48 resultados para MAXIMUM-LIKELIHOOD ESTIMATORS

em Université de Lausanne, Switzerland


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We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux et al. (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods [Authors]

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SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

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BACKGROUND: In vitro aggregating brain cell cultures containing all types of brain cells have been shown to be useful for neurotoxicological investigations. The cultures are used for the detection of nervous system-specific effects of compounds by measuring multiple endpoints, including changes in enzyme activities. Concentration-dependent neurotoxicity is determined at several time points. METHODS: A Markov model was set up to describe the dynamics of brain cell populations exposed to potentially neurotoxic compounds. Brain cells were assumed to be either in a healthy or stressed state, with only stressed cells being susceptible to cell death. Cells may have switched between these states or died with concentration-dependent transition rates. Since cell numbers were not directly measurable, intracellular lactate dehydrogenase (LDH) activity was used as a surrogate. Assuming that changes in cell numbers are proportional to changes in intracellular LDH activity, stochastic enzyme activity models were derived. Maximum likelihood and least squares regression techniques were applied for estimation of the transition rates. Likelihood ratio tests were performed to test hypotheses about the transition rates. Simulation studies were used to investigate the performance of the transition rate estimators and to analyze the error rates of the likelihood ratio tests. The stochastic time-concentration activity model was applied to intracellular LDH activity measurements after 7 and 14 days of continuous exposure to propofol. The model describes transitions from healthy to stressed cells and from stressed cells to death. RESULTS: The model predicted that propofol would affect stressed cells more than healthy cells. Increasing propofol concentration from 10 to 100 μM reduced the mean waiting time for transition to the stressed state by 50%, from 14 to 7 days, whereas the mean duration to cellular death reduced more dramatically from 2.7 days to 6.5 hours. CONCLUSION: The proposed stochastic modeling approach can be used to discriminate between different biological hypotheses regarding the effect of a compound on the transition rates. The effects of different compounds on the transition rate estimates can be quantitatively compared. Data can be extrapolated at late measurement time points to investigate whether costs and time-consuming long-term experiments could possibly be eliminated.

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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.

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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

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OBJECTIVES: In this population-based study, reference values were generated for renal length, and the heritability and factors associated with kidney length were assessed. METHODS: Anthropometric parameters and renal ultrasound measurements were assessed in randomly selected nuclear families of European ancestry (Switzerland). The adjusted narrow sense heritability of kidney size parameters was estimated by maximum likelihood assuming multivariate normality after power transformation. Gender-specific reference centiles were generated for renal length according to body height in the subset of non-diabetic non-obese participants with normal renal function. RESULTS: We included 374 men and 419 women (mean ± SD, age 47 ± 18 and 48 ± 17 years, BMI 26.2 ± 4 and 24.5 ± 5 kg/m(2), respectively) from 205 families. Renal length was 11.4 ± 0.8 cm in men and 10.7 ± 0.8 cm in women; there was no difference between right and left renal length. Body height, weight and estimated glomerular filtration rate (eGFR) were positively associated with renal length, kidney function negatively, age quadratically, whereas gender and hypertension were not. The adjusted heritability estimates of renal length and volume were 47.3 ± 8.5 % and 45.5 ± 8.8 %, respectively (P < 0.001). CONCLUSION: The significant heritability of renal length and volume highlights the familial aggregation of this trait, independently of age and body size. Population-based references for renal length provide a useful guide for clinicians. KEY POINTS: • Renal length and volume are heritable traits, independent of age and size. • Based on a European population, gender-specific reference values/percentiles are provided for renal length. • Renal length correlates positively with body length and weight. • There was no difference between right and left renal lengths in this study. • This negates general teaching that the left kidney is larger and longer.

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C4 photosynthesis is an adaptation derived from the more common C3 photosynthetic pathway that confers a higher productivity under warm temperature and low atmospheric CO2 concentration [1, 2]. C4 evolution has been seen as a consequence of past atmospheric CO2 decline, such as the abrupt CO2 fall 32-25 million years ago (Mya) [3-6]. This relationship has never been tested rigorously, mainly because of a lack of accurate estimates of divergence times for the different C4 lineages [3]. In this study, we inferred a large phylogenetic tree for the grass family and estimated, through Bayesian molecular dating, the ages of the 17 to 18 independent grass C4 lineages. The first transition from C3 to C4 photosynthesis occurred in the Chloridoideae subfamily, 32.0-25.0 Mya. The link between CO2 decrease and transition to C4 photosynthesis was tested by a novel maximum likelihood approach. We showed that the model incorporating the atmospheric CO2 levels was significantly better than the null model, supporting the importance of CO2 decline on C4 photosynthesis evolvability. This finding is relevant for understanding the origin of C4 photosynthesis in grasses, which is one of the most successful ecological and evolutionary innovations in plant history.

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BACKGROUND: We estimated the heritability of three measures of glomerular filtration rate (GFR) in hypertensive families of African descent in the Seychelles (Indian Ocean). METHODS: Families with at least two hypertensive siblings and an average of two normotensive siblings were identified through a national hypertension register. Using the ASSOC program in SAGE (Statistical Analysis in Genetic Epidemiology), the age- and gender-adjusted narrow sense heritability of GFR was estimated by maximum likelihood assuming multivariate normality after power transformation. ASSOC can calculate the additive polygenic component of the variance of a trait from pedigree data in the presence of other familial correlations. The effects of body mass index (BMI), blood pressure, natriuresis, along with sodium to potassium ratio in urine and diabetes, were also tested as covariates. RESULTS: Inulin clearance, 24-hour creatinine clearance, and GFR based on the Cockcroft-Gault formula were available for 348 persons from 66 pedigrees. The age- and gender-adjusted correlations (+/- SE) were 0.51 (+/- 0.04) between inulin clearance and creatinine clearance, 0.53 (+/- 0.04) between inulin clearance and Cockcroft-Gault formula and 0.66 (+/- 0.03) between creatinine clearance and Cockcroft-Gault formula. The age- and gender-adjusted heritabilities (+/- SE) of GFR were 0.41 (+/- 0.10) for inulin clearance, 0.52 (+/- 0.13) for creatinine clearance, and 0.82 (+/- 0.09) for Cockcroft-Gault formula. Adjustment for BMI slightly lowered the correlations and heritabilities for all measurements whereas adjustment for blood pressure had virtually no effect. CONCLUSION: The significant heritability estimates of GFR in our sample of families of African descent confirm the familial aggregation of this trait and justify further analyses aimed at discovering genetic determinants of GFR.

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Bipolar disorder has a genetic component, but the mode of inheritance remains unclear. A previous genome scan conducted in 70 European families led to detect eight regions linked to bipolar disease. Here, we present an investigation of whether the phenotypic heterogeneity of the disorder corresponds to genetic heterogeneity in these regions using additional markers and an extended sample of families. The MLS statistic was used for linkage analyses. The predivided sample test and the maximum likelihood binomial methods were used to test genetic homogeneity between early-onset bipolar type I (cut-off of 22 years) and other types of the disorder (later onset of bipolar type I and early-onset bipolar type II), using a total of 138 independent bipolar-affected sib-pairs. Analysis of the extended sample of families supports linkage in four regions (2q14, 3p14, 16p23, and 20p12) of the eight regions of linkage suggested by our previous genome scan. Heterogeneity testing revealed genetic heterogeneity between early and late-onset bipolar type I in the 2q14 region (P = 0.0001). Only the early form of the bipolar disorder but not the late form appeared to be linked to this region. This region may therefore include a genetic factor either specifically involved in the early-onset bipolar type I or only influencing the age at onset (AAO). Our findings illustrate that stratification according to AAO may be valuable for the identification of genetic vulnerability polymorphisms.

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Backgrounds and Aims The spatial separation of stigmas and anthers (herkogamy) in flowering plants functions to reduce self-pollination and avoid interference between pollen dispersal and receipt. Little is known about the evolutionary relationships among the three main forms of herkogamy - approach, reverse and reciprocal herkogamy (distyly) - or about transitions to and from a non-herkogamous condition. This problem was examined in Exochaenium (Gentianaceae), a genus of African herbs that exhibits considerable variation in floral morphology, including the three forms of herkogamy. Methods Using maximum parsimony and maximum likelihood methods, the evolutionary history of herkogamic and non-herkogamic conditions was reconstructed from a molecular phylogeny of 15 species of Exochaenium and four outgroup taxa, based on three chloroplast regions, the nuclear ribosomal internal transcribed spacer (ITS1 and 2) and the 5·8S gene. Ancestral character states were determined and the reconstructions were used to evaluate competing models for the origin of reciprocal herkogamy. Key results Reciprocal herkogamy originated once in Exochaenium from an ancestor with approach herkogamy. Reverse herkogamy and the non-herkogamic condition homostyly were derived from heterostyly. Distylous species possessed pendent, slightly zygomorphic flowers, and the single transition to reverse herkogamy was associated with the hawkmoth pollination syndrome. Reductions in flower size characterized three of four independent transitions from reciprocal herkogamy to homostyly. Conclusions The results support Lloyd and Webb's model in which distyly originated from an ancestor with approach herkogamy. They also demonstrate the lability of sex organ deployment and implicate pollinators, or their absence, as playing an important role in driving transitions among herkogamic and non-herkogamic conditions.

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Plasmodium falciparum is the parasite responsible for the most acute form of malaria in humans. Recently, the serine repeat antigen (SERA) in P. falciparum has attracted attention as a potential vaccine and drug target, and it has been shown to be a member of a large gene family. To clarify the relationships among the numerous P. falciparum SERAs and to identify orthologs to SERA5 and SERA6 in Plasmodium species affecting rodents, gene trees were inferred from nucleotide and amino acid sequence data for 33 putative SERA homologs in seven different species. (A distance method for nucleotide sequences that is specifically designed to accommodate differing GC content yielded results that were largely compatible with the amino acid tree. Standard-distance and maximum-likelihood methods for nucleotide sequences, on the other hand, yielded gene trees that differed in important respects.) To infer the pattern of duplication, speciation, and gene loss events in the SERA gene family history, the resulting gene trees were then "reconciled" with two competing Plasmodium species tree topologies that have been identified by previous phylogenetic studies. Parsimony of reconciliation was used as a criterion for selecting a gene tree/species tree pair and provided (1) support for one of the two species trees and for the core topology of the amino acid-derived gene tree, (2) a basis for critiquing fine detail in a poorly resolved region of the gene tree, (3) a set of predicted "missing genes" in some species, (4) clarification of the relationship among the P. falciparum SERA, and (5) some information about SERA5 and SERA6 orthologs in the rodent malaria parasites. Parsimony of reconciliation and a second criterion--implied mutational pattern at two key active sites in the SERA proteins-were also seen to be useful supplements to standard "bootstrap" analysis for inferred topologies.

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Interpretability and power of genome-wide association studies can be increased by imputing unobserved genotypes, using a reference panel of individuals genotyped at higher marker density. For many markers, genotypes cannot be imputed with complete certainty, and the uncertainty needs to be taken into account when testing for association with a given phenotype. In this paper, we compare currently available methods for testing association between uncertain genotypes and quantitative traits. We show that some previously described methods offer poor control of the false-positive rate (FPR), and that satisfactory performance of these methods is obtained only by using ad hoc filtering rules or by using a harsh transformation of the trait under study. We propose new methods that are based on exact maximum likelihood estimation and use a mixture model to accommodate nonnormal trait distributions when necessary. The new methods adequately control the FPR and also have equal or better power compared to all previously described methods. We provide a fast software implementation of all the methods studied here; our new method requires computation time of less than one computer-day for a typical genome-wide scan, with 2.5 M single nucleotide polymorphisms and 5000 individuals.

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Background and aims Recent studies have adopted a broad definition of Sapindaceae that includes taxa traditionally placed in Aceraceae and Hippocastanaceae, achieving monophyly but yielding a family difficult to characterize and for which no obvious morphological synapomorphy exists. This expanded circumscription was necessitated by the finding that the monotypic, temperate Asian genus Xanthoceras, historically placed in Sapindaceae tribe Harpullieae, is basal within the group. Here we seek to clarify the relationships of Xanthoceras based on phylogenetic analyses using a dataset encompassing nearly 3/4 of sapindaceous genera, comparing the results with information from morphology and biogeography, in particular with respect to the other taxa placed in Harpullieae. We then re-examine the appropriateness of maintaining the current broad, morphologically heterogeneous definition of Sapindaceae and explore the advantages of an alternative family circumscription. Methods Using 243 samples representing 104 of the 142 currently recognized genera of Sapindaceae s. lat. (including all in Harpullieae), sequence data were analyzed for nuclear (ITS) and plastid (matK, rpoB, trnD-trnT, trnK-matK, trnL-trnF and trnS-trnG) markers, adopting the methodology of a recent family-wide study, performing single-gene and total evidence analyses based on maximum likelihood (ML) and maximum parsimony (MP) criteria, and applying heuristic searches developed for large datasets, viz, a new strategy implemented in RAxML (for ML) and the parsimony ratchet (for MP). Bootstrap analyses were performed for each method to test for congruence between markers. Key results Our findings support earlier suggestions that Harpullieae are polyphyletic: Xanthoceras is confirmed as sister to all other sampled taxa of Sapindaceae s. lat.; the remaining members belong to three other clades within Sapindaceae s. lat., two of which correspond respectively to the groups traditionally treated as Aceraceae and Hippocastanaceae, together forming a clade sister to the largely tropical Sapindaceae s. str., which is monophyletic and morphologically coherent provided Xanthoceras is excluded. Conclusion To overcome the difficulties of a broadly circumscribed Sapindaceae, we resurrect the historically recognized temperate families Aceraceae and Hippocastanaceae, and describe a new family, Xanthoceraceae, thus adopting a monophyletic and easily characterized circumscription of Sapindaceae nearly identical to that used for over a century.