of production of the Brazilian banking system : a comparison of four statistical models in the context of data envelopment analysis

This paper uses an output oriented Data Envelopment Analysis (DEA) measure of technical efficiency to assess the technical efficiencies of the Brazilian banking system. Four approaches to estimation are compared in order to assess the significance of factors affecting inefficiency. These are nonparametric Analysis of Covariance, maximum likelihood using a family of exponential distributions, maximum likelihood using a family of truncated normal distributions, and the normal Tobit model. The sole focus of the paper is on a combined measure of output and the data analyzed refers to the year 2001. The factors of interest in the analysis and likely to affect efficiency are bank nature (multiple and commercial), bank type (credit, business, bursary and retail), bank size (large, medium, small and micro), bank control (private and public), bank origin (domestic and foreign), and non-performing loans. The latter is a measure of bank risk. All quantitative variables, including non-performing loans, are measured on a per employee basis. The best fits to the data are provided by the exponential family and the nonparametric Analysis of Covariance. The significance of a factor however varies according to the model fit although it can be said that there is some agreements between the best models. A highly significant association in all models fitted is observed only for nonperforming loans. The nonparametric Analysis of Covariance is more consistent with the inefficiency median responses observed for the qualitative factors. The findings of the analysis reinforce the significant association of the level of bank inefficiency, measured by DEA residuals, with the risk of bank failure.

Biomechanical Performance of Flexible Intramedullary Nails With End Caps Tested in Distal Segmental Defects of Pediatric Femur Models

Background: Unstable distal femoral fractures in children are challenging lesions with restricted surgical options for adequate stabilization. Elastic nails have become popular for treating femoral shaft fractures, yet they are still challenging for using in distal fractures. The aim of this study was to test whether end caps (CAP) inserted into the nail extremity improved the mechanical stabilization of a segmental defect at the distal femoral metaphyseal-diaphyseal junction created in an artificial pediatric bone model. Methods: Two 3.5-mm titanium elastic nails (TEN) were introduced intramedullary into pediatric femur models, and a 7.0-mm-thick segmental defect was created at the distal diaphyseal-metaphyseal junction. Nondestructive 4-point bending, axial-bending, and torsion tests were conducted. After this, the end caps were inserted into the external tips of the nails and then screwed into the bone cortex. The mechanical tests were repeated. Stiffness, displacement, and torque were analyzed using the Wilcoxon nonparametric test for paired samples. Results: In the combined axial-bending tests, the TEN + CAP combination was 8.75% stiffer than nails alone (P < 0.01); in torsion tests, the TEN + CAP was 14% stiffer than nails alone (P < 0.01). In contrast, the 4-point bending test did not show differences between the methods (P = 0.91, stiffness; P = 0.51, displacement). Thus, the end caps contributed to an increase in the construct stability for torsion and axial-bending forces but not for 4-point bending forces. Conclusions: These findings indicate that end caps fitted to elastic nails may contribute to the stabilization of fractures that our model mimics (small distal fragment, bone comminution, and distal bone fragment loss).

Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part aggress with the more general information bound calculations of Robins, Hsieh, and Newey (1995). By verifying the conditions of Murphy and Van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.

Efficiency of the Sieved-NPMLE in CAR-Missing Data Models

We consider nonparametric missing data models for which the censoring mechanism satisfies coarsening at random and which allow complete observations on the variable X of interest. W show that beyond some empirical process conditions the only essential condition for efficiency of an NPMLE of the distribution of X is that the regions associated with incomplete observations on X contain enough complete observations. This is heuristically explained by describing the EM-algorithm. We provide identifiably of the self-consistency equation and efficiency of the NPMLE in order to make this statement rigorous. The usual kind of differentiability conditions in the proof are avoided by using an identity which holds for the NPMLE of linear parameters in convex models. We provide a bivariate censoring application in which the condition and hence the NPMLE fails, but where other estimators, not based on the NPMLE principle, are highly inefficient. It is shown how to slightly reduce the data so that the conditions hold for the reduced data. The conditions are verified for the univariate censoring, double censored, and Ibragimov-Has'minski models.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

Comparing Input- and Output-Oriented Measures of Technical Efficiency to Determine Local Returns to Scale in DEA Models

This paper shows how one can infer the nature of local returns to scale at the input- or output-oriented efficient projection of a technically inefficient input-output bundle, when the input- and output-oriented measures of efficiency differ.

Nonparametric Message Passing Methods for Cooperative Localization and Tracking

The objective of this thesis is the development of cooperative localization and tracking algorithms using nonparametric message passing techniques. In contrast to the most well-known techniques, the goal is to estimate the posterior probability density function (PDF) of the position of each sensor. This problem can be solved using Bayesian approach, but it is intractable in general case. Nevertheless, the particle-based approximation (via nonparametric representation), and an appropriate factorization of the joint PDFs (using message passing methods), make Bayesian approach acceptable for inference in sensor networks. The well-known method for this problem, nonparametric belief propagation (NBP), can lead to inaccurate beliefs and possible non-convergence in loopy networks. Therefore, we propose four novel algorithms which alleviate these problems: nonparametric generalized belief propagation (NGBP) based on junction tree (NGBP-JT), NGBP based on pseudo-junction tree (NGBP-PJT), NBP based on spanning trees (NBP-ST), and uniformly-reweighted NBP (URW-NBP). We also extend NBP for cooperative localization in mobile networks. In contrast to the previous methods, we use an optional smoothing, provide a novel communication protocol, and increase the efficiency of the sampling techniques. Moreover, we propose novel algorithms for distributed tracking, in which the goal is to track the passive object which cannot locate itself. In particular, we develop distributed particle filtering (DPF) based on three asynchronous belief consensus (BC) algorithms: standard belief consensus (SBC), broadcast gossip (BG), and belief propagation (BP). Finally, the last part of this thesis includes the experimental analysis of some of the proposed algorithms, in which we found that the results based on real measurements are very similar with the results based on theoretical models.

Adaptable Bayesian classifier for spatiotemporal nonparametric moving object detection strategies

Electronic devices endowed with camera platforms require new and powerful machine vision applications, which commonly include moving object detection strategies. To obtain high-quality results, the most recent strategies estimate nonparametrically background and foreground models and combine them by means of a Bayesian classifier. However, typical classifiers are limited by the use of constant prior values and they do not allow the inclusion of additional spatiodependent prior information. In this Letter, we propose an alternative Bayesian classifier that, unlike those reported before, allows the use of additional prior information obtained from any source and depending on the spatial position of each pixel.