The trends of labor market in Bangladesh and its determinants

In this paper, we have tried to find out specially the features of unemployment-underemployment scenario. As we know, like auction market labor market is not perfectly competitive. For various heterogeneities, it has some distinct features. In Bangladesh, unemployment and underemployment problems arrive due to the lack of effective demand for labor. Hence, in this paper we desire to focus the demand determinants of labor in Bangladesh. In this case, we have emphasized on manufacturing sector, which is the emerging sector of Bangladesh economy both from the employment generation and from economic growth perspectives. To estimate the demand determinants we have used ARDL model where the estimation period is from 1980 to 2002

Properties and numerical evaluation of the Rosenblatt distribution

This paper studies various distributional properties of the Rosenblatt distribution. We begin by describing a technique for computing the cumulants. We then study the expansion of the Rosenblatt distribution in terms of shifted chi-squared distributions. We derive the coefficients of this expansion and use these to obtain the L\'{e}vy-Khintchine formula and derive asymptotic properties of the L\'{e}vy measure. This allows us to compute the cumulants, moments, coefficients in the chi-square expansion and the density and cumulative distribution functions of the Rosenblatt distribution with a high degree of precision. Tables are provided and software written to implement the methods described here is freely available by request from the authors.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ421 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Distribution functions of Poisson random integrals: Analysis and computation

We want to compute the cumulative distribution function of a one-dimensional Poisson stochastic integral I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds), where $N$ is a Poisson random measure with control measure $n$ and \krnl is a suitable kernel function. We do so by combining a Kolmogorov-Feller equation with a finite-difference scheme. We provide the rate of convergence of our numerical scheme and illustrate our method on a number of examples. The software used to implement the procedure is available on demand and we demonstrate its use in the paper.Comment: 28 pages, 8 figure

The empirical process of some long-range dependent sequences with an application to U-statistics

Let (Xj)∞ j = 1 be a stationary, mean-zero Gaussian process with covariances r(k) = EXk + 1 X1 satisfying r(0) = 1 and r(k) = k-DL(k) where D is small and L is slowly varying at infinity. Consider the two-parameter empirical process for G(Xj), $\bigg\{F_N(x, t) = \frac{1}{N} \sum^{\lbrack Nt \rbrack}_{j = 1} \lbrack 1\{G(X_j) \leq x\} - P(G(X_1) \leq x) \rbrack; // -\infty < x < + \infty, 0 \leq t \leq 1\bigg\},$ where G is any measurable function. Noncentral limit theorems are obtained for FN(x, t) and they are used to derive the asymptotic behavior of some suitably normalized von Mises statistics and U-statistics based on the G(Xj)'s. The limiting processes are structurally different from those encountered in the i.i.d. case

A survey of functional laws of the iterated logarithm for self-similar processes

A process X(t) is self-similar with index H > 0 if the finite-dimensional distributions of X(at) are identical to those of aHX(t) for all a > 0. Consider self-similar processes X(t) that are Gaussian or that can be represented throught Wiener-Itô integrals. The paper surveys functional laws of the iterated logarithm for such processes X(t) and for sequences whose normalized sums coverage weakly to X(t). The goal is to motivate the results by including outline of proofs and by highlighting relationships between the various assumptions. The paper starts with a general discussion fo functional laws of the iterated logarithm, states some of their formulations and sketches the reproducing kernal Hilbert space set-up.ECS-80-15585 - National Science Foundatio

Structure of the third moment of the generalized Rosenblatt distribution

The Rosenblatt distribution appears as limit in non-central limit theorems. The generalized Rosenblatt distribution is obtained by allowing different power exponents in the kernel that defines the usual Rosenblatt distribution. We derive an explicit formula for its third moment, correcting the one in \citet{maejima:tudor:2012:selfsimilar} and \citet{tudor:2013:analysis}. Evaluating this formula numerically, we are able to confirm that the class of generalized Hermite processes is strictly richer than the class of Hermite processes

Generalized Hermite processes, discrete chaos and limit theorems

We introduce a broad class of self-similar processes $\{Z(t),t\ge 0\}$ called generalized Hermite process. They have stationary increments, are defined on a Wiener chaos with Hurst index $H\in (1/2,1)$, and include Hermite processes as a special case. They are defined through a homogeneous kernel $g$, called "generalized Hermite kernel", which replaces the product of power functions in the definition of Hermite processes. The generalized Hermite kernels $g$ can also be used to generate long-range dependent stationary sequences forming a discrete chaos process $\{X(n)\}$. In addition, we consider a fractionally-filtered version $Z^\beta(t)$ of $Z(t)$, which allows $H\in (0,1/2)$. Corresponding non-central limit theorems are established. We also give a multivariate limit theorem which mixes central and non-central limit theorems.Comment: Corrected some error

Behavior of the generalized Rosenblatt process at extreme critical exponent values

The generalized Rosenblatt process is obtained by replacing the single critical exponent characterizing the Rosenblatt process by two different exponents living in the interior of a triangular region. What happens to that generalized Rosenblatt process as these critical exponents approach the boundaries of the triangle? We show by two different methods that on each of the two symmetric boundaries, the limit is non-Gaussian. On the third boundary, the limit is Brownian motion. The rates of convergence to these boundaries are also given. The situation is particularly delicate as one approaches the corners of the triangle, because the limit process will depend on how these corners are approached. All limits are in the sense of weak convergence in C[0,1]. These limits cannot be strengthened to convergence in L2(Ω).Supported in part by NSF Grants DMS-10-07616 and DMS-13-09009 at Boston University. (DMS-10-07616 - NSF at Boston University; DMS-13-09009 - NSF at Boston University)Accepted manuscrip