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Limit Distribution (limit + distribution)
Selected AbstractsModelling curved S,N curvesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2005S. LORÉN ABSTRACT The fatigue limit distribution is estimated using fatigue data and under the assumption that the fatigue limit is random. The stress levels for the broken and unbroken specimens are used. For the broken specimen the number of cycles to failure is also used. By combining the finite life and fatigue limit distribution it is possible to get the probability of not surviving a certain life. This probability is used to estimate a curved S,N curve by using the method of likelihood. The whole S,N curve is estimated at the same time. These curves show the predictive life given a certain stress level. The life and the quantile of the fatigue limit distribution are also predicted by using profile predictive likelihood. In this way the scatter around the S,N curve as well as the uncertainty of the S,N curve are taken into account. [source] Bootstrapping a weighted linear estimator of the ARCH parametersJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2009Arup Bose Abstract., A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal. [source] Range Unit-Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and OutliersJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2006Felipe Aparicio Abstract., Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long-wave patterns observed not only in unit-root time series but also in series following more complex data-generating mechanisms. To this end, our testing device analyses the unit-root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit-root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit-root tests on near-unit-root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward,backward range unit-root (FB-RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey,Fuller unit-root test on exchange rate series. [source] Testing Stochastic Cycles in Macroeconomic Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2001L. A. Gil-Alana A particular version of the tests of Robinson (1994) for testing stochastic cycles in macroeconomic time series is proposed in this article. The tests have a standard limit distribution and are easy to implement in raw time series. A Monte Carlo experiment is conducted, studying the size and the power of the tests against different alternatives, and the results are compared with those based on other tests. An empirical application using historical US annual data is also carried out at the end of the article. [source] Limits of zeros of orthogonal polynomials on the circleMATHEMATISCHE NACHRICHTEN, Issue 12-13 2005Barry Simon Abstract We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a question of P. Turán): namely, for n < N , one can freely prescribe the n -th polynomial and N , n zeros of the N -th one. We shall also describe all possible limit sets of zeros within the unit disk. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] The Likelihood Ratio Test for the Rank of a Cointegration Submatrix,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2006Paolo Paruolo Abstract This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent,transitory decompositions and of subhypotheses related to neutrality and long-run Granger noncausality. The proposed test has a chi-squared limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable. [source] A stochastic model for solitonsRANDOM STRUCTURES AND ALGORITHMS, Issue 1 2004Yoshiaki Itoh Abstract The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg-like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514,3519]. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004 [source] The ,(2) limit in the random assignment problemRANDOM STRUCTURES AND ALGORITHMS, Issue 4 2001David J. Aldous Abstract The random assignment (or bipartite matching) problem asks about An=min,,,c(i,,,(i)), where (c(i,,j)) is a n×n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations ,. Mézard and Parisi (1987) used the replica method from statistical physics to argue nonrigorously that EAn,,(2)=,2/6. Aldous (1992) identified the limit in terms of a matching problem on a limit infinite tree. Here we construct the optimal matching on the infinite tree. This yields a rigorous proof of the ,(2) limit and of the conjectured limit distribution of edge-costs and their rank-orders in the optimal matching. It also yields the asymptotic essential uniqueness property: every almost-optimal matching coincides with the optimal matching except on a small proportion of edges. ©2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 381,418, 2001 [source] Nonlinear econometric models with cointegrated and deterministically trending regressorsTHE ECONOMETRICS JOURNAL, Issue 1 2001Yoosoon Chang This paper develops an asymptotic theory for a general class of nonlinear non-stationary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergence rate and the limiting distribution are critically dependent upon the type of the regression function. For integrable regression functions, the parameter estimates converge at a reduced n1/4 rate and have mixed normal limit distributions. On the other hand, if the regression functions are homogeneous at infinity, the convergence rates are determined by the degree of the asymptotic homogeneity and the limit distributions are non-Gaussian. It is shown that nonlinear least squares generally yields inefficient estimators and invalid tests, just as in linear nonstationary regressions. The paper proposes a methodology to overcome such difficulties. The approach is simple to implement, produces efficient estimates and leads to tests that are asymptotically chi-square. It is implemented in empirical applications in much the same way as the fully modified estimator of Phillips and Hansen. [source] | |||||||||||||