Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.

ML approaches to channel estimation for pilot-aided multi-rate DS/CDMA systems

This paper analyzes the asymptotic performance of maximum likelihood (ML) channel estimation algorithms in wideband code division multiple access (WCDMA) scenarios. We concentrate on systems with periodic spreading sequences (period larger than or equal to the symbol span) where the transmitted signal contains a code division multiplexed pilot for channel estimation purposes. First, the asymptotic covariances of the training-only, semi-blind conditional maximum likelihood (CML) and semi-blind Gaussian maximum likelihood (GML) channelestimators are derived. Then, these formulas are further simplified assuming randomized spreading and training sequences under the approximation of high spreading factors and high number of codes. The results provide a useful tool to describe the performance of the channel estimators as a function of basicsystem parameters such as number of codes, spreading factors, or traffic to training power ratio.

Little evidence for association between the TGFBR1*6A variant and colorectal cancer: a family-based association study on non-syndromic family members from Australia and Spain.

Genome-wide linkage studies have identified the 9q22 chromosomal region as linked with colorectal cancer (CRC) predisposition. A candidate gene in this region is transforming growth factor beta receptor 1 (TGFBR1). Investigation of TGFBR1 has focused on the common genetic variant rs11466445, a short exonic deletion of nine base pairs which results in truncation of a stretch of nine alanine residues to six alanine residues in the gene product. While the six alanine (*6A) allele has been reported to be associated with increased risk of CRC in some population based study groups this association remains the subject of robust debate. To date, reports have been limited to population-based case-control association studies, or case-control studies of CRC families selecting one affected individual per family. No study has yet taken advantage of all the genetic information provided by multiplex CRC families. Methods: We have tested for an association between rs11466445 and risk of CRC using several family-based statistical tests in a new study group comprising members of non-syndromic high risk CRC families sourced from three familial cancer centres, two in Australia and one in Spain. Results: We report a finding of a nominally significant result using the pedigree-based association test approach (PBAT; p = 0.028), while other family-based tests were non-significant, but with a p-value < 0.10 in each instance. These other tests included the Generalised Disequilibrium Test (GDT; p = 0.085), parent of origin GDT Generalised Disequilibrium Test (GDT-PO; p = 0.081) and empirical Family-Based Association Test (FBAT; p = 0.096, additive model). Related-person case-control testing using the 'More Powerful' Quasi-Likelihood Score Test did not provide any evidence for association (M-QL5; p = 0.41). Conclusions: After conservatively taking into account considerations for multiple hypothesis testing, we find little evidence for an association between the TGFBR1*6A allele and CRC risk in these families. The weak support for an increase in risk in CRC predisposed families is in agreement with recent meta-analyses of case-control studies, which estimate only a modest increase in sporadic CRC risk among 6*A allele carriers.

Hausman tests for inefficient estimators: application to demand for health care service (revised)

The Hausman (1978) test is based on the vector of differences of two estimators. It is usually assumed that one of the estimators is fully efficient, since this simplifies calculation of the test statistic. However, this assumption limits the applicability of the test, since widely used estimators such as the generalized method of moments (GMM) or quasi maximum likelihood (QML) are often not fully efficient. This paper shows that the test may easily be implemented, using well-known methods, when neither estimator is efficient. To illustrate, we present both simulation results as well as empirical results for utilization of health care services.

Indirect likelihood inference

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic - for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator which we refer to as a Bayesian Indirect Likelihood (BIL) estimator. In most cases, the density of the statistic will be of unknown form, and we develop simulated versions of the MIL and BIL estimators. We show that the indirect likelihood estimators are consistent and asymptotically normally distributed, with the same asymptotic variance as that of the corresponding efficient two-step GMM estimator based on the same statistic. However, our likelihood-based estimators, by taking into account the full finite-sample distribution of the statistic, are higher order efficient relative to GMM-type estimators. Furthermore, in many cases they enjoy a bias reduction property similar to that of the indirect inference estimator. Monte Carlo results for a number of applications including dynamic and nonlinear panel data models, a structural auction model and two DSGE models show that the proposed estimators indeed have attractive finite sample properties.

On the inefficiency of the restricted maximum likelihood

The restricted maximum likelihood is preferred by many to the full maximumlikelihood for estimation with variance component and other randomcoefficientmodels, because the variance estimator is unbiased. It is shown that thisunbiasednessis accompanied in some balanced designs by an inflation of the meansquared error.An estimator of the cluster-level variance that is uniformly moreefficient than the fullmaximum likelihood is derived. Estimators of the variance ratio are alsostudied.

ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers

This paper addresses the estimation of the code-phase(pseudorange) and the carrier-phase of the direct signal received from a direct-sequence spread-spectrum satellite transmitter. Thesignal is received by an antenna array in a scenario with interferenceand multipath propagation. These two effects are generallythe limiting error sources in most high-precision positioning applications.A new estimator of the code- and carrier-phases is derivedby using a simplified signal model and the maximum likelihood(ML) principle. The simplified model consists essentially ofgathering all signals, except for the direct one, in a component withunknown spatial correlation. The estimator exploits the knowledgeof the direction-of-arrival of the direct signal and is much simplerthan other estimators derived under more detailed signal models.Moreover, we present an iterative algorithm, that is adequate for apractical implementation and explores an interesting link betweenthe ML estimator and a hybrid beamformer. The mean squarederror and bias of the new estimator are computed for a numberof scenarios and compared with those of other methods. The presentedestimator and the hybrid beamforming outperform the existingtechniques of comparable complexity and attains, in manysituations, the Cramér–Rao lower bound of the problem at hand.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

Likelihood inferences with interval-censored data

En l’anàlisi de la supervivència el problema de les dades censurades en un interval es tracta, usualment,via l’estimació per màxima versemblança. Amb l’objectiu d’utilitzar una expressió simplificada de la funció de versemblança, els mètodes estàndards suposen que les condicions que produeixen la censura no afecten el temps de fallada. En aquest article formalitzem les condicions que asseguren la validesa d’aquesta versemblança simplificada. Així, precisem diferents condicions de censura no informativa i definim una condició de suma constant anàloga a la derivada en el context de censura per la dreta. També demostrem que les inferències obtingudes amb la versemblançaa simplificada són correctes quan aquestes condicions són certes. Finalment, tractem la identificabilitat de la funció distribució del temps de fallada a partir de la informació observada i estudiem la possibilitat de contrastar el compliment de la condició de suma constant.

Likelihood-based approaches to modeling demand for medical care

We review recent likelihood-based approaches to modeling demand for medical care. A semi-nonparametric model along the lines of Cameron and Johansson's Poisson polynomial model, but using a negative binomial baseline model, is introduced. We apply these models, as well a semiparametric Poisson, hurdle semiparametric Poisson, and finite mixtures of negative binomial models to six measures of health care usage taken from the Medical Expenditure Panel survey. We conclude that most of the models lead to statistically similar results, both in terms of information criteria and conditional and unconditional prediction. This suggests that applied researchers may not need to be overly concerned with the choice of which of these models they use to analyze data on health care demand.

Quasi-Potency and Cyclic subgroup separability

We study the profinite topology on discrete groups and in particular the property of cyclic subgroup separability. We investigate the class of quasi-potent, cyclic subgroup separable groups, producing many examples and showing how it behaves with respect to certain group constructions.