Normality under uncertainty

Consider the demand for a good whose consumption be chosen prior to the resolution of uncertainty regarding income. How do changes in the distribution of income affect the demand for this good? In this paper we show that normality, is sufficient to guarantee that consumption increases of the Radon-Nikodym derivative of the new distribution with respect to the old is non-decreasing in the whole domain. However, if only first order stochastic dominance is assumed more structure must be imposed on preferences to guanantee the validity of the result. Finally a converse of the first result also obtains. If the change in measure is characterized by non-decreasing Radon-Nicodyn derivative, consumption of such a good will always increase if and only if the good is normal.

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.

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to theproblem of nondata aided symbol-timing estimation for linearmodulations. The study is performed under the unconditionalmaximum likelihood framework where the carrier-frequencyerror is included as a nuisance parameter in the mathematicalderivation. The second-order moments of the received signal arefound to be the sufficient statistics for the problem at hand and theyallow the provision of a robust performance in the presence of acarrier-frequency error uncertainty. We particularly focus on theexploitation of the cyclostationary property of linear modulations.This enables us to derive simple and closed-form symbol-timingestimators which are found to be based on the well-known squaretiming recovery method by Oerder and Meyr. Finally, we generalizethe OM method to the case of linear modulations withoffset formats. In this case, the square-law nonlinearity is foundto provide not only the symbol-timing but also the carrier-phaseerror.

Non-monotone insurance contracts and their empirical consequences

The goal of this paper is to show the possibility of a non-monotone relation between coverage ans risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuous parameter which is correlated with lenience and for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cosr of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and iplies a positive correlation between overage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the SCP be broken, but also the monotonocity of contracts, i.e., the prediction that high (low) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case there are some coverage levels associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation between coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to desentangle single crossing ans non single croosing under an ex-post zero correlation result: the monotonicity of coverage as a function os riskiness. Since by controlling for risk aversion (no asymmetric information), coverage is monotone function of riskiness, this also fives a test for asymmetric information. Finally, we relate this theoretical results to empirical tests in the recent literature, specially the Dionne, Gouruéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variables (asymmetric information) can bias the sign of the correlation of equilibrium variables conditioning on all observable variables. We show that this may be the case when the omitted variables have a non-monotonic relation with the observable ones. Moreover, because this non-dimensional does not capture this deature. Hence, our main results is to point out the importance of the SPC in testing predictions of the hidden information models.

Essays on asymmetric information problems without the single-crossing property: applications to corporate finance

The objective of this dissertation is to re-examine classical issues in corporate finance, applying a new analytical tool. The single-crossing property, also called Spence-irrlees condition, is not required in the models developed here. This property has been a standard assumption in adverse selection and signaling models developed so far. The classical papers by Guesnerie and Laffont (1984) and Riley (1979) assume it. In the simplest case, for a consumer with a privately known taste, the single-crossing property states that the marginal utility of a good is monotone with respect to the taste. This assumption has an important consequence to the result of the model: the relationship between the private parameter and the quantity of the good assigned to the agent is monotone. While single crossing is a reasonable property for the utility of an ordinary consumer, this property is frequently absent in the objective function of the agents for more elaborate models. The lack of a characterization for the non-single crossing context has hindered the exploration of models that generate objective functions without this property. The first work that characterizes the optimal contract without the single-crossing property is Araújo and Moreira (2001a) and, for the competitive case, Araújo and Moreira (2001b). The main implication is that a partial separation of types may be observed. Two sets of disconnected types of agents may choose the same contract, in adverse selection problems, or signal with the same levei of signal, in signaling models.

Non-monotone insurence contracts and their empirical consequences

The goal of t.his paper is to show the possibility of a non-monot.one relation between coverage and risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuou.'l parameter which is correlated with lenience and, for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cost of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and implies a positive correlation between coverage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the sep be broken, but also the monotonicity of contracts, i.e., the prediction that high (Iow) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case t,here are some coverage leveIs associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation bet,ween coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to disentangle single crossing and non single crossing under an ex-post zero correlation result: the monotonicity of coverage as a function of riskiness. Since by controlling for risk aversion (no asymmetric informat, ion), coverage is a monotone function of riskiness, this also gives a test for asymmetric information. Finally, we relate this theoretical results to empirica! tests in the recent literature, specially the Dionne, Gouriéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variabIes (asymmetric information) can bias the sign of the correlation of equilibrium variabIes conditioning on ali observabIe variabIes. We show that this may be t,he case when the omitted variabIes have a non-monotonic reIation with t,he observable ones. Moreover, because this non-monotonic reIat,ion is deepIy reIated with the failure of the SCP in one-dimensional screening problems, the existing lit.erature on asymmetric information does not capture t,his feature. Hence, our main result is to point Out the importance of t,he SCP in testing predictions of the hidden information models.

Monotone Constrained Tensor-product B-spline with application to screening studies

When different markers are responsive to different aspects of a disease, combination of multiple markers could provide a better screening test for early detection. It is also resonable to assume that the risk of disease changes smoothly as the biomarker values change and the change in risk is monotone with respect to each biomarker. In this paper, we propose a boundary constrained tensor-product B-spline method to estimate the risk of disease by maximizing a penalized likelihood. To choose the optimal amount of smoothing, two scores are proposed which are extensions of the GCV score (O'Sullivan et al. (1986)) and the GACV score (Ziang and Wahba (1996)) to incorporate linear constraints. Simulation studies are carried out to investigate the performance of the proposed estimator and the selection scores. In addidtion, sensitivities and specificities based ona pproximate leave-one-out estimates are proposed to generate more realisitc ROC curves. Data from a pancreatic cancer study is used for illustration.

Smooth Estimation of a Monotone Density

We investigate the interplay of smoothness and monotonicity assumptions when estimating a density from a sample of observations. The nonparametric maximum likelihood estimator of a decreasing density on the positive half line attains a rate of convergence at a fixed point if the density has a negative derivative. The same rate is obtained by a kernel estimator, but the limit distributions are different. If the density is both differentiable and known to be monotone, then a third estimator is obtained by isotonization of a kernel estimator. We show that this again attains the rate of convergence and compare the limit distributors of the three types of estimators. It is shown that both isotonization and smoothing lead to a more concentrated limit distribution and we study the dependence on the proportionality constant in the bandwidth. We also show that isotonization does not change the limit behavior of a kernel estimator with a larger bandwidth, in the case that the density is known to have more than one derivative.

Property Condition Disclosure Law: Why Did States Mandate 'Seller Tell All'?

Thirty-six US states have already enacted some form of seller's property condition disclosure law. At a time when there is a movement in this direction nationally, this paper attempts to ascertain the factors that lead states to adopt disclosure law. Motivation for the study stems from the fact that not all states have yet adopted the law, and states that have enacted the law have done so in different years. The analytical structure employs hazard models, using a unique set of economic and institutional attributes for a panel of 50 US States spanning 21 years, from 1984 to 2004. The proportional hazard analysis of law adoption reveals that greater number of disciplinary actions tends to favor passage of the law. Greater broker supervision, implying generally higher awareness among real estate agents, seems to have a negative impact on the likelihood of a state adopting a property condition disclosure law.

Maximum likelihood estimation of new state space models for operational modal analysis

The modal analysis of a structural system consists on computing its vibrational modes. The experimental way to estimate these modes requires to excite the system with a measured or known input and then to measure the system output at different points using sensors. Finally, system inputs and outputs are used to compute the modes of vibration. When the system refers to large structures like buildings or bridges, the tests have to be performed in situ, so it is not possible to measure system inputs such as wind, traffic, . . .Even if a known input is applied, the procedure is usually difficult and expensive, and there are still uncontrolled disturbances acting at the time of the test. These facts led to the idea of computing the modes of vibration using only the measured vibrations and regardless of the inputs that originated them, whether they are ambient vibrations (wind, earthquakes, . . . ) or operational loads (traffic, human loading, . . . ). This procedure is usually called Operational Modal Analysis (OMA), and in general consists on to fit a mathematical model to the measured data assuming the unobserved excitations are realizations of a stationary stochastic process (usually white noise processes). Then, the modes of vibration are computed from the estimated model. The first issue investigated in this thesis is the performance of the Expectation- Maximization (EM) algorithm for the maximum likelihood estimation of the state space model in the field of OMA. The algorithm is described in detail and it is analysed how to apply it to vibration data. After that, it is compared to another well known method, the Stochastic Subspace Identification algorithm. The maximum likelihood estimate enjoys some optimal properties from a statistical point of view what makes it very attractive in practice, but the most remarkable property of the EM algorithm is that it can be used to address a wide range of situations in OMA. In this work, three additional state space models are proposed and estimated using the EM algorithm: • The first model is proposed to estimate the modes of vibration when several tests are performed in the same structural system. Instead of analyse record by record and then compute averages, the EM algorithm is extended for the joint estimation of the proposed state space model using all the available data. • The second state space model is used to estimate the modes of vibration when the number of available sensors is lower than the number of points to be tested. In these cases it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors). Here, the proposed state space model and the EM algorithm are used to estimate the modal parameters taking into account the data of all setups. • And last, a state space model is proposed to estimate the modes of vibration in the presence of unmeasured inputs that cannot be modelled as white noise processes. In these cases, the frequency components of the inputs cannot be separated from the eigenfrequencies of the system, and spurious modes are obtained in the identification process. The idea is to measure the response of the structure corresponding to different inputs; then, it is assumed that the parameters common to all the data correspond to the structure (modes of vibration), and the parameters found in a specific test correspond to the input in that test. The problem is solved using the proposed state space model and the EM algorithm. Resumen El análisis modal de un sistema estructural consiste en calcular sus modos de vibración. Para estimar estos modos experimentalmente es preciso excitar el sistema con entradas conocidas y registrar las salidas del sistema en diferentes puntos por medio de sensores. Finalmente, los modos de vibración se calculan utilizando las entradas y salidas registradas. Cuando el sistema es una gran estructura como un puente o un edificio, los experimentos tienen que realizarse in situ, por lo que no es posible registrar entradas al sistema tales como viento, tráfico, . . . Incluso si se aplica una entrada conocida, el procedimiento suele ser complicado y caro, y todavía están presentes perturbaciones no controladas que excitan el sistema durante el test. Estos hechos han llevado a la idea de calcular los modos de vibración utilizando sólo las vibraciones registradas en la estructura y sin tener en cuenta las cargas que las originan, ya sean cargas ambientales (viento, terremotos, . . . ) o cargas de explotación (tráfico, cargas humanas, . . . ). Este procedimiento se conoce en la literatura especializada como Análisis Modal Operacional, y en general consiste en ajustar un modelo matemático a los datos registrados adoptando la hipótesis de que las excitaciones no conocidas son realizaciones de un proceso estocástico estacionario (generalmente ruido blanco). Posteriormente, los modos de vibración se calculan a partir del modelo estimado. El primer problema que se ha investigado en esta tesis es la utilización de máxima verosimilitud y el algoritmo EM (Expectation-Maximization) para la estimación del modelo espacio de los estados en el ámbito del Análisis Modal Operacional. El algoritmo se describe en detalle y también se analiza como aplicarlo cuando se dispone de datos de vibraciones de una estructura. A continuación se compara con otro método muy conocido, el método de los Subespacios. Los estimadores máximo verosímiles presentan una serie de propiedades que los hacen óptimos desde un punto de vista estadístico, pero la propiedad más destacable del algoritmo EM es que puede utilizarse para resolver un amplio abanico de situaciones que se presentan en el Análisis Modal Operacional. En este trabajo se proponen y estiman tres modelos en el espacio de los estados: • El primer modelo se utiliza para estimar los modos de vibración cuando se dispone de datos correspondientes a varios experimentos realizados en la misma estructura. En lugar de analizar registro a registro y calcular promedios, se utiliza algoritmo EM para la estimación conjunta del modelo propuesto utilizando todos los datos disponibles. • El segundo modelo en el espacio de los estados propuesto se utiliza para estimar los modos de vibración cuando el número de sensores disponibles es menor que vi Resumen el número de puntos que se quieren analizar en la estructura. En estos casos es usual realizar varios ensayos cambiando la posición de los sensores de un ensayo a otro (múltiples configuraciones de sensores). En este trabajo se utiliza el algoritmo EM para estimar los parámetros modales teniendo en cuenta los datos de todas las configuraciones. • Por último, se propone otro modelo en el espacio de los estados para estimar los modos de vibración en la presencia de entradas al sistema que no pueden modelarse como procesos estocásticos de ruido blanco. En estos casos, las frecuencias de las entradas no se pueden separar de las frecuencias del sistema y se obtienen modos espurios en la fase de identificación. La idea es registrar la respuesta de la estructura correspondiente a diferentes entradas; entonces se adopta la hipótesis de que los parámetros comunes a todos los registros corresponden a la estructura (modos de vibración), y los parámetros encontrados en un registro específico corresponden a la entrada en dicho ensayo. El problema se resuelve utilizando el modelo propuesto y el algoritmo EM.

Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

Responses in carcass lean pH at 24 hours post-mortem in lines of Large White pigs selected for growth rate on a fixed ration over a set time

A restricted maximum likelihood analysis applied to an animal model showed no significant differences (P > 0.05) in pH value of the longissimus dorsi measured at 24 h post-mortem (pH24) between high and low lines of Large White pigs selected over 4 years for post-weaning growth rate on restricted feeding. Genetic and phenotypic correlations between pH24 and production and carcass traits were estimated using all performance testing records combined with the pH24 measurements (5.05–7.02) on slaughtered animals. The estimate of heritability for pH24 was moderate (0.29 ± 0.18). Genetic correlations between pH24 and production or carcass composition traits, except for ultrasonic backfat (UBF), were not significantly different from zero. UBF had a moderate, positive genetic correlation with pH24 (0.24 ± 0.33). These estimates of genetic correlations affirmed that selection for increased growth rate on restricted feeding is likely to result in limited changes in pH24 and pork quality since the selection does not put a high emphasis on reduced fatness.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

Mapping the likelihood of foot-and-mouth disease introduction along the border between Brazil and Paraguay.

The objective of this work was to apply fuzzy majority multicriteria group decision?making to determine risk areas for foot?and?mouth disease (FMD) introduction along the border between Brazil and Paraguay. The study was conducted in three municipalities in the state of Mato Grosso do Sul, Brazil, located along the border with Paraguay. Four scenarios were built, applying the following linguistic quantifiers to describe risk factors: few, half, many, and most. The three criteria considered to be most likely to affect the vulnerability to introduction of FMD, according to experts? opinions, were: the introduction of animals in the farm, the distance from the border, and the type of property settlements. The resulting maps show a strong spatial heterogeneity in the risk of FMD introduction. The used methodology brings out a new approach that can be helpful to policy makers in the combat and eradication of FMD.

Didanosine-loaded Chitosan Microspheres Optimized By Surface-response Methodology: A Modified Maximum Likelihood Classification" Approach Formulation For Reverse Transcriptase Inhibitors."

Didanosine-loaded chitosan microspheres were developed applying a surface-response methodology and using a modified Maximum Likelihood Classification. The operational conditions were optimized with the aim of maintaining the active form of didanosine (ddI), which is sensitive to acid pH, and to develop a modified and mucoadhesive formulation. The loading of the drug within the chitosan microspheres was carried out by ionotropic gelation technique with sodium tripolyphosphate (TPP) as cross-linking agent and magnesium hydroxide (Mg(OH)2) to assure the stability of ddI. The optimization conditions were set using a surface-response methodology and applying the Maximum Likelihood Classification, where the initial chitosan concentration, TPP and ddI concentration were set as the independent variables. The maximum ddI-loaded in microspheres (i.e. 1433mg of ddI/g chitosan), was obtained with 2% (w/v) chitosan and 10% TPP. The microspheres depicted an average diameter of 11.42μm and ddI was gradually released during 2h in simulated enteric fluid.