Some comments concerning a curious singularity

1979 ◽  
Vol 16 (2) ◽  
pp. 440-444 ◽  
Author(s):  
Paul D. Feigin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Discrete Time ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimation ◽  
Continuous Observation ◽  
Time Model ◽  
Limit Theory ◽  
Discrete Time Model ◽  
True Value

Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt. Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.

Some comments concerning a curious singularity

1979 ◽  
Vol 16 (02) ◽  
pp. 440-444 ◽  
Author(s):  
Paul D. Feigin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Discrete Time ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimation ◽  
Continuous Observation ◽  
Time Model ◽  
Limit Theory ◽  
Discrete Time Model ◽  
True Value

Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt . Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.

scholarly journals On Polarization Dependent Equalization in 5G mmWave Systems

2019 ◽  
Author(s):  
Farah Arabian ◽  
Michael Rice
Keyword(s):  
Maximum Likelihood ◽  
Discrete Time ◽  
Matched Filter ◽  
Time Model ◽  
Discrete Time Model ◽  
Selection Diversity ◽  
Optimum Combining ◽  
Linear Equalizer ◽  
Frequency Selective ◽  
Frequency Selective Channels

<p>The outputs of a cross-polarized antenna can produce a pair of different parallel frequency-selective channels. The optimum combining strategy is derived from maximum likelihood principles and used to define an equivalent discrete-time model. The simulated post-equalizer BER results show that optimum combining produces the best results, selection diversity can provide reasonably good results, and that both optimum combining and selection diversity can be superior to linear equalizer operating on the </p> <p>channel obtained by combining the antenna outputs before applying a channel matched filter.</p> <br>

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (4) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Maximum likelihood estimation for continuous-time stochastic processes

1976 ◽  
Vol 8 (4) ◽  
pp. 712-736 ◽  
Author(s):  
Paul David Feigin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Processes ◽  
Continuous Time ◽  
Asymptotic Theory ◽  
Likelihood Estimation ◽  
Diffusion Approximations ◽  
Limit Theory

This paper is mainly concerned with the asymptotic theory of maximum likelihood estimation for continuous-time stochastic processes. The role of martingale limit theory in this theory is developed. Some analogues of classical statistical concepts and quantities are also suggested. Various examples that illustrate parts of the theory are worked through, producing new results in some cases. The role of diffusion approximations in estimation is also explored.

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (04) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn ; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p 0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p 0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Maximum Likelihood Estimation of Central-City Food Trading Areas

1972 ◽  
Vol 9 (2) ◽  
pp. 154-159 ◽  
Author(s):  
George H. Haines ◽  
Leonard S. Simon ◽  
Marcus Alexis
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Central City ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Store Choice ◽  
Home Consumption

A maximum likelihood estimate of the parameter in the Huff model of consumer store choice is derived and its properties are discussed. A method for obtaining a numerical value for the estimator is presented. The procedure is exemplified by estimating trading areas for food purchased for in-home consumption.

scholarly journals The estimation of bacterial densities from dilution series

1951 ◽  
Vol 49 (1) ◽  
pp. 26-35 ◽  
Author(s):  
D. J. Finney
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimation ◽  
Probit Analysis ◽  
Bacterial Density ◽  
Loss Of Information ◽  
Dilution Series ◽  
Quantal Responses

A transformation devised by Mather is applied to give a new scheme for computing the maximum likelihood estimate of a bacterial density from the evidence of a dilution series. Tables are provided to expedite the application of the method; with their aid, the calculations take a from similar to, but much simpler than, those for probit analysis of quantal responses.Maximum likelihood estimation is compared with the method proposed by Fisher. The latter has the advantage of extreme simplicity, at least for series to which existing tables can be applied, and the loss of information involved in its use may often be compensated by the saving of time in calculation. An experimenter who has fairly reliable prior indications of an approximate value for the density, however, ought to concentrate his attention on dilutions that he believes will contain between 4 and 1/4 organisms per sample; he must not apply Fisher's method to his results, but the maximum likehood estimate will be so much more precise than any estimate from an experimental design using more extreme dilutions as to repay the small additional labour in computation.

Sign in / Sign up

Export Citation Format

Share Document