Optimal Asymptotic Properties of Maximum Likelihood Estimators of Parameters of Some Econometric Models PDF Download
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Author: Mary Kathleen Vickers
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ISBN:
Category : Asymptotes
Languages : en
Pages : 312
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Book Description
Four theorems are proven, which simplify the application to econometric models of Weiss's theorem on asymptotic properties of maximum likelihood estimators in nonstandard cases. The theorems require, roughly: the uniform convergence in any compact sets of the unknown parameters of the expection of the Hessian matrix of the log likelihood function; and the uniform convergence to 0 in the same sense of the variance of the same quantities. The fourth theorem allows one to conclude that the optimal properties hold on an image set of the parameters when the map satisfies certain smoothness conditions, and the first three theorems are satisfied for the original parameter set. These four theorems are applied to autoregressive models, nonlinear models, systems of equations, and probit and logit models to infer optimal asymptotic properties. (Author).
Author: Mary Kathleen Vickers
Publisher:
ISBN:
Category : Asymptotes
Languages : en
Pages : 312
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Book Description
Four theorems are proven, which simplify the application to econometric models of Weiss's theorem on asymptotic properties of maximum likelihood estimators in nonstandard cases. The theorems require, roughly: the uniform convergence in any compact sets of the unknown parameters of the expection of the Hessian matrix of the log likelihood function; and the uniform convergence to 0 in the same sense of the variance of the same quantities. The fourth theorem allows one to conclude that the optimal properties hold on an image set of the parameters when the map satisfies certain smoothness conditions, and the first three theorems are satisfied for the original parameter set. These four theorems are applied to autoregressive models, nonlinear models, systems of equations, and probit and logit models to infer optimal asymptotic properties. (Author).
Author: Mary Kathleen Vickers
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ISBN:
Category :
Languages : en
Pages : 140
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Author: Jeffrey M. Wooldridge
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ISBN:
Category : Econometrics
Languages : en
Pages : 544
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Author: Robert Ernest Tarone
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ISBN:
Category :
Languages : en
Pages : 190
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Author: Xingbai Xu
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ISBN:
Category :
Languages : en
Pages : 194
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Spatial econometrics has been obtained more and more attention in the recent years. The spatial autoregressive (SAR) model is one of the most widely used and studied models in spatial econometrics. So far, most studies have been focused on linear SAR models. However, some types of spatial or network data, for example, censored data or discrete choice data, are very common and useful, but not suitable to study by a linear SAR model. That is why I study an SAR Tobit model and an SAR binary choice model in this dissertation. Chapter 1 studies a Tobit model with spatial autoregressive interactions. We consider the maximum likelihood estimation (MLE) for this model and analyze asymptotic properties of the estimator based on the spatial near-epoch dependence (NED) of the dependent variable process generated from the model structure. We show that the MLE is consistent and asymptotically normally distributed. Monte Carlo experiments are performed to verify finite sample properties of the estimator. Chapter 2 extends the MLE estimation of the SAR Tobit model studied in Chapter 1 to distribution-free estimation. We examine the sieve MLE of the model, where the disturbances are i.i.d. with an unknown distribution. This model can be applied to spatial econometrics and social networks when data are censored. We show that related variables are spatial NED. An important contribution of this chapter is that I develop some exponential inequalities for spatial NED random fields, which are also useful in other semiparametric studies when spatial correlation exists. With these inequalities, we establish the consistency of the estimator. Asymptotic distributions of structural parameters of the model are derived from a functional central limit theorem and projection. Simulations show that the sieve MLE can improve the finite sample performance upon misspecified normal MLEs, in terms of reduction in the bias and standard deviation. As an empirical application, we examine the school district income surtax rates in Iowa. Our results show that the spatial spillover effects are significant, but they may be overestimated if disturbances are restricted to be normally distributed. Chapter 3 studies the method of simulated moments (MSM) estimation of a binary choice game model with network links, where the network peer effects are non-negative, and there might be only one or few networks in the sample. The proposed estimation method can be applied to studies with binary dependent variables in the fields of empirical IO, social network and spatial econometrics. The model might have multiple Nash equilibria. We assume that the maximum Nash equilibrium, which always exists and is strongly coalition-proof and Pareto optimal, is selected. The challenging econometric issues are the possible correlation among all dependent variables and the discontinuous functional form of our simulated moments. We overcome these challenges via the empirical process theory and derive the spatial NED of the dependent variable. We establish a criterion for an NED random field to be stochastically equicontinuous and we apply it to develop the consistency and asymptotic normality of the estimator. We examine computational issues and finite sample properties of the MSM by some Monte Carlo experiments.
Author: Stanford University. Department of Statistics
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ISBN:
Category : Time-series analysis
Languages : en
Pages : 318
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The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k> or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix with equal elements along its five central diagonals, and zeroes elsewhere. The asymptotic normality follows from a central limit theorem for normalized sums of random variables that are dependent of order k, where k tends to infinity with T. An alternative form of the estimator facilitates the calculations and the analysis of the role of k, without changing the asymptotic properties.
Author: Naoto Kunitomo
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ISBN:
Category : Econometrics
Languages : en
Pages : 208
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Author: Stanford University. Department of Statistics
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ISBN:
Category : Analysis of variance
Languages : en
Pages : 556
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The problem considered is the estimation of the parameters in the mixed model of the analysis of variance, assuming normality of the random effects and errors. Both asymptotic properties of such estimates as the size of the design increases and numerical procedures for their calculation are discussed. Estimation is carried out by the method of maximum likelihood. It is shown that there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal and asymptotically efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix as the size of the design increases. This is accomplished using a Taylor series expansion of the log-likelihood. (Modified author abstract).
Author: R. D. H. Heijmans
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Author: R. D. H. Heijmans
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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