scholarly journals GENERALIZATION OF GMM TO A CONTINUUM OF MOMENT CONDITIONS

2000 ◽  
Vol 16 (6) ◽  
pp. 797-834 ◽  
Author(s):  
Marine Carrasco ◽  
Jean-Pierre Florens
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Diffusion Processes ◽  
Generalized Method Of Moments ◽  
Efficient Estimation ◽  
Conditional Moment ◽  
Cross Sectional ◽  
Moment Conditions ◽  
Optimal Estimator ◽  
The Moment

This paper proposes a version of the generalized method of moments procedure that handles both the case where the number of moment conditions is finite and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its values in an interval. The objective function to minimize is then the norm of the moment conditions in a Hilbert space. The estimator is shown to be consistent and asymptotically normal. The optimal estimator is obtained by minimizing the norm of the moment conditions in the reproducing kernel Hilbert space associated with the covariance. We show an easy way to calculate this estimator. Finally, we study properties of a specification test using overidentifying restrictions. Results of this paper are useful in many instances where a continuum of moment conditions arises. Examples include efficient estimation of continuous time regression models, cross-sectional models that satisfy conditional moment restrictions, and scalar diffusion processes.

scholarly journals ON THE ASYMPTOTIC EFFICIENCY OF GMM

2013 ◽  
Vol 30 (2) ◽  
pp. 372-406 ◽  
Author(s):  
Marine Carrasco ◽  
Jean-Pierre Florens
Keyword(s):  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Asymptotic Variance ◽  
Inner Product ◽  
Method Of Moment ◽  
Conditional Moment ◽  
Moment Conditions ◽  
Gmm Estimator ◽  
The Moment ◽  
Semiparametric Efficiency Bound

The efficiency of the generalized method of moment (GMM) estimator is addressed by using a characterization of its variance as an inner product in a reproducing kernel Hilbert space. We show that the GMM estimator is asymptotically as efficient as the maximum likelihood estimator if and only if the true score belongs to the closure of the linear space spanned by the moment conditions. This result generalizes former ones to autocorrelated moments and possibly infinite number of moment restrictions. Second, we derive the semiparametric efficiency bound when the observations are known to be Markov and satisfy a conditional moment restriction. We show that it coincides with the asymptotic variance of the optimal GMM estimator, thus extending results by Chamberlain (1987,Journal of Econometrics34, 305–33) to a dynamic setting. Moreover, this bound is attainable using a continuum of moment conditions.

Level-Based Estimation of Dynamic Panel Models

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Gabriel Montes-Rojas ◽  
Walter Sosa-Escudero ◽  
Federico Zincenko
Keyword(s):  
Monte Carlo ◽  
Panel Data ◽  
Dynamic Panel Data ◽  
Data Models ◽  
Efficient Estimation ◽  
Panel Data Models ◽  
Dynamic Panel ◽  
Dynamic Panel Data Models ◽  
Moment Conditions ◽  
Optimal Estimator

AbstractThis paper develops an alternative estimator for linear dynamic panel data models based on parameterizing the covariances between covariates and unobserved time-invariant effects. A GMM framework is used to derive an optimal estimator based on moment conditions in levels, with no efficiency loss compared to the classic alternatives like (Arellano, M., and S. Bond. 1991. “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.” Review of Economic Studies 58 (2): 277–297), (Ahn, S. C., and P. Schmidt. 1995. “Efficient Estimation of Models for Dynamic Panel Data.” Journal of Econometrics 68 (1): 5–27) and (Ahn, S. C., and P. Schmidt. 1997. “Efficient Estimation of Dynamic Panel Data Models: Alternative Assumptions and Simplified Estimation.” Journal of Econometrics 76: 309–321). Still, we show analytically and by Monte Carlo simulations that the new procedure leads to efficiency improvements for certain data generating processes. The framework also leads to a very simple test for unobserved effects.

CONSISTENCY OF PLUG-IN ESTIMATORS OF UPPER CONTOUR AND LEVEL SETS

2011 ◽  
Vol 28 (2) ◽  
pp. 309-327 ◽  
Author(s):  
Neşe Yildiz
Keyword(s):  
Objective Function ◽  
Method Of Moments ◽  
Level Sets ◽  
Generalized Method Of Moments ◽  
Hausdorff Metric ◽  
Dimensional Parameter ◽  
Moment Conditions ◽  
Finite Dimensional ◽  
The Moment ◽  
Parameter Values

This paper studies the problem of estimating the set of finite-dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This paper also suggests extremum estimators that with probability approaching 1 agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. In particular, it is shown that the set of minimizers of the sample generalized method of moments (GMM) objective function is consistent for the set of minimizers of the population GMM objective function in Hausdorff metric.

scholarly journals Indirect Inference: Which Moments to Match?

Econometrics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 14 ◽  
Author(s):  
David Frazier ◽  
Eric Renault
Keyword(s):  
Structural Parameters ◽  
Generalized Method Of Moments ◽  
Estimation Procedure ◽  
Efficient Estimation ◽  
Indirect Inference ◽  
General Context ◽  
Moment Matching ◽  
Parameter Matching ◽  
The Moment ◽  
Two Step Estimation

The standard approach to indirect inference estimation considers that the auxiliary parameters, which carry the identifying information about the structural parameters of interest, are obtained from some recently identified vector of estimating equations. In contrast to this standard interpretation, we demonstrate that the case of overidentified auxiliary parameters is both possible, and, indeed, more commonly encountered than one may initially realize. We then revisit the “moment matching” and “parameter matching” versions of indirect inference in this context and devise efficient estimation strategies in this more general framework. Perhaps surprisingly, we demonstrate that if one were to consider the naive choice of an efficient Generalized Method of Moments (GMM)-based estimator for the auxiliary parameters, the resulting indirect inference estimators would be inefficient. In this general context, we demonstrate that efficient indirect inference estimation actually requires a two-step estimation procedure, whereby the goal of the first step is to obtain an efficient version of the auxiliary model. These two-step estimators are presented both within the context of moment matching and parameter matching.

scholarly journals EXISTENCE AND CHARACTERIZATION OF CONDITIONAL DENSITY PROJECTIONS

2015 ◽  
Vol 32 (4) ◽  
pp. 947-987 ◽  
Author(s):  
Ivana Komunjer ◽  
Giuseppe Ragusa
Keyword(s):  
Strong Duality ◽  
Efficient Estimation ◽  
Conditional Density ◽  
Conditional Moment ◽  
Simulation Based ◽  
Density Forecasting ◽  
Projection Problem ◽  
Moment Models ◽  
The Moment

In this paper we propose primitive conditions under which a projection of a conditional density onto a set defined by conditional moment restrictions exists and is unique. Moreover, we provide an analytic expression of the obtained projection. The range of applications where conditional density projections are used is wide. The derived results are potentially useful in a variety of areas including: semiparametric efficient estimation and optimal testing in (conditional) moment models, Bayesian prior determination and inference in semiparametric models, density forecasting, and simulation-based econometric analysis.Regarding existence, we propose three different combinations of assumptions that are all sufficient to show that the projection exists and is unique. The proposed conditions exhibit a clear trade off between restrictions put on the divergence between the conditional densities and on the moment function which defines the projection set. Depending on the nature of the application, the researcher can pick and choose which set of conditions to use. Our second set of results characterizes the projection. The expression for the projected density is new though not surprising given the previously obtained results for the unconditional case. The projection is characterized by the dual of the original projection problem. In establishing the strong duality, however, we work with a constraint qualification condition that is weaker than that used by Borwein and Lewis (1991a, 1992a, 1993 in their seminal work concerning the unconditional case.

scholarly journals Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data

2016 ◽  
Vol 20 (1) ◽  
Author(s):  
Kyungsub Lee
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Generalized Method Of Moments ◽  
Estimation Method ◽  
Stochastic Volatility Model ◽  
Variation Method ◽  
Moment Conditions ◽  
Volatility Model ◽  
Return Distributions ◽  
The Moment

AbstractWe discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model. We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with a generalized method of moments estimation based on the successive relation between realized moments and their lagged values.

scholarly journals Sensitivity analysis using approximate moment condition models

2021 ◽  
Vol 12 (1) ◽  
pp. 77-108 ◽  
Author(s):  
Timothy B. Armstrong ◽  
Michal Kolesár
Keyword(s):  
Generalized Method Of Moments ◽  
Moment Condition ◽  
Potential Bias ◽  
Moment Conditions ◽  
Gmm Estimator ◽  
Moment Selection ◽  
Weighting Matrix ◽  
Automobile Demand ◽  
The Moment ◽  
The One

We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.

Hubungan Antara Menyusui Dengan Involusi Uterus Pada Ibu Nifas Fisiologis Di RSIA Aura Syifa Kabupaten Kediri

1970 ◽  
Vol 5 (2) ◽  
pp. 64
Author(s):  
Eny Sendra ◽  
Dewi Indriani
Keyword(s):  
Breast Feeding ◽  
Sampling Technique ◽  
Chi Square ◽  
Cross Sectional ◽  
Fisher Test ◽  
Key Word ◽  
Chi Square Test ◽  
The Moment

Breast feeding is giving milk to be drunk to the baby from the breast. Uterus involution is a process how the uterus return to the condition back, before pregnanting after bearing. At the moment of suckling, happens a stimulus and brings the hormones out, such as oksitosin uses not only to stimulate some muscles constraction but also to stimulate the uterus, so that the process of uterus involution happens foster. According to the explanations above, the research aimed to know about the correlation between breast feeding and uterus involution. This research’s design was, cross sectional by the population of all childbirth mothers approximately 50 persons / month. By using accidental sampling technique we got 21 sample respondents. The place of research in RSIA Aura Syifa in Kediri Regency on 16th until 22nd of June 2009. From this research’s result, we got 14 persons (66,67%) with normal uterus involution, suckled in a good way, one person (4,67%) with normal uterus involution, suckled in a wrong way, 2 persons (9,52%) with abnormal uterus involution, suckled in a good way and 4 persons (19,05%) with abnormal uterus involution, suckled in a wrong way. Statistic test which used chi-square test, counted the probability frequency in advance, from that we got 3 columns with the score, less than 5, so that chi-square can not be continued and by doing exact fisher test, the score was 0,001. Because P with the grade mistake 0,05 smaller, so the conclusion was “Ho” is rejected, it meant “there was correlation between suckling and uterus involution”. Key Word : Breast feeding, uterus involution

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

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