Let X1,...,X-n be independent observations on a random variable X. This paper considers a class of omnibus procedures for testing the hypothesis that the unknown distribution of X belongs to the family of Cauchy laws....
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Let X1,...,X-n be independent observations on a random variable X. This paper considers a class of omnibus procedures for testing the hypothesis that the unknown distribution of X belongs to the family of Cauchy laws. The test statistics are weighted integrals of the squared modulus of the difference between the empirical characteristic function of the suitably standardized data and the characteristicfunction of the standard Cauchy distribution. A large-scale simulation study shows that the new tests compare favorably with the classical goodness-of-fit tests for the Cauchy distribution, based on the empirical distribution function. For small sample sizes and short-tailed alternatives, the uniformly most powerful invariant test of Cauchy versus normal beats all other tests under discussion.
A test based on the studentized empirical characteristic function calculated in a single point is derived. An empirical power comparison is made between this test and tests like the Epps-Pulley, Shapiro-Wilks, Anderso...
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A test based on the studentized empirical characteristic function calculated in a single point is derived. An empirical power comparison is made between this test and tests like the Epps-Pulley, Shapiro-Wilks, Anderson-Darling and other tests for normality. It is shown to outperform the more complicated Epps-Pulley test based on the empirical characteristic function and a Cramer-von Mises type expression in a simulation study. The test performs especially good in large samples and the derived test statistic has an asymptotic normal distribution which is easy to apply.
Matched Field Processing (MFP) is an inversion technique often employed in source localization applications. Conventional MFP approaches are incapable of producing precise results in the presence of extremely impulsiv...
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Matched Field Processing (MFP) is an inversion technique often employed in source localization applications. Conventional MFP approaches are incapable of producing precise results in the presence of extremely impulsive noises, which are typically present in actual applications such as underwater acoustics. This is because the covariance matrix for this category of noises does not converge. Moreover, impulsive noise suppression algorithms fail to provide accurate results. Particularly, fractional lower order moment (FLOM)-based approaches have an unbounded output, and data trimming methods introduce uncertainty into the estimation covariance matrix. In this study, a novel MFP method employing the empirical characteristic function (ECF) is developed. The desirable properties of the characteristicfunction (CF) result in a robust localization method that is ideally suited for extremely strong tailed noise environments. Using the CF array output, a new covariance-like matrix that can be used in MFP methods has been constructed. To demonstrate the efficiency of the ECF-MFP technique, experiments are conducted in a water tank. Experimental results reveal that this method is very robust in the presence of very heavy tailed noise, a low signal-to-noise ratio, and a tiny sample size. Additionally, it outperforms previous approaches in terms of resolution probability.
The known functional form of the conditional characteristicfunction (CCF) of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimato...
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The known functional form of the conditional characteristicfunction (CCF) of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimators of the parameters of affine diffusions, and of asset pricing models in which the state vectors follow affine diffusions. Both 'time-domain' estimators, based on Fourier inversion of the CCF, and 'frequency-domain' estimators, based directly on the CCF, are constructed. A method-of-moments estimator based on the CCF is shown to approximate the efficiency of maximum likelihood for affine diffusion and asset pricing models. (C) 2001 Elsevier Science S.A. All rights reserved.
In this paper, we evaluate the mean square error (MSE) performance of empirical characteristic function (ECF) based signal level estimator in a binary communication system. By calculating Cramer-Rao lower bound (CRLB)...
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In this paper, we evaluate the mean square error (MSE) performance of empirical characteristic function (ECF) based signal level estimator in a binary communication system. By calculating Cramer-Rao lower bound (CRLB) we investigate the performance of the ECF based estimator in the presence of Laplace and Gaussian mixture noises. We have derived an analytic expression for the variance of the ECF based estimator which shows that it is asymptotically unbiased and consistent. Simulation and analytic results indicate that the ECF based level estimator outperforms the previously proposed estimators in some signal to noise ratio (SNR) regions when the observation noise distribution is unknown. (C) 2019 Elsevier Inc. All rights reserved.
Parameter estimation for the skew-normal distribution is challenging, since the profile likelihood function of shape parameter has a stationary point at zero, which hampers the use of traditional methods, such as maxi...
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Parameter estimation for the skew-normal distribution is challenging, since the profile likelihood function of shape parameter has a stationary point at zero, which hampers the use of traditional methods, such as maximum likelihood method. We present a modified empirical characteristic function method to perform parameter estimation for the skew-normal distribution. The proposed approach is flexible and easy to implement. We show that the estimators converge to the true values in probability. The simulation study and data analysis suggest that the proposed method performs well, even for the case of small sample size.
In this paper a class of goodness-of-fit tests for the Laplace distribution is proposed. The tests are based on a weighted integral involving the empirical characteristic function. The consistency of the tests as well...
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In this paper a class of goodness-of-fit tests for the Laplace distribution is proposed. The tests are based on a weighted integral involving the empirical characteristic function. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to. the first nonzero component of Neyman's smooth test for this distribution. The new tests are compared with other omnibus tests for the Laplace distribution.
This paper analyses the discretisation error in computing the empirical characteristic function via the Fast Fourier Transform. Based on an interpretation of the discretisation scheme as a pre-smoothing, we obtain nat...
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This paper analyses the discretisation error in computing the empirical characteristic function via the Fast Fourier Transform. Based on an interpretation of the discretisation scheme as a pre-smoothing, we obtain naturally a correction and possible generalizations, and derive exact and approximate formulas for the root mean square error involved. Some numerical evaluations are made, showing the accuracy of our approximate formula and the low value of the above root mean square error.
This paper considers discretisation errors involved in using the Fast Fourier Transform to compute the empirical characteristic function efficiently. A simple improvement to the usual histogram discretisation scheme i...
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This paper considers discretisation errors involved in using the Fast Fourier Transform to compute the empirical characteristic function efficiently. A simple improvement to the usual histogram discretisation scheme is shown to reduce the mean square error considerably, as the grid size tends to zero. Simulation results show that the improvement is just as good in practical cases. The theoretical results are applied to the efficient calculation of kernel density estimates, described in Silverman (1982).
This article examines the class of continuous-time stochastic processes commonly known as affine diffusions (AD's) and affine jump diffusions (AJD's). By deriving the joint characteristicfunction, we are able...
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This article examines the class of continuous-time stochastic processes commonly known as affine diffusions (AD's) and affine jump diffusions (AJD's). By deriving the joint characteristicfunction, we are able to examine the statistical properties as well as develop an efficient estimation technique based on empirical characteristic functions (ECF's) and a generalized method of moments (GMM) estimation procedure based on exact moment conditions. We demonstrate that our methods are particularly useful when the diffusions involve latent variables. Our approach is illustrated with a detailed examination of a continuous-time stochastic volatility (SV) model, along with an empirical application using S&P 500 index returns.
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