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Asymptotic Normality of Parameter Estimators for~Mixed Fractional Brownian Motion with Trend
Austrian Journal of Statistics, 2023 We investigate the mixed fractional Brownian motion of the form Xt = θt+σWt +κBtH , driven by a standard Brownian motion W and a fractional Brownian motion B H with Hurst parameter H.
Kostiantyn Ralchenko, Mykyta Yakovliev
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Miskolc Mathematical NotesThe present paper derives convergence rates and asymptotic normality of a class of M ...
Ahmed Ghezal, Imane Zemmouri
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Asymptotic Normality in Nonparametric Methods
The Annals of Mathematical Statistics, 1968 Let $U_1, U_2, \cdots, U_N$ be a random sample from a population with a continuous distribution function and $R_i, i = 1, \cdots, N,$ be the rank of $U_i$ among the $N$ observations. Asymptotic normality is studied for the statistics of the type \begin{equation*}\tag{0.1} \sum^N_{i=1} \sum^N_{j=1} c_{ij}a_N(R_i/N, R_j/N),\end{equation*} where constants
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Asymptotically Normal Estimators for Zipf’s Law [PDF]
Sankhya A, 2018 Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated. We use the number of different words in a text and similar statistics to construct asymptotically normal ...
Mikhail Chebunin, Artyom Kovalevskii
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Asymptotic Distribution of Normalized Arithmetical Functions [PDF]
Proceedings of the American Mathematical Society, 1974 Let f ( n ) f(n) be an arbitrary arithmetical function and let A N {A_N} and B N {B_N} be sequences of real numbers with 0 > B N
Erdős, Paul, Galambos, Janos
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Robust Estimations for the Tail Index of Weibull-Type Distribution
Risks, 2018 Based on suitable left-truncated or censored data, two flexible classes of M-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination.
Chengping Gong, Chengxiu Ling
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Asymptotic Normality of Bispectral Estimates
The Annals of Mathematical Statistics, 1966 The work presented here is a continuation of that presented in an earlier paper, M. Rosenblatt and J. Van Ness [15], in which the basic properties (unbiasedness and consistency) of certain estimates of the bispectrum and bispectral density are discussed.
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Asymptotic normality of winsorized means
Stochastic Processes and their Applications, 1988 Given independent, identically distributed random variables \(X_ 1,...,X_ n\), let \(r_ n\) and \(s_ n\) be specified integers satisfying \(1\leq r_ n, s_ n\leq n/2\). A Winsorized mean is constructed by replacing the \(s_ n\) smallest observations and the \(r_ n\) largest observations by the \(s_ n th\) smallest observation and the \(r_ n th\) largest
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Further results on asymptotic normality II
Metrika, 1972 Starting fromLe Cam [1956], it was shown inMichel andPfanzagl [1970] that — under certain regularity conditions — a dominated family of probability measures withEuclidean parameter space behaves approximately like a family of normal distributions, if each probability measure is the independent product of a great number of identical components.
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Asymptotic normality in Monte Carlo integration [PDF]
Mathematics of Computation, 1976 To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators J 1 ′ J’_1 and J 2 ′ J’_2 based on 2N and 4N observations, respectively, of the function. He also considered estimators D 1 2
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