Relevant bibliographies by topics / Asymptotic distribution

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Asymptotic distribution'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Asymptotic distribution"

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Miyazawa, Masakiyo. "Martingale approach for tail asymptotic problems in the gener­alized Jackson network." Probability and Mathematical Statistics 37, no. 2 (May 14, 2018): 395–430. http://dx.doi.org/10.19195/0208-4147.37.2.11.

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MARTINGALE APPROACH FOR TAIL ASYMPTOTIC PROBLEMS IN THE GENERALIZED JACKSON NETWORKWe study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network GJN for short, assumingits stability. For the two-station case, this problem has recently been solved in the logarithmic sense for the marginal stationary distributions under the setting that arrival processes and service times are of phase-type. In this paper, we study similar tail asymptotic problems on the stationary distribution, but problems and assumptions are different. First, the asymptotics are studied not only for the marginal distribution but also the stationary probabilities of state sets of small volumes. Second, the interarrival and service times are generally distributed and light tailed, but of phase-type in some cases. Third, we also study the case that there are more than two stations, although the asymptotic results are less complete. For them, we develop a martingale method, which has been recently applied to a single queue with many servers by the author.
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WANG, Frank Xuyan. "Shape Factor Asymptotic Analysis I." Journal of Advanced Studies in Finance 11, no. 2 (December 22, 2020): 108. http://dx.doi.org/10.14505//jasf.v11.2(22).05.

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We proposed using shape factor to distinguish probability distributions, and using relative minimum or maximum values of shape factor to locate distribution parameter allowable ranges for distribution fitting in our previous study. In this paper, the shape factor asymptotic analysis is employed to study such conditional minimum or maximum, to cross validate results found from numerical study and empirical formula we obtained and published earlier. The shape factor defined as kurtosis divided by skewness squared is characterized as the unique maximum choice of among all factors that is greater than or equal to 1 for all probability distributions. For all distributions from a specific distribution family, there may exists such that. The least upper bound of all such is defined as the distribution family’s characteristic number. The useful extreme values of the shape factor for various distributions that are found numerically before, the Beta, Kumaraswamy, Weibull, and GB2 distributions are derived using asymptotic analysis. The match of the numerical and the analytical results may arguably be considered proof of each other. The characteristic numbers of these distributions are also calculated. The study of the extreme value of the shape factor, or the shape factor asymptotic analysis, help reveal properties of the original shape factor, and reveal relationship between distributions, such as that between the Kumaraswamy distribution and the Weibull distribution.
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KUMAR, C. SATHEESH, and G. V. ANILA. "Asymptotic curved normal distribution." Journal of Statistical Research 52, no. 2 (March 11, 2019): 173–86. http://dx.doi.org/10.47302/2018520204.

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Here we introduce a new class of skew normal distribution as a generalization of the extended skew curved normal distribution of Kumar and Anusree (J. Statist. Res., 2017) and investigate some of its important statistical properties. The location-scale extension of the proposed class of distribution is also defined and discussed the estimation of its parameters by method of maximum likelihood. Further, a real life data set is considered for illustrating the usefulness of the model and a brief simulation study is attempted for assessing the performance of the estimators.
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Shimizu, Eiji, and Hiroshi Shiraishi. "An asymptotic distribution of compound Poisson distribution." Cogent Mathematics 3, no. 1 (August 29, 2016): 1221614. http://dx.doi.org/10.1080/23311835.2016.1221614.

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Tanaka, Katsuto. "Asymptotic expansions for time series statistics." Journal of Applied Probability 23, A (1986): 211–27. http://dx.doi.org/10.2307/3214354.

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Asymptotic expansions for the distributions of estimators and test statistics are derived in connection with time series models. The expansions relate to marginal and joint distributions together with the percentiles of marginal distributions. We also consider transforming a statistic so that the transformed statistic has a distribution that coincides with its asymptotic distribution up to a higher order.
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Tanaka, Katsuto. "Asymptotic expansions for time series statistics." Journal of Applied Probability 23, A (1986): 211–27. http://dx.doi.org/10.1017/s0021900200117097.

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Asymptotic expansions for the distributions of estimators and test statistics are derived in connection with time series models. The expansions relate to marginal and joint distributions together with the percentiles of marginal distributions. We also consider transforming a statistic so that the transformed statistic has a distribution that coincides with its asymptotic distribution up to a higher order.
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Kahounová, Jana. "Asymptotic Probability Distribution of Sample Maximum." Acta Oeconomica Pragensia 16, no. 3 (June 1, 2008): 40–46. http://dx.doi.org/10.18267/j.aop.103.

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Lyons, Russell. "Mixing and asymptotic distribution modulo 1." Ergodic Theory and Dynamical Systems 8, no. 4 (December 1988): 597–619. http://dx.doi.org/10.1017/s0143385700004715.

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AbstractIf μ is a probability measure which is invariant and ergodic with respect to the transformationx↦qxon the circle ℝ/ℤ, then according to the ergodic theorem, {qnx} has the asymptotic distribution μ for μ-a.e.x. On the other hand, Weyl showed that when μ is Lebesgue measure, λ, and {mj} is an arbitrary sequence of integers increasing strictly to ∞, the asymptotic distribution of {mjx} is λ for λ-a.e.x. Here, we investigate the asymptotic distributions of {mjx} μ-a.e. for fairly arbitrary {mj} under some strong mixing conditions on μ. The result is a kind of stable ergodicity: the distributions are obtained from simple operations applied to μ. The ideas extend to the situation of a sequence of transformationsx↦qnxwhere invariance is not present. This gives us information about many Riesz products and Bernoulli convolutions. Finally, we apply the theory to resolve some questions aboutH-sets.
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Coffman, Donna L., Alberto Maydeu-Olivares, and Jaume Arnau. "Asymptotic Distribution Free Interval Estimation." Methodology 4, no. 1 (January 2008): 4–9. http://dx.doi.org/10.1027/1614-2241.4.1.4.

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Abstract. Confidence intervals for the intraclass correlation coefficient (ICC) have been proposed under the assumption of multivariate normality. We propose confidence intervals which do not require distributional assumptions. We performed a simulation study to assess the coverage rates of normal theory (NT) and asymptotically distribution free (ADF) intervals. We found that the ADF intervals performed better than the NT intervals when kurtosis was greater than 4. When violations of distributional assumptions were not too severe, both the intervals performed about the same. The point estimate of the ICC was robust to distributional violations. We provide R code for computing the ADF confidence intervals for the ICC.
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Barral, Julien, and Yan-Hui Qu. "Multifractals in Weyl asymptotic distribution." Nonlinearity 24, no. 10 (September 2, 2011): 2785–811. http://dx.doi.org/10.1088/0951-7715/24/10/008.

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Dissertations / Theses on the topic "Asymptotic distribution"

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Hofmann, Glenn, Erhard Cramer, N. Balakrishnan, and Gerd Kunert. "An Asymptotic Approach to Progressive Censoring." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200201539.

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Progressive Type-II censoring was introduced by Cohen (1963) and has since been the topic of much research. The question stands whether it is sensible to use this sampling plan by design, instead of regular Type-II right censoring. We introduce an asymptotic progressive censoring model, and find optimal censoring schemes for location-scale families. Our optimality criterion is the determinant of the 2x2 covariance matrix of the asymptotic best linear unbiased estimators. We present an explicit expression for this criterion, and conditions for its boundedness. By means of numerical optimization, we determine optimal censoring schemes for the extreme value, the Weibull and the normal distributions. In many situations, it is shown that these progressive schemes significantly improve upon regular Type-II right censoring.
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Baligh, Mohammadhadi. "Analysis of the Asymptotic Performance of Turbo Codes." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/883.

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Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.
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Stewart, Michael. "Asymptotic methods for tests of homogeneity for finite mixture models." Connect to full text, 2002. http://hdl.handle.net/2123/855.

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Thesis (Ph. D.)--University of Sydney, 2002.
Title from title screen (viewed Apr. 28, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliography. Also available in print form.
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Unger, William Ramsay. "Asymptotics of increasing trees." Thesis, The University of Sydney, 1993. https://hdl.handle.net/2123/26633.

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This thesis addresses the problem of finding the asymptotic average path length in species of increasing trees. A version of Joyal’s theory of species, L—species, is used to derive power series identities for simple increasing trees and give them bijective proofs. The main identity involved here is an autonomous, nonlinear, ordinary differential equation. Asymptotic results on the number and average path length of these species are derived by analysis of the singularities of these power series when they are treated as analytic functions. The result is a general method for finding the asymptotic number of and asymptotic average path length in increasing trees defined by a single differential equation. In the particular case Where there is a uniform upper bound on the number of descendents a vertex has (and in some other cases) the method can be simply automated using a symbolic algebra package such as MAPLE. It is found that the expected path length of a tree in a species of increasing trees with the above restriction is asymptotically proportional to n log n, where n is the number of vertices in the tree. By contrast, it is shown, using similar combinatorial methods, that labelled, non—increasing trees and unlabelled trees, to which similar analytic methods apply, have path length asymptotically proportional to n*sqrt(n).
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Heimbürger, Axel. "Asymptotic Distribution of Two-Protected Nodes in m-ary Search Trees." Thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-151318.

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In this report, the number of two-protected nodes in m-ary search trees is studied i.e., nodes with distance at least two to any leaf in the tree. This is of interest since the protected nodes describe local properties close to the leaves of the m-ary search trees. This is done by using a generalised Pólya urn model and relating this urn model to how the tree evolves after each new key is inserted into the tree. It is proven that the number of two-protected nodes in m-ary search trees is asymptotically normally distributed when m = 4, 5, 6 which is the main result. This is in agreement with previously known results for m = 2, 3, which were obtained by using the same approach. The method and algorithms are presented in such a way that it simpli_es calculations for larger m. Based on the results for m = 2,…, 6 conjectures are made providing a possible way to extend these results for larger m < 26.
I detta examensarbete studeras antalet tvåskyddade noder i m-ära sökträd. En nod kallas tvaskyddad ifall den ar minst två kanter fran ett löv i trädet. Dessa noder är av intresse eftersom de beskriver lokala egenskaper nära löven i de m-ära sökträden. Detta studeras genom att använda en generaliserad Pólya urna och genom att relatera denna urna till hur ett m-ärt sökträd expanderar när nya nycklar placeras in i trädet. Det bevisas att antalet tvåskyddade noder i ett m-ärt sökträd har en asymptotiskt normalfördelad sannolikhetsfördelning för m = 4, 5, 6 när antalet nycklar i trädet går mot oändligheten. Detta stämmer överens med tidigare resultat för m = 2, 3, som har bevisats genom att använda samma metod. Metoden och algoritmerna som används för att beräkna dessa resultat presenteras på ett sådant sätt att de går att applicera på större m utan modifiering. Givet resultaten för m = 2,…, 6 presenteras en möjlig väg för att expandera dessa resultat för större m.
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Mwawasi, Grace Makanda. "Approximations and asymptotic expansions for the distribution of quadratic and bilinear forms." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56952.

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In this thesis, approximations and asymptotic expansions to the distribution of quadratic and bilinear forms in normal random variables are discussed.
Chi-square type approximations, normal approximations, the mixture approximation and the laplacian approximation to the exact distribution of positive definite and indefinite quadratic forms and bilinear forms are discussed. Several asymptotic results are also discussed.
Some numerical computations giving probabilities and percentage points and also some simulation for the distribution function of quadratic and bilinear forms are given to give more insight into the approximations.
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Breimesser, Sandra Verena. "Asymptotic value distribution for solutions of the Schrödinger equation and Herglotz functions." Thesis, University of Hull, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272024.

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Bulger, Daniel. "The high energy asymptotic distribution of the eigenvalues of the scattering matrix." Thesis, King's College London (University of London), 2013. https://kclpure.kcl.ac.uk/portal/en/theses/the-high-energy-asymptotic-distribution-of-the-eigenvalues-of-the-scattering-matrix(541fc908-ff77-4f0f-b3ba-af1fe53e19dd).html.

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We determine the high energy asymptotic density of the eigenvalues of the scat- tering matrix associated with the operators H0 = −∆ and H = (i∇ + A)2 + V (x), where V : Rd → R is a smooth short-range real-valued electric potential and A = (A1, . . . , Ad) : Rd → Rd is a smooth short-range magnetic vector-potential. Two cases are considered. The first case is where the magnetic vector-potential is non-zero. The spectral density of the associated scattering matrix in this case is expressed as an integral solely in terms of the magnetic vector-potential A. The second case considered is where the magnetic vector-potential is identically zero. Again the spectral density of the scattering matrix is expressed as an integral, this time in terms of the poten- tial V . These results share similar characteristics to results pertaining to semiclassical asymptotics for pseudodifferential operators.
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Joyner, James Thomas. "ASYMPTOTIC ANALYSIS OF FRONTAL POLYMERIZATION IN A MEDIUM WITH PERIODIC MONOMER DISTRIBUTION." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1153773428.

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Balabdaoui, Fadoua. "Nonparametric estimation of a k-monotone density : a new asymptotic distribution theory /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/8964.

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Books on the topic "Asymptotic distribution"

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Asymptotic distribution theory in nonparametric statistics. Braunschweig: Vieweg, 1985.

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Denker, Manfred. Asymptotic Distribution Theory in Nonparametric Statistics. Wiesbaden: Vieweg+Teubner Verlag, 1985. http://dx.doi.org/10.1007/978-3-663-14229-4.

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Levendorskiĭ, Serge. Asymptotic distribution of eigenvalues of differential operators. Dordrecht [Netherlands]: Kluwer Academic Publishers, 1990.

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N, Bhattacharya R. Asymptotic statistics. Basel: Birkhäuser Verlag, 1990.

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Levendorskiǐ, Serge. Asymptotic Distribution of Eigenvalues of Differential Operators. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1918-1.

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Palka, Zbigniew. Asymptotic properties of random graphs. Warszawa: Państwowe Wydawn. Nauk., 1988.

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Ibragimov, I. A., N. Balakrishnan, and Valery B. Nevzorov. Asymptotic methods in probability and statistics with applications. New York: Springer Science+Business Media, 2001.

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Safarov, Yu. The asymptotic distribution of eigenvalues of partial differential operators. Providence, R.I: American Mathematical Society, 1997.

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Small, Christopher G. Expansions and asymptotics for statistics. Boca Raton: Chapman & Hall/CRC, 2010.

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Fraser, D. A. S. Ancillaries and third order significance. Toronto, Ont: University of Toronto, Department of Statistics, 1993.

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Book chapters on the topic "Asymptotic distribution"

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Pflug, Georg Ch. "On an Argmax-Distribution Connected to the Poisson Process." In Asymptotic Statistics, 123–29. Heidelberg: Physica-Verlag HD, 1994. http://dx.doi.org/10.1007/978-3-642-57984-4_9.

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Ferguson, Thomas S. "Asymptotic Distribution of Sample Quantiles." In A Course in Large Sample Theory, 87–93. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-4549-5_13.

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Ivanov, Alexander V. "Approximation by a Normal Distribution." In Asymptotic Theory of Nonlinear Regression, 79–153. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8877-5_3.

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Rio, Emmanuel. "Empirical Distribution Functions." In Asymptotic Theory of Weakly Dependent Random Processes, 113–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-54323-8_7.

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Denker, Manfred. "U-statistics." In Asymptotic Distribution Theory in Nonparametric Statistics, 1–50. Wiesbaden: Vieweg+Teubner Verlag, 1985. http://dx.doi.org/10.1007/978-3-663-14229-4_1.

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Denker, Manfred. "Differentiable statistical functionals." In Asymptotic Distribution Theory in Nonparametric Statistics, 51–97. Wiesbaden: Vieweg+Teubner Verlag, 1985. http://dx.doi.org/10.1007/978-3-663-14229-4_2.

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Denker, Manfred. "Statistics based on ranking methods." In Asymptotic Distribution Theory in Nonparametric Statistics, 98–168. Wiesbaden: Vieweg+Teubner Verlag, 1985. http://dx.doi.org/10.1007/978-3-663-14229-4_3.

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Denker, Manfred. "Contiguity and efficiency." In Asymptotic Distribution Theory in Nonparametric Statistics, 169–98. Wiesbaden: Vieweg+Teubner Verlag, 1985. http://dx.doi.org/10.1007/978-3-663-14229-4_4.

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Parring, Anne-Mai. "The Asymptotic Distribution of Regression Parameters." In Contributions to Statistics, 205–12. Heidelberg: Physica-Verlag HD, 1995. http://dx.doi.org/10.1007/978-3-662-12516-8_22.

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Móri, Tamás F. "Asymptotic Joint Distribution of Cover Times." In Runs and Patterns in Probability, 307–27. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4613-3635-8_20.

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Conference papers on the topic "Asymptotic distribution"

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Zhao Chenhao, Song Xiangdong, and Zhang Huijuan. "An asymptotic distribution of a specific beta distribution." In International Conference on Automatic Control and Artificial Intelligence (ACAI 2012). Institution of Engineering and Technology, 2012. http://dx.doi.org/10.1049/cp.2012.0998.

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BICKIS, MIKELIS G. "THE ASYMPTOTIC DISTRIBUTION OF SPACINGS OF ORDER STATISTICS." In Proceedings of Statistics 2001 Canada: The 4th Conference in Applied Statistics. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2002. http://dx.doi.org/10.1142/9781860949531_0004.

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Delmas, Jean-Pierre, Abdelkader Oukaci, and Pascal Chevalier. "Asymptotic distribution of GLR for impropriety of complex signals." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5495920.

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Oudin, M., and J. P. Delmas. "Asymptotic generalized eigenvalue distribution of Toeplitz block Toeplitz matrices." In ICASSP 2008 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2008. http://dx.doi.org/10.1109/icassp.2008.4518358.

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Rathi, V. "On the asymptotic weight distribution of regular LDPC ensembles." In Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. IEEE, 2005. http://dx.doi.org/10.1109/isit.2005.1523729.

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Clausen, A., and D. Cochran. "Asymptotic non-null distribution of the generalized coherence estimate." In 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258). IEEE, 1999. http://dx.doi.org/10.1109/icassp.1999.756187.

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Levin, Georgy, and Sergey Loyka. "On Asymptotic Outage Capacity Distribution of Correlated MIMO Channels." In 2007 International Symposium on Signals, Systems, and Electronics, URSI ISSSE 2007. IEEE, 2007. http://dx.doi.org/10.1109/issse.2007.4294468.

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Duan, D. W., and Y. Rahmat-Samii. "Three-parameter (3-P) aperture distribution: asymptotic characteristics and applications." In IEEE Antennas and Propagation Society International Symposium 1992 Digest. IEEE, 1992. http://dx.doi.org/10.1109/aps.1992.221921.

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Shin, Hongjoon, Woosung Nam, Younghun Jung, and Jun-Haeng Heo. "Asymptotic Variance of Regional Growth Curve for Generalized Logistic Distribution." In World Environmental and Water Resources Congress 2009. Reston, VA: American Society of Civil Engineers, 2009. http://dx.doi.org/10.1061/41036(342)474.

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GUO, RENKUAN. "SMALL SAMPLE ASYMPTOTIC DISTRIBUTION OF COST-RELATED RELIABILITY RISK MEASURE." In Proceedings of the 2nd International Workshop (AIWARM 2006). WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773760_0071.

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Reports on the topic "Asymptotic distribution"

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Simpson, Douglas G., Raymond J. Carroll, and David Ruppert. M-Estimation for Discrete Data. Asymptotic Distribution Theory and Implications. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada162779.

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Simpson, Douglas G., Raymond J. Carroll, and David Ruppert. M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications. Fort Belvoir, VA: Defense Technical Information Center, November 1985. http://dx.doi.org/10.21236/ada168532.

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Gupta, Shanti S., and Friedrich Liese. Asymptotic Distribution of the Random Regret Risk for Selecting Exponential Populations. Fort Belvoir, VA: Defense Technical Information Center, April 1998. http://dx.doi.org/10.21236/ada358189.

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Babu, C. J., and C. R. Rao. Joint Asymptotic Distribution of Marginal Quantiles and Quantile Functions in Samples from a Multivariate Population. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada193385.

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5

Fang, C., and P. R. Krishnaiah. On Asymptotic Distribution of the Test Statistic for the Mean of the Non-Isotropic Principal Component. Fort Belvoir, VA: Defense Technical Information Center, May 1985. http://dx.doi.org/10.21236/ada158255.

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Chernoff, Herman, and Eric Lander. Asymptotic Distribution of the Likelihood Ratio Test That a Mixture of Two Binomials is a Single Binomial. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada236714.

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Amengual, Dante, Xinyue Bei, Marine Carrasco, and Enrique Sentana. Score-type tests for normal mixtures. CIRANO, January 2023. http://dx.doi.org/10.54932/uxsg1990.

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Testing normality against discrete normal mixtures is complex because some parameters turn increasingly underidentified along alternative ways of approaching the null, others are inequality constrained, and several higher-order derivatives become identically 0. These problems make the maximum of the alternative model log-likelihood function numerically unreliable. We propose score-type tests asymptotically equivalent to the likelihood ratio as the largest of two simple intuitive statistics that only require estimation under the null. One novelty of our approach is that we treat symmetrically both ways of writing the null hypothesis without excluding any region of the parameter space. We derive the asymptotic distribution of our tests under the null and sequences of local alternatives. We also show that their asymptotic distribution is the same whether applied to observations or standardized residuals from heteroskedastic regression models. Finally, we study their power in simulations and apply them to the residuals of Mincer earnings functions.
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Missov, Trifon I., and Maxim S. Finkelstein. Admissible mixing distributions for a general class of mixture survival models with known asymptotics. Rostock: Max Planck Institute for Demographic Research, May 2011. http://dx.doi.org/10.4054/mpidr-wp-2011-004.

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Bouezmarni, Taoufik, Mohamed Doukali, and Abderrahim Taamouti. Copula-based estimation of health concentration curves with an application to COVID-19. CIRANO, 2022. http://dx.doi.org/10.54932/mtkj3339.

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COVID-19 has created an unprecedented global health crisis that caused millions of infections and deaths worldwide. Many, however, argue that pre-existing social inequalities have led to inequalities in infection and death rates across social classes, with the most-deprived classes are worst hit. In this paper, we derive semi/non-parametric estimators of Health Concentration Curve (HC) that can quantify inequalities in COVID-19 infections and deaths and help identify the social classes that are most at risk of infection and dying from the virus. We express HC in terms of copula function that we use to build our estimators of HC. For the semi-parametric estimator, a parametric copula is used to model the dependence between health and socio-economic variables. The copula function is estimated using maximum pseudo-likelihood estimator after replacing the cumulative distribution of health variable by its empirical analogue. For the non-parametric estimator, we replace the copula function by a Bernstein copula estimator. Furthermore, we use the above estimators of HC to derive copula-based estimators of health Gini coeffcient. We establish the consistency and the asymptotic normality of HC’s estimators. Using different data-generating processes and sample sizes, a Monte-Carlo simulation exercise shows that the semiparametric estimator outperforms the smoothed nonparametric estimator, and that the latter does better than the empirical estimator in terms of Integrated Mean Squared Error. Finally, we run an extensive empirical study to illustrate the importance of HC’s estimators for investigating inequality in COVID-19 infections and deaths in the U.S. The empirical results show that the inequalities in state’s socio-economic variables like poverty, race/ethnicity, and economic prosperity are behind the observed inequalities in the U.S.’s COVID-19 infections and deaths.
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Kott, Phillip S. Better Coverage Intervals for Estimators from a Complex Sample Survey. RTI Press, February 2020. http://dx.doi.org/10.3768/rtipress.2020.mr.0041.2002.

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Coverage intervals for a parameter estimate computed using complex survey data are often constructed by assuming the parameter estimate has an asymptotically normal distribution and the measure of the estimator’s variance is roughly chi-squared. The size of the sample and the nature of the parameter being estimated render this conventional “Wald” methodology dubious in many applications. I developed a revised method of coverage-interval construction that “speeds up the asymptotics” by incorporating an estimated measure of skewness. I discuss how skewness-adjusted intervals can be computed for ratios, differences between domain means, and regression coefficients.
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