Semiparametric IV Estimation with Parameter Dependent Instruments

1992 ◽  
Vol 8 (3) ◽  
pp. 403-406
Author(s):  
Paul Rilstone
Keyword(s):  
Nonparametric Estimation ◽  
Method Of Moments ◽  
Conditional Expectation ◽  
Asymptotic Efficiency ◽  
Functional Form ◽  
Moment Equations ◽  
Unknown Parameters ◽  
Iv Estimation ◽  
Sample Moment ◽  
Parameter Dependent

A well-known result in the method of moments literature is that the efficient instruments for the estimation of a model are functions of the conditional expectation of its gradient. Some recent studies have suggested the nonparametric estimation of these instruments when they are of unknown functional form. When these instruments in turn depend on the unknown parameters it has been suggested that these be replaced by preliminary consistent estimates. It is shown here that solving the sample moment equations simultaneously over the instruments and the residuals of the model will generally produce the same asymptotic efficiency and avoid the disadvantages inherent with the use of preliminary estimates.

Adaptive Controller and Observer Design for a Class of Nonlinear Systems

2005 ◽  
Vol 128 (3) ◽  
pp. 712-717 ◽  
Author(s):  
Yongliang Zhu ◽  
Prabhakar R. Pagilla
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Adaptive Controller ◽  
Observer Design ◽  
Dynamic Friction ◽  
Unknown Parameters ◽  
Single Link ◽  
Suitable Form ◽  
Parameter Dependent

Design of a stable adaptive controller and observer for a class of nonlinear systems that contain product of unmeasurable states and unknown parameters is considered. The nonlinear system is cast into a suitable form based on which a stable adaptive controller and observer are designed using a parameter dependent Lyapunov function. The class of nonlinear systems considered is practically relevant; mechanical systems with dynamic friction fall into this category. Experimental results on a single-link mechanical system with dynamic friction are shown for the proposed design.

scholarly journals Mixture of Lindley and Inverse Weibull Distributions: Properties and Estimation

2021 ◽  
Vol 20 ◽  
pp. 134-143
Author(s):  
A. S. Al-Moisheer ◽  
A. F. Daghestani ◽  
K. S. Sultan
Keyword(s):  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Weibull Distributions ◽  
Unknown Parameters ◽  
Data Application ◽  
Rate Functions ◽  
And Behavior

In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.

scholarly journals Instrumental Variables and GMM: Estimation and Testing

2003 ◽  
Vol 3 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Christopher F. Baum ◽  
Mark E. Schaffer ◽  
Steven Stillman
Keyword(s):  
Instrumental Variables ◽  
Method Of Moments ◽  
Diagnostic Tests ◽  
Generalized Method Of Moments ◽  
Test Procedures ◽  
Gmm Estimation ◽  
Iv Estimation ◽  
Gmm Estimates

We discuss instrumental variables (IV) estimation in the broader context of the generalized method of moments (GMM), and describe an extended IV estimation routine that provides GMM estimates as well as additional diagnostic tests. Stand-alone test procedures for heteroskedasticity, overidentification, and endogeneity in the IV context are also described.

Uncertain Circuit Equation

2021 ◽  
Vol 14 (03) ◽  
Author(s):  
Yang Liu
Keyword(s):  
Differential Equation ◽  
Method Of Moments ◽  
Time Domain ◽  
Electrical Circuit ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Liu Process ◽  
The Time Domain ◽  
Steady State Solutions ◽  
Transient And Steady State

Differential equation is a powerful tool for investigating the transient and steady-state solutions of electrical circuit in the time domain. By considering the noise in actual circuit system, this paper first presents an uncertain circuit equation, which is a type of differential equation driven by Liu process. Then the solution of uncertain circuit equation and the inverse uncertainty distribution of solution are derived. Following that, two applications of solution are provided as well. Based on the observations, the method of moments is used to estimate the unknown parameters in uncertain circuit equation. In addition, a paradox for stochastic circuit equation is also given.

scholarly journals Re-estimating the relationship between inequality and growth

2018 ◽  
Vol 71 (4) ◽  
pp. 824-847
Author(s):  
Nathalie Scholl ◽  
Stephan Klasen
Keyword(s):  
Functional Form ◽  
Positive Association ◽  
Transition Countries ◽  
Special Role ◽  
Significant Positive Association ◽  
Data Set ◽  
Full Sample ◽  
Iv Estimation ◽  
The Relationship

Abstract In this paper, we revisit the inequality–growth relationship using an enhanced panel data set with improved inequality data. We explicitly take into account the special role of transition (post-Soviet) countries and add an instrumental variable (IV) estimation to add a causal interpretation to our findings. Our analysis is based on the specification used by Forbes in her 2000 paper, but we also address functional form concerns raised by Banerjee and Duflo three years later. We arrive at three main findings: First, the significant positive association between inequality and economic growth in the full sample is entirely driven by transition countries. Second, this relationship in transition countries is not robust to the inclusion of separate time effects. Lastly, it appears that this association is not causal but rather driven by the particular timing of the transition. Results from IV estimation confirm our interpretation of the observed positive relationship in the overall sample as non-causal.

Grouping corrections and maximum likelihood equations

1950 ◽  
Vol 46 (1) ◽  
pp. 106-110 ◽  
Author(s):  
D. V. Lindley
Keyword(s):  
Maximum Likelihood ◽  
Method Of Moments ◽  
Population Parameter ◽  
Normal Curve ◽  
Inference Method ◽  
Inference Problem ◽  
Sample Moment ◽  
Continuous Population

1. Any mention of the word ‘grouping’ immediately brings to a statistician's mind the Sheppard corrections. These are usually used to make inferences about the underlying ungrouped population from observations made on the grouped population, but it is important to realize that, as stated and proved, they have nothing to do with sampling or inference and are merely expressions for the moments of one population in terms of the moments of another population derived from it. They can only be used for the inference problem when allied to the method of moments. This method, as formulated by K. Pearson, consists in taking for θ* the estimate of the population parameter θ, the same function of the sample moments mi that θ is of the population moments μi, each mi being an estimate of the corresponding μi. If the population is grouped the mi are estimates of the , the grouped population moments, so we require θ as a function of the to apply Pearson's method. This can be done since θ is known as a function of the µi and the µi are known as functions of the by the corrections. Use of the Sheppard corrections with any other inference method, even when this method, when applied to the continuous population, yields an estimate which is a sample moment, so far as I am aware, has not been examined except for the normal curve.

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