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.

European collaborative study of early-onset bipolar disorder: Evidence for genetic heterogeneity on 2q14 according to age at onset.

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.

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

Adaptively weighted maximum likelihood estimation of discrete distributions

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.

Cytogenetic response to imatinib in chronic myeloid leukaemia patients: concentration dependency and associated influences under field-conditions

Introduction: Imatinib, a first-line drug for chronic myeloid leukaemia (CML), has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations >=1000 ng/ml (Cmin) have been associated with improved molecular and complete cytogenetic response (CCyR). The pharmacological monitoring project of EUTOS (European Treatment and Outcome Study) was launched to validate retrospectively the correlation between Cmin and response in a large population of patients followed by central TDM in Bordeaux.¦Methods: 1898 CML patients with first TDM 0-9 years after imatinib initiation, providing cytogenetic data along with demographic and comedication (37%) information, were included. Individual Cmin, estimated by non-linear regression (NONMEM), was adjusted to initial standard dose (400 mg/day) and stratified at 1000 ng/ml. Kaplan-Meier estimates of overall cumulative CCyR rates (stratified by sex, age, comedication and Cmin) were compared using asymptotic logrank k-sample test for interval-censored data. Differences in Cmin were assessed by Wilcoxon test.¦Results: There were no significant differences in overall cumulative CCyR rates between Cmin strata, sex and comedication with P-glycoprotein inhibitors/inducers or CYP3A4 inhibitors (p >0.05). Lower rates were observed in 113 young patients <30 years (p = 0.037; 1-year rates: 43% vs 60% in older patients), as well as in 29 patients with CYP3A4 inducers (p = 0.001, 1-year rates: 40% vs 66% without). Higher rates were observed in 108 patients on organic-cation-transporter-1 (hOCT-1) inhibitors (p = 0.034, 1-year rates: 83% vs 56% without). Considering 1-year CCyR rates, a trend towards better response for Cmin above 1000 ng/ml was observed: 64% (95%CI: 60-69%) vs 59% (95%CI: 56-61%). Median Cmin (400 mg/day) was significantly reduced in male patients (732 vs 899ng/ml, p <0.001), young patients <30 years (734 vs 802 ng/ml, p = 0.037) and under CYP3A4 inducers (758 vs 859 ng/ml, p = 0.022). Under hOCT-1 inhibitors, Cmin was increased (939 vs 827 ng/ml, p = 0.038).¦Conclusion: Based on observational TDM data, the impact of imatinib Cmin >1000 ng/ml on CCyR was not salient. Young CML patients (<30 years) and patients taking CYP3A4 inducers probably need close monitoring and possibly higher imatinib doses, due to lower Cmin along with lower CCyR rates. Patients taking hOCT-1 inhibitors seem in contrast to have improved CCyR response rates. The precise role for imatinib TDM remains to be established prospectively.

Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

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.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Partial cricotracheal resection for congenital subglottic stenosis in children: the effect of concomitant anomalies.

OBJECTIVE: To review the surgical outcomes of partial cricotracheal resection in children with severe congenital subglottic stenosis and define the effect of concomitant anomalies or syndromes affecting outcome. METHODS: Forty-one children with subglottic stenosis of congenital and mixed (acquired on congenital) etiologies who underwent partial cricotracheal resection were identified from a prospectively collected database. Children with congenital subglottic stenosis and concomitant anomalies/syndromes were compared to children with congenital subglottic stenosis with no syndromes or concomitant anomalies. Operation-specific decannulation rates and complication rates were the primary outcome measures. We performed a two-sample test of proportion using the STATA-10 software for categorical variables to detect differences in proportions. Significance was set at p value<0.05. RESULTS: Twenty-seven (66%) of 41 children had concomitant anomalies/syndromes and 14 (34%) had congenital subglottic stenosis without concomitant anomalies/syndromes. Four patients needed revision surgery in the concomitant anomaly group and two patients needed revision surgery in the non concomitant anomaly group before achieving decannulation. The operation-specific decannulation rate in the concomitant anomaly group was 85% and 86% in the non anomaly group. When compared to children without concomitant anomaly, children with concomitant anomalies were more likely to have delayed decannulation following partial cricotracheal resection. However, this difference was not found to be statistically significant. The complication and operation-specific decannulation rates after partial cricotracheal resection were comparable to children without concomitant anomalies. Mortality rate was 11% (three of 27 patients) in the group with associated congenital anomalies or syndromes. Two patients succumbed to the primary pathology and one patient died due to tracheostomy-tube obstruction. There was no post-operative death in the non anomaly group. CONCLUSION: Partial cricotracheal resection can be done safely and effectively in children with concomitant anomalies/syndromes to achieve decannulation. The post-operative course may be prolonged but the decannulation and the complication rates are comparable to those children with congenital subglottic stenosis without concomitant anomalies.

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

Multicointegration, polynomial cointegration and I(2) cointegration with structural breaks. An application to the sustainability of the US external deficit

In this paper we model the multicointegration relation, allowing for one structural break. Since multicointegration is a particular case of polynomial or I(2) cointegration, our proposal can also be applied in these cases. The paper proposes the use of a residualbased Dickey-Fuller class of statistic that accounts for one known or unknown structural break. Finite sample performance of the proposed statistic is investigated by using Monte Carlo simulations, which reveals that the statistic shows good properties in terms of empirical size and power. We complete the study with an empirical application of the sustainability of the US external deficit. Contrary to existing evidence, the consideration of one structural break leads to conclude in favour of the sustainability of the US external deficit.

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.

Tuulivoimalan staattoripakan puristusrakenteen kehittäminen

Diplomityössä tutkittiin voidaanko tuulivoimalan generaattorin staattoripakan puristamisessa hyödyntää komposiittista rakenneratkaisua. Tyypillisesti generaattorissa staattorin teräslevyt puristetaan erilaisilla teräsrakenteilla toisiaan vasten. Tavoitteena oli selvittää, voidaanko puristavan komposiittirakenteen osana hyödyntää liimaliitosta tai laminoitua liitosta. Tarkoitus oli etsiä rakenteeseen soveltuva liima ja liimaliitoksen arvot tai laminoitu rakenne ja sille soveltuvat materiaalit ja suoritustapa. Työssä on perehdytty erilaisiin tuulivoimalatyyppeihin, sekä niissä käytettäviin kesto- ja vierasmagnetoituihin generaattorityyppeihin. Tämän lisäksi on tarkasteltu niissä käytettävien staattorien valmistusvaihtoehtoja ja syitä miksi niissä olevat teräslevyt on puristettava toisiaan vasten. Samalla on luotu katsaus nykyisin käytössä oleviin rakenteisiin, joilla puristus voidaan toteuttaa. Liimauksesta on käsitelty perusteoriaa, sekä seikkoja jotka vaikuttavat liimaliitoksen kestoon. Työssä tutkittavaan liitokseen soveltuvien liimojen ominaisuuksia on käsitelty. Myös laminoituun liitokseen jo aiemmin kovettuneeseen komposiittiin on perehdytty. Tutkittavaan rakenteeseen soveltuvia hartsi- ja lasikuitutyyppejä on esitelty. Komposiittien mekaaniseen liittämiseen on lyhyesti perehdytty. Työssä suoritettiin useita vetokokeita, joilla selvitettiin puristusrakenteen tutkimista varten valmistettujen koekappaleiden suurin vetokuormankesto. Vetokokeiden perusteella voitiin valita soveltuvin rakenne staattorin puristamiseksi.