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).

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 Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

scholarly journals An Integrated Framework for the Inference of Viral Population History From Reconstructed Genealogies

Genetics ◽  
2000 ◽  
Vol 155 (3) ◽  
pp. 1429-1437
Author(s):  
Oliver G Pybus ◽  
Andrew Rambaut ◽  
Paul H Harvey
Keyword(s):  
Maximum Likelihood ◽  
Sequence Data ◽  
Demographic History ◽  
Population History ◽  
Maximum Likelihood Estimates ◽  
Viral Population ◽  
True Parameter ◽  
Subtype B ◽  
Exponential Growth Model ◽  
Parameter Values

Abstract We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.

Sign in / Sign up

Export Citation Format

Share Document