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Moments Estimators (moment + estimator)

Distribution by Scientific Domains

Mathematics and Statistics	71%

Selected Abstracts

Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population

BIOMETRICS, Issue 4 2007
Louis-Paul Rivest
Summary This article revisits Chao's (1989, Biometrics45, 427,438) lower bound estimator for the size of a closed population in a mark,recapture experiment where the capture probabilities vary between animals (model Mh). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (Mth) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for Mth. Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment. [source]

Estimation in integer-valued moving average models

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2001
Kurt Brännäs
Abstract The paper presents new characterizations of the integer-valued moving average model. For four model variants, we give moments and probability generating functions. Yule,Walker and conditional least-squares estimators are obtained and studied by Monte Carlo simulation. A new generalized method of moment estimator based on probability generating functions is presented and shown to be consistent and asymptotically normal. The small sample performance is in some instances better than those of alternative estimators. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Identifiability and Estimation of Causal Effects in Randomized Trials with Noncompliance and Completely Nonignorable Missing Data

BIOMETRICS, Issue 3 2009
Hua Chen
Summary In this article, we first study parameter identifiability in randomized clinical trials with noncompliance and missing outcomes. We show that under certain conditions the parameters of interest are identifiable even under different types of completely nonignorable missing data: that is, the missing mechanism depends on the outcome. We then derive their maximum likelihood and moment estimators and evaluate their finite-sample properties in simulation studies in terms of bias, efficiency, and robustness. Our sensitivity analysis shows that the assumed nonignorable missing-data model has an important impact on the estimated complier average causal effect (CACE) parameter. Our new method provides some new and useful alternative nonignorable missing-data models over the existing latent ignorable model, which guarantees parameter identifiability, for estimating the CACE in a randomized clinical trial with noncompliance and missing data. [source]

MSM Estimators of European Options on Assets with Jumps

MATHEMATICAL FINANCE, Issue 2 2001
João Amaro de Matos
This paper shows that, under some regularity conditions, the method of simulated moments estimator of European option pricing models developed by Bossaerts and Hillion (1993) can be extended to the case where the prices of the underlying asset follow Lévy processes, which allow for jumps, with no losses on their asymptotic properties, still allowing for the joint test of the model. [source]

The statistics of refractive error maps: managing wavefront aberration analysis without Zernike polynomials

OPHTHALMIC AND PHYSIOLOGICAL OPTICS, Issue 3 2009
D. Robert Iskander
Abstract The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps. [source]

Covariate Adjusted Correlation Analysis with Application to,FMR1,Premutation Female Carrier Data

BIOMETRICS, Issue 3 2009
Damla, entürk
Summary Motivated by molecular data on female premutation carriers of the fragile X mental retardation 1 (FMR1) gene, we present a new method of covariate adjusted correlation analysis to examine the association of messenger RNA (mRNA) and number of CGG repeat expansion in the,FMR1,gene. The association between the molecular variables in female carriers needs to adjust for activation ratio (ActRatio), a measure which accounts for the protective effects of one normal X chromosome in females carriers. However, there are inherent uncertainties in the exact effects of ActRatio on the molecular measures of interest. To account for these uncertainties, we develop a flexible adjustment that accommodates both additive and multiplicative effects of ActRatio nonparametrically. The proposed adjusted correlation uses local conditional correlations, which are local method of moments estimators, to estimate the Pearson correlation between two variables adjusted for a third observable covariate. The local method of moments estimators are averaged to arrive at the final covariate adjusted correlation estimator, which is shown to be consistent. We also develop a test to check the nonparametric joint additive and multiplicative adjustment form. Simulation studies illustrate the efficacy of the proposed method. (Application to,FMR1,premutation data on 165 female carriers indicates that the association between mRNA and CGG repeat after adjusting for ActRatio is stronger.) Finally, the results provide independent support for a specific jointly additive and multiplicative adjustment form for ActRatio previously proposed in the literature. [source]

Measurement Error in a Random Walk Model with Applications to Population Dynamics

BIOMETRICS, Issue 4 2006
John Staudenmayer
Summary Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets. [source]