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.

Accelerated failure time models with log-concave errors

2019 ◽  
Vol 23 (2) ◽  
pp. 251-268
Author(s):  
Ruixuan Liu ◽  
Zhengfei Yu
Keyword(s):  
Maximum Likelihood ◽  
Failure Time ◽  
Maximum Likelihood Estimates ◽  
Accelerated Failure Time ◽  
Time Data ◽  
Dimensional Parameter ◽  
Nonparametric Maximum Likelihood Estimator ◽  
Finite Dimensional ◽  
Accelerated Failure Time Models ◽  
Accelerated Failure

Summary We study accelerated failure time models in which the survivor function of the additive error term is log-concave. The log-concavity assumption covers large families of commonly used distributions and also represents the aging or wear-out phenomenon of the baseline duration. For right-censored failure time data, we construct semiparametric maximum likelihood estimates of the finite-dimensional parameter and establish the large sample properties. The shape restriction is incorporated via a nonparametric maximum likelihood estimator of the hazard function. Our approach guarantees the uniqueness of a global solution for the estimating equations and delivers semiparametric efficient estimates. Simulation studies and empirical applications demonstrate the usefulness of our method.

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.

On Updating Algorithms and Inference for Stochastic Point Processes

1975 ◽  
Vol 12 (S1) ◽  
pp. 239-259 ◽  
Author(s):  
D. Vere-Jones
Keyword(s):  
Stochastic Process ◽  
Maximum Likelihood ◽  
Stochastic Approximation ◽  
Approximation Theory ◽  
Point Processes ◽  
Maximum Likelihood Estimates ◽  
Doubly Stochastic ◽  
Stochastic Point Processes ◽  
Asymptotically Efficient ◽  
Estimation And Filtering

This paper is an attempt to interpret and extend, in a more statistical setting, techniques developed by D. L. Snyder and others for estimation and filtering for doubly stochastic point processes. The approach is similar to the Kalman-Bucy approach in that the updating algorithms can be derived from a Bayesian argument, and lead ultimately to equations which are similar to those occurring in stochastic approximation theory. In this paper the estimates are derived from a general updating formula valid for any point process. It is shown that almost identical formulae arise from updating the maximum likelihood estimates, and on this basis it is suggested that in practical situations the sequence of estimates will be consistent and asymptotically efficient. Specific algorithms are derived for estimating the parameters in a doubly stochastic process in which the rate alternates between two levels.

Note on some properties of maximum likelihood estimates

1949 ◽  
Vol 45 (4) ◽  
pp. 536-544 ◽  
Author(s):  
P. H. Diananda
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Unknown Parameter ◽  
Maximum Likelihood Estimates ◽  
Independent Observations

The properties of (1) consistency and (2) asymptotic normality of maximum likelihood estimates of one unknown parameter, for independent observations, have been discussed rigorously by Cramér ((1), p. 500) and Doob (2). These properties were first stated by Fisher (3).

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.

Asymptotic properties of intensity estimators for Poisson shot-noise processes

1991 ◽  
Vol 28 (03) ◽  
pp. 568-583
Author(s):  
Friedrich Liese ◽  
Volker Schmidt
Keyword(s):  
Asymptotic Normality ◽  
Stochastic Processes ◽  
Point Process ◽  
Shot Noise ◽  
Poisson Point Process ◽  
Asymptotic Properties ◽  
Weak Consistency ◽  
Long Run ◽  
Consistency And Asymptotic Normality ◽  
Poisson Shot Noise

Stochastic processes {X(t)} of the form X(t) = Σ n f(t – Tn ) are considered, where {Tn } is a stationary Poisson point process with intensity λ and f: R → R is an unknown response function. Conditions are obtained for weak consistency and asymptotic normality of estimators of λ based on long-run observations of {X(t)}.

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