CONSISTENCY AND ASYMPTOTIC NORMALITY OF SIEVE ML ESTIMATORS UNDER LOW-LEVEL CONDITIONS

2014 ◽  
Vol 30 (5) ◽  
pp. 1021-1076 ◽  
Author(s):  
Herman J. Bierens
Keyword(s):  
Asymptotic Normality ◽  
Density Function ◽  
Choice Model ◽  
Likelihood Estimation ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Low Level ◽  
Asymptotically Normal ◽  
Finite Dimensional ◽  
Image Position

This paper considers sieve maximum likelihood estimation of seminonparametric (SNP) models with an unknown density function as non-Euclidean parameter, next to a finite-dimensional parameter vector. The density function involved is modeled via an infinite series expansion, so that the actual parameter space is infinite-dimensional. It will be shown that under low-level conditions the sieve estimators of these parameters are consistent, and the estimators of the Euclidean parameters are$\sqrt N$asymptotically normal, given a random sample of sizeN. The latter result is derived in a different way than in the sieve estimation literature. It appears that this asymptotic normality result is in essence the same as for the finite dimensional case. This approach is motivated and illustrated by an SNP discrete choice model.

Regression for randomly sampled spatial series: the trigonometric case

1986 ◽  
Vol 23 (A) ◽  
pp. 275-289 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Point Process ◽  
Maximum Likelihood Estimates ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
Spatial Series ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Asymptotically Efficient

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

Regression for randomly sampled spatial series: the trigonometric case

1986 ◽  
Vol 23 (A) ◽  
pp. 275-289
Author(s):  
David R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Point Process ◽  
Maximum Likelihood Estimates ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
Spatial Series ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Asymptotically Efficient

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j } are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient. Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j } is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

scholarly journals A NOTE ON GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION OF SEMIPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS

2016 ◽  
Vol 33 (5) ◽  
pp. 1242-1258 ◽  
Author(s):  
Naoya Sueishi
Keyword(s):  
Empirical Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Unknown Parameters ◽  
Conditional Moment ◽  
Finite Dimensional ◽  
Dimensional Parameters ◽  
Image Position ◽  
Asymptotically Efficient ◽  
Moment Restriction

This paper proposes an empirical likelihood-based estimation method for semiparametric conditional moment restriction models, which contain finite dimensional unknown parameters and unknown functions. We extend the results of Donald, Imbens, and Newey (2003, Journal of Econometrics 117, 55–93) by allowing unknown functions to be included in the conditional moment restrictions. We approximate unknown functions by a sieve method and estimate the finite dimensional parameters and unknown functions jointly. We establish consistency and derive the convergence rate of the estimator. We also show that the estimator of the finite dimensional parameters is $\sqrt n$-consistent, asymptotically normally distributed, and asymptotically efficient.

SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR TRANSFORMATION MODELS UNDER CONDITIONAL QUANTILE RESTRICTION

2014 ◽  
Vol 32 (2) ◽  
pp. 458-497 ◽  
Author(s):  
Zhengyu Zhang
Keyword(s):  
Linear Transformation ◽  
Semiparametric Estimation ◽  
Transformation Model ◽  
Dimensional Parameter ◽  
Conditional Quantile ◽  
Infinite Dimensional ◽  
Linear Transformation Model ◽  
Partially Linear ◽  
Linear Transformation Models ◽  
Image Position

This article is concerned with semiparametric estimation of a partially linear transformation model under conditional quantile restriction with no parametric restriction imposed either on the link functional form or on the error term distribution. We describe for the finite-dimensional parameter a$\sqrt n$-consistent estimator which combines the features of Chen (2010)’s maximum integrated score estimator as well as Lee (2003)’s average quantile regression. We show the remaining two infinite-dimensional unknown functions in the model can be separately identified and propose estimators for these functions based on the marginal integration method. Furthermore, a simple approach is proposed to estimate the average partial quantile effect. Two important extensions, i.e., random censoring as well as estimating a transformation model with an endogenous regressor are also considered.

scholarly journals Maximum-likelihood estimation of the parameters of a four-parameter class of probability distributions

1988 ◽  
Vol 31 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Siegfried H. Lehnigk
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Initial Shape ◽  
Definition Of ◽  
Image Position

We shall concern ourselves with the class of continuous, four-parameter, one-sided probability distributions which can be characterized by the probability density function (pdf) classIt depends on the four parameters: shift c ∈ R, scale b > 0, initial shape p < 1, and terminal shape β > 0. For p ≦ 0, the definition of f(x) can be completed by setting f(c) = β/bΓ(β−1)>0 if p = 0, and f(c) = 0 if p < 0. For 0 < p < 1, f(x) remains undefined at x = c; f(x)↑ + ∞ as x↓c.

scholarly journals NONPARAMETRIC ESTIMATION OF SEMIPARAMETRIC TRANSFORMATION MODELS

2016 ◽  
Vol 33 (4) ◽  
pp. 839-873 ◽  
Author(s):  
Jean-Pierre Florens ◽  
Senay Sokullu
Keyword(s):  
Nonparametric Estimation ◽  
Asymptotic Properties ◽  
Transformation Models ◽  
Dimensional Parameter ◽  
Independence Assumption ◽  
Finite Dimensional ◽  
The Mean ◽  
Semiparametric Transformation ◽  
Image Position ◽  
Nonparametric Estimates

In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form:H(Y) =φ(Z) +X′β+UwhereH,φare unknown functions,βis an unknown finite-dimensional parameter vector and the variables (Y,Z) are endogenous. Identification of the model and asymptotic properties of the estimator are analyzed under the mean independence assumption between the error term and the instruments. We show that the estimators are consistent, and a$\sqrt N$-convergence rate and asymptotic normality for$\hat \beta$can be attained. The simulations demonstrate that our nonparametric estimates fit the data well.

scholarly journals Infinite dimensional representations of

1990 ◽  
Vol 32 (1) ◽  
pp. 25-33 ◽  
Author(s):  
A. Dean ◽  
F. Zorzitto
Keyword(s):  
Dynkin Diagram ◽  
Finite Dimension ◽  
Vector Spaces ◽  
Closed Field ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Linear Maps ◽  
Image Position ◽  
Subspace Problem ◽  
Extended Dynkin Diagram

By a representation of the extended Dynkin diagram we shall mean a list of 5 vector spaces P, E1, E2, E3, E4 over an algebraically closed field K, and 4 linear maps a1, a2, a3, a4 as shown.The spaces need not be of finite dimension.In their solution of the 4-subspace problem [6], Gelfand and Ponomarev have classified such representations when the spaces are finite dimensional. A representation like (1) can also be viewed as a module over the K-algebra R4 consisting of all 5 × 5 matrices having zeros off the first row and off the main diagonal.

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