The Laplace approximation is used to perform maximum likelihood estimation of univariate and multivariate stochastic volatility (SV) models. It is shown that the implementation of the Laplace approximation is greatly simplified by the use of a numerical technique known as automatic differentiation (AD). Several algorithms are proposed and comparedwith some existingmaximum likelihoodmethods usin...

where x = l , 2, . . . ; r > 0 , a > I (ar a + r > 0 , (a)~=a(a+l)...(a-kx--1), and r log F(z)/dz is the digamma or the psi function. The distribution (1.1) will be referred to as DGa (a, r). In this paper we extend DGa (a, r) to a multivariate distribution. The digamma distribution is closely related to the logarithmic series distribution LSr (0) defined by (1.2) P r [ X = x ; 0 ] = 0 ~ / ( l ...

In this paper, I consider multivariate analogues of the extended gamma density, which will provide multivariate extensions to Tsallis statistics and superstatistics. By making use of the pathway parameter β, multivariate generalized gamma density can be obtained from the model considered here. Some of its special cases and limiting cases are also mentioned. Conditional density, best predictor f...

Anastasios Plataniotis and Petros Dellaportas [email protected] [email protected] Department of Statistics, Athens University of Economics and Business, Greece Summary: We introduce a broad class of multivariate stochastic volatility models where transformed eigenvalues and Givens rotation angles are assumed to be AR(1) processes. This decomposition retains the required positive definite structure of...

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investiga...

In this paper, we introduce a new multivariate Weibull (MVW) distribution with many interesting properties. We obtain the maximum likelihood estimate (MLE) of the parameters and their asymptotic multivariate normal (AMVN) distribution in MVWmodel. We propose large sample studentized tests for testing multivariate exponentiality and also tests for independence and identical marginals of the comp...

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the al...

We consider deconvolution problems where the observations are equal in distribution to Here the random variables in the sums are independent, the E i are exponentially distributed, the L i are Laplace distributed and Y has an unknown distribution F which we want to estimate. The constants i or i are given. These problems include exponential, gamma and Laplace deconvolution. We derive inversion ...

In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/I queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/I, R/G/I queues, where R is the class of distributions with rational Laplace tran...

From a suitable integral representation of the Laplace transform of a positive semi–definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furth...