| 1. |
- Ahmad, M. Rauf
(författare)
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Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality
- 2017
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 46:8, s. 3738-3753
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Tidskriftsartikel (refereegranskat)abstract
- A test for homogeneity of g 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n(i), i = 1, ..., g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n(i), p . Under the null hypothesis, the test is extended for common covariance matrix to be of a specified structure, including sphericity. Theory of U-statistics is employed in constructing the tests and deriving their limits. Simulations are used to show the accuracy of tests.
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| 2. |
- Ahmad, M. Rauf, et al.
(författare)
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Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality
- 2015
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 44:7, s. 1387-1398
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Tidskriftsartikel (refereegranskat)abstract
- Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp >> n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.
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| 3. |
- Ankargren, Sebastian, et al.
(författare)
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On the least-squares model averaging interval estimator
- 2018
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 47:1, s. 118-132
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Tidskriftsartikel (refereegranskat)abstract
- In many applications of linear regression models, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty, least-squares frequentist model averaging has been proposed recently. We show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. The finite-sample confidence intervals based on approximations to the asymptotic distributions are also equivalent if the parameter of interest is a linear function of the regression coefficients. Furthermore, we demonstrate that this equivalence also holds for prediction intervals constructed in the same fashion.
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| 4. |
- Baxevani, Anastassia, et al.
(författare)
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Random spectral measure for non Gaussian moving averages
- 2018
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 47:2, s. 448-462
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Tidskriftsartikel (refereegranskat)abstract
- We study the distribution of phases and amplitudes for the spectral representation of weighted moving averages of a general noise measure. The simple independent structure, known for the Gaussian case, and involving Rayleigh amplitude and uniform phase distributions, is lost for the non Gaussian noise case. We show that the amplitude/phase distributions exhibit a rich and more complex structure depending not just on the covariance of the process but specifically on the form of the kernel and the noise distribution. We present a theoretical tool for studying these distributions that follows from a proof of the spectral theorem that yields an explicit expression for the spectral measure. The main interest is in noise measures based on second-order Lévy motions since such measures are easily available through independent sampling. We approximate the spectral stochastic measure by independent noise increments which allows us to obtain amplitude/phase distributions that is of fundamental interest for analyzing processes in the frequency domain. For the purpose of approximating the moving average process through sums of trigonometric functions, we assess the mean square error of discretization of the spectral representation. For a specified accuracy, the approximation is explicitly given. We illustrate the method for the moving averages driven by the Laplace motion.
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| 5. |
- Bodnar, Rostyslav, et al.
(författare)
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Multivariate autoregressive extreme value process and its application for modeling the time series properties of the extreme daily asset prices
- 2016
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 45:12, s. 3421-3440
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Tidskriftsartikel (refereegranskat)abstract
- In this article we suggest a new multivariate autoregressive process for modeling time-dependent extreme value distributed observations. The idea behind the approach is to transform the original observations to latent variables that are univariate normally distributed. Then the vector autoregressive DCC model is fitted to the multivariate latent process. The distributional properties of the suggested model are extensively studied. The process parameters are estimated by applying a two-stage estimation procedure. We derive a prediction interval for future values of the suggested process. The results are applied in an empirically study by modeling the behavior of extreme daily stock prices.
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| 6. |
- Canhanga, Betuel, 1980-, et al.
(författare)
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Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities
- 2018
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 47:6, s. 1328-1349
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Tidskriftsartikel (refereegranskat)abstract
- The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.
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| 7. |
- Cronie, Ottmar, et al.
(författare)
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The discretely observed immigration-death process : Likelihood inference and spatiotemporal applications
- 2016
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis Group. - 0361-0926 .- 1532-415X. ; 45:18, s. 5279-5298
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Tidskriftsartikel (refereegranskat)abstract
- We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.
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| 8. |
- Dai, Deliang, 1953-, et al.
(författare)
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Expected and unexpected values of Individual Mahalanobis Distances
- 2017
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 46:18, s. 8999-9006
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Tidskriftsartikel (refereegranskat)abstract
- This paper derives first-order sampling moments of individual Mahalanobis distances (MD) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c, 0 ⩽ c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second order moments are also supplied to give some additional insight to the matter.
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| 9. |
- El Maroufy, H., et al.
(författare)
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Final outcome probabilities for SIR epidemic model
- 2016
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 45:8, s. 2426-2437
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Tidskriftsartikel (refereegranskat)abstract
- We consider an SIR stochastic epidemic model in which new infections occur at rate f(x, y), where x and y are, respectively, the number of susceptibles and infectives at the time of infection and f is a positive sequence of real functions. A simple explicit formula for the final size distribution is obtained. Some efficient recursive methods are proved for the exact calculation of this distribution. In addition, we give a Gaussian approximation for the final distribution using a diffusion process approximation.
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| 10. |
- Forchini, Giovanni, et al.
(författare)
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Modified first-difference estimator in a panel data model with unobservable factors both in the errors and the regressors when the time dimension is small
- 2017
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 46:24, s. 12226-12239
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Tidskriftsartikel (refereegranskat)abstract
- Panel data models with factor structures in both the errors and the regressors have received considerable attention recently. In these models, the errors and the regressors are correlated and the standard estimators are inconsistent. This paper shows that, for such models, a modified first-difference estimator (in which the time and the cross-sectional dimensions are interchanged) is consistent as the cross-sectional dimension grows but the time dimension is small. Although the estimator has a non standard asymptotic distribution, t and F tests have standard asymptotic distribution under the null hypothesis.
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