and Moore, A. H. (1967) Asymptotic variances and covariances

2016 ◽  
pp. 318-321
Keyword(s):  
Asymptotic Variances

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.

ON LOCAL INACCURACY RATES AND ASYMPTOTIC VARIANCES

1987 ◽  
Vol 5 (1-2) ◽  
Author(s):  
Jana Jurečková ◽  
C.M. Kallenberg
Keyword(s):  
Asymptotic Variances

scholarly journals Realized Multi-Power Variation Process for Jump Detection in the Nigerian All Share Index

2021 ◽  
Vol 52 (3) ◽  
pp. 397-412
Author(s):  
Mabel Adeosun ◽  
Olabisi Ugbebor
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Models ◽  
Asymptotic Properties ◽  
Higher Order ◽  
Asymptotic Results ◽  
Jump Detection ◽  
Limit Distributions ◽  
Price Process ◽  
Variation Process ◽  
Asymptotic Variances

In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process.

Estimation of the variance for the multitype Galton–Watson process

1982 ◽  
Vol 19 (2) ◽  
pp. 408-414 ◽  
Author(s):  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator ◽  
Asymptotic Results ◽  
Variance Matrix ◽  
Individual Offspring ◽  
Watson Process ◽  
Asymptotic Variances

This paper is concerned with the estimation of the variance for the multitype Galton-Watson process X = {Xn = (Xn(1),…, Xn(p)); n ≧ 0}. Two estimators for the variance matrix are obtained and asymptotic results for the estimators are given. The first is a maximum likelihood estimator based upon knowledge of individual offspring sizes, the second estimator is based on parent-offspring type combination counts only. Estimators for the asymptotic variances of the Asmussen and Keiding estimator and Becker estimator are also proposed.

scholarly journals Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

2020 ◽  
Vol 13 (12) ◽  
pp. 298
Author(s):  
Yuan Gao ◽  
Lingju Chen ◽  
Jiancheng Jiang ◽  
Honglong You
Keyword(s):  
Nonparametric Estimation ◽  
Ruin Probability ◽  
Risk Model ◽  
Estimation Method ◽  
Asymptotic Distributions ◽  
Classical Risk Model ◽  
Compound Poisson Risk Model ◽  
The Fourier Transform ◽  
The Classical Risk Model ◽  
Asymptotic Variances

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

Asymptotic properties of the least-squares method for estimating transfer functions and disturbance spectra

1992 ◽  
Vol 24 (02) ◽  
pp. 412-440 ◽  
Author(s):  
Lennart Ljung ◽  
Bo Wahlberg
Keyword(s):  
Transfer Function ◽  
Finite Order ◽  
Transfer Functions ◽  
Least Squares Method ◽  
Asymptotic Properties ◽  
Model Order ◽  
Asymptotically Normal ◽  
Strongly Consistent ◽  
True System ◽  
Asymptotic Variances

The problem of estimating the transfer function of a linear system, together with the spectral density of an additive disturbance, is considered. The set of models used consists of linear rational transfer functions and the spectral densities are estimated from a finite-order autoregressive disturbance description. The true system and disturbance spectrum are, however, not necessarily of finite order. We investigate the properties of the estimates obtained as the number of observations tends to ∞ at the same time as the model order employed tends to ∞. It is shown that the estimates are strongly consistent and asymptotically normal, and an expression for the asymptotic variances is also given. The variance of the transfer function estimate at a certain frequency is related to the signal/noise ratio at that frequency and the model orders used, as well as the number of observations. The variance of the noise spectral estimate relates in a similar way to the squared value of the true spectrum.

ASYMPTOTIC INFERENCE ON THE MOVING AVERAGE IMPACT MATRIX IN COINTEGRATED I (2) VAR SYSTEMS

2002 ◽  
Vol 18 (3) ◽  
pp. 673-690 ◽  
Author(s):  
Paolo Paruolo
Keyword(s):  
Moving Average ◽  
Impact Factors ◽  
Standard Errors ◽  
Linear Combinations ◽  
Asymptotic Standard Errors ◽  
Vector Autoregressive ◽  
Average Impact ◽  
The Common ◽  
Row Space ◽  
Asymptotic Variances

This paper provides asymptotic standard errors for the moving average (MA) impact matrix for the second differences of a vector autoregressive (VAR) process integrated of order 2, I(2). Standard errors of the row space of the MA impact matrix are also provided; bases of this row space define the common I(2) trends linear combinations. These standard errors are then used to formulate Wald-type tests. The MA impact matrix is shown to be linked to impact factors that measure the total effect of disequilibrium errors on the growth rate of the system. Most of the relevant limit distributions are Gaussian, and we report artificial regressions that can be used to calculate the estimators of the asymptotic variances. The use of the techniques proposed in the paper is illustrated on UK money data.

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