Optimal robust estimates using the Hellinger distance

Optimal robust M-estimates of a multidimensional parameter are described using Hampel's infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance.We show that these two measures coincide with similar ones defined by Yohai using the Kullback-Leibler divergence, and therefore the corresponding optimal estimates coincide too.We also give an example where we fit a negative binomial distribution to a real dataset of "days of stay in hospital" using the optimal robust estimates.

Robust Estimates of the Negative Binomial Model

We consider robust parametric procedures for univariate discrete distributions, focusing on the negative binomial model. The procedures are based on three steps: ?First, a very robust, but possibly inefficient, estimate of the model parameters is computed. ?Second, this initial model is used to identify outliers, which are then removed from the sample. ?Third, a corrected maximum likelihood estimator is computed with the remaining observations. The final estimate inherits the breakdown point (bdp) of the initial one and its efficiency can be significantly higher. Analogous procedures were proposed in [1], [2], [5] for the continuous case. A comparison of the asymptotic bias of various estimates under point contamination points out the minimum Neyman's chi-squared disparity estimate as a good choice for the initial step. Various minimum disparity estimators were explored by Lindsay [4], who showed that the minimum Neyman's chi-squared estimate has a 50% bdp under point contamination; in addition, it is asymptotically fully efficient at the model. However, the finite sample efficiency of this estimate under the uncontaminated negative binomial model is usually much lower than 100% and the bias can be strong. We show that its performance can then be greatly improved using the three step procedure outlined above. In addition, we compare the final estimate with the procedure described in

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Detection rate of FNA cytology in medullary thyroid carcinoma: a meta-analysis.

BACKGROUND: The early detection of medullary thyroid carcinoma (MTC) can improve patient prognosis, because histological stage and patient age at diagnosis are highly relevant prognostic factors. As a consequence, delay in the diagnosis and/or incomplete surgical treatment should correlate with a poorer prognosis for patients. Few papers have evaluated the specific capability of fine-needle aspiration cytology (FNAC) to detect MTC, and small series have been reported. This study conducts a meta-analysis of published data on the diagnostic performance of FNAC in MTC to provide more robust estimates. RESEARCH DESIGN AND METHODS: A comprehensive computer literature search of the PubMed/MEDLINE, Embase and Scopus databases was conducted by searching for the terms 'medullary thyroid' AND 'cytology', 'FNA', 'FNAB', 'FNAC', 'fine needle' or 'fine-needle'. The search was updated until 21 March 2014, and no language restrictions were used. RESULTS: Fifteen relevant studies and 641 MTC lesions that had undergone FNAC were included. The detection rate (DR) of FNAC in patients with MTC (diagnosed as 'MTC' or 'suspicious for MTC') on a per lesion-based analysis ranged from 12·5% to 88·2%, with a pooled estimate of 56·4% (95% CI: 52·6-60·1%). The included studies were statistically heterogeneous in their estimates of DR (I-square >50%). Egger's regression intercept for DR pooling was 0·03 (95% CI: -3·1 to 3·2, P = 0·9). The study that reported the largest MTC series had a DR of 45%. Data on immunohistochemistry for calcitonin in diagnosing MTC were inconsistent for the meta-analysis. CONCLUSIONS: The presented meta-analysis demonstrates that FNAC is able to detect approximately one-half of MTC lesions. These findings suggest that other techniques may be needed in combination with FNAC to diagnose MTC and avoid false negative results.

The truncated mean of an asymmetric distribution

This paper investigates a simple procedure to estimate robustly the mean of an asymmetric distribution. The procedure removes the observations which are larger or smaller than certain limits and takes the arithmetic mean of the remaining observations, the limits being determined with the help of a parametric model, e.g., the Gamma, the Weibull or the Lognormal distribution. The breakdown point, the influence function, the (asymptotic) variance, and the contamination bias of this estimator are explored and compared numerically with those of competing estimates.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Analysis of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole georadar data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a time-domain waveform inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little-to-no trade-off between the wavelet estimation and the tomographic imaging procedures.

Source-wavelet estimation during full-waveform inversion of ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole ground-penetrating radar (GPR) data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a recently published time-domain inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity of both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little to no trade-off between the wavelet estimation and the tomographic imaging procedures.

Etude de la variation interlaboratoire du test de dépistage prénatal des défauts de fermeture du tube neural [Interlaboratory variation in the prenatal screening test for neural tube closing defects].

Early detection of neural-tude defects is possible by determining Alpha-fetoprotein (AFP) in maternal serum. 16'685 pregnant women were observed. Three methods for the determination of the "normal" range are compared. The first one, already used in similar studies, makes use of a constant multiple of the median. The other two ones make use of robust estimates of location and scale. Their comparison shows the interest of the robust methods to reduce the interlaboratory variability.

Use of fine-needle aspirate calcitonin to detect medullary thyroid carcinoma: A systematic review.

BACKGROUND: The measurement of calcitonin in washout fluids of thyroid nodule aspirate (FNA-calcitonin) has been reported as accurate to detect medullary thyroid carcinoma (MTC). The results from these studies have been promising and the most updated version of ATA guidelines quoted for the first time that "FNA findings that are inconclusive or suggestive of MTC should have calcitonin measured in the FNA washout fluid." Here we aimed to systematically review published data on this topic to provide more robust estimates. RESEARCH DESIGN AND METHODS: A comprehensive computer literature search of the medical databases was conducted by searching for the terms "calcitonin" AND "washout." The search was updated until April 2015. RESULTS: Twelve relevant studies, published between 2007 and 2014, were found. Overall, 413 thyroid nodules or neck lymph nodes underwent FNA-calcitonin, 95 were MTC lesions and 93 (97.9%) of these were correctly detected by this measurement regardless of their cytologic report. CONCLUSIONS: The present study shows that the above ATA recommendation is well supported. Almost all MTC lesions are correctly detected by FNA-calcitonin and this technique should be used to avoid false negative or inconclusive results from cytology. The routine determination of serum calcitonin in patients undergoing FNA should improve the selection of patients at risk for MTC, guiding the use of FNA-calcitonin in the same FNA sample and providing useful information to the cytopathologist for the morphological assessment and the application of tailored ancillary tests.

Robust parametric indirect estimates of the expected cost of a hospital stay with covariates and censored data.

We consider the problem of estimating the mean hospital cost of stays of a class of patients (e.g., a diagnosis-related group) as a function of patient characteristics. The statistical analysis is complicated by the asymmetry of the cost distribution, the possibility of censoring on the cost variable, and the occurrence of outliers. These problems have often been treated separately in the literature, and a method offering a joint solution to all of them is still missing. Indirect procedures have been proposed, combining an estimate of the duration distribution with an estimate of the conditional cost for a given duration. We propose a parametric version of this approach, allowing for asymmetry and censoring in the cost distribution and providing a mean cost estimator that is robust in the presence of extreme values. In addition, the new method takes covariate information into account.

Velocity estimates for signal propagation leading to systemic jasmonic acid accumulation in wounded Arabidopsis.

The wound response prohormone jasmonic acid (JA) accumulates rapidly in tissues both proximal and distal to injury sites in plants. Using quantitative liquid chromatography-mass spectrometry after flash freezing of tissues, we found that JA accumulated within 30 s of injury in wounded Arabidopsis leaves (p = 3.5 e(-7)). JA augmentation distal to wounds was strongest in unwounded leaves with direct vascular connections to wounded leaves wherein JA levels increased significantly within 120 s of wounding (p = 0.00027). This gave conservative and statistically robust temporal boundaries for the average velocity of the long distance signal leading to distal JA accumulation in unwounded leaves of 3.4-4.5 cm min(-1). Like JA, transcripts of the JA synthesis gene LIPOXYGENASE2 (LOX2) and the jasmonate response gene JAZ10.3 also accumulated to higher levels in directly interconnected leaves than in indirectly connected leaves. JA accumulation in a lox2-1 mutant plant was initiated rapidly after wounding then slowed progressively compared with the wild type (WT). Despite this, JAZ10.3 expression in the two genotypes was similar. Free cyclopentenone jasmonate levels were similar in both resting WT and lox2-1. In contrast, bound cyclopentenone jasmonates (arabidopsides) were far lower in lox2-1 than in the WT. The major roles of LOX2 are to generate arabidopsides and the large levels of JA that accumulate proximal to the wound. LOX2 is not essential for some of the most rapid events elicited by wounding.

Robust accelerated failure time regression

Robust estimators for accelerated failure time models with asymmetric (or symmetric) error distribution and censored observations are proposed. It is assumed that the error model belongs to a log-location-scale family of distributions and that the mean response is the parameter of interest. Since scale is a main component of mean, scale is not treated as a nuisance parameter. A three steps procedure is proposed. In the first step, an initial high breakdown point S estimate is computed. In the second step, observations that are unlikely under the estimated model are rejected or down weighted. Finally, a weighted maximum likelihood estimate is computed. To define the estimates, functions of censored residuals are replaced by their estimated conditional expectation given that the response is larger than the observed censored value. The rejection rule in the second step is based on an adaptive cut-off that, asymptotically, does not reject any observation when the data are generat ed according to the model. Therefore, the final estimate attains full efficiency at the model, with respect to the maximum likelihood estimate, while maintaining the breakdown point of the initial estimator. Asymptotic results are provided. The new procedure is evaluated with the help of Monte Carlo simulations. Two examples with real data are discussed.

Reliable selfing rate estimates from imperfect population genetic data.

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.

Estimates of radiation-absorbed dose to kidneys in patients treated with 90Y-ibritumomab tiuxetan.

The aim of the present study was to retrospectively estimate the absorbed dose to kidneys in 17 patients treated in clinical practice with 90Y-ibritumomab tiuxetan for non-Hodgkin's lymphoma, using appropriate dosimetric approaches available. METHODS: The single-view effective point source method, including background subtraction, is used for planar quantification of renal activity. Since the high uptake in the liver affects the activity estimate in the right kidney, the dose to the left kidney serves as a surrogate for the dose to both kidneys. Calculation of absorbed dose is based on the Medical Internal Radiation Dose methodology with adjustment for patient kidney mass. RESULTS: The median dose to kidneys, based on the left kidney only, is 2.1 mGy/MBq (range, 0.92-4.4), whereas a value of 2.5 mGy/MBq (range, 1.5-4.7) is obtained, considering the activity in both kidneys. CONCLUSIONS: Irrespective of the method, doses to kidneys obtained in the present study were about 10 times higher than the median dose of 0.22 mGy/MBq (range, 0.00-0.95) were originally reported from the study leading to Food and Drug Administration approval. Our results are in good agreement with kidney-dose estimates recently reported from high-dose myeloablative therapy with 90Y-ibritumomab tiuxetan.