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Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2013, Volume 19, Issue 3, pp. 1006 - 1027
...}} \ {\mathrm{X}}_{\mathrm{i}}$ and ${\mathrm{V}}_{\mathrm{n}}^{2}={\mathrm{\Sigma }}_{\mathrm{i}=1}^{\mathrm{n}} \ {\mathrm{X}}_{\mathrm{i}}^{2}$ . A Cramér type moderate deviation for the maximum of the self-normalized sums max 1... 
Mathematical moments | Mathematical theorems | Random variables | Statistics | Independent random variables | Maximum of self-normalized sums | STATISTICS & PROBABILITY | maximum of self-normalized sums | independent random variables | INDEPENDENT RANDOM-VARIABLES | PROBABILITIES
Journal Article
Electronic Journal of Probability, ISSN 1083-6489, 01/2009, Volume 14, pp. 1181 - 1197
.... In this paper we discuss the moderate deviations of the maximum of the self-normalized sums. In particular, we prove that P(max(1 <= k <= n) S-k >= x V-n)/(1 - Phi(x... 
Moderate deviation | Self-normalized sum | Large deviation | THEOREM | moderate deviation | self-normalized sum | STATISTICS & PROBABILITY | INDEPENDENT RANDOM-VARIABLES | PROBABILITIES
Journal Article
by Wu, QY and Jiang, YY
FILOMAT, ISSN 0354-5180, 2019, Volume 33, Issue 8, pp. 2471 - 2488
For many forensic traces (inks, fibres, paints, ...) the chemical characterization of dyes or pigments is currently performed with reliable techniques that... 
MATHEMATICS | MOMENT INEQUALITIES | RATES | MATHEMATICS, APPLIED | self-normalized products of sums of partial sums | MAXIMUM | rho(-)-mixing random variables | almost sure central limit theorem | CENTRAL-LIMIT-THEOREM
Journal Article
07/2013
...}r type moderate deviation for the maximum of the self-normalized sums $\max_{1\leq k\leq n}S_k/V_n$ is obtained. In particular, for identically distributed... 
Journal Article
The Annals of Probability, ISSN 0091-1798, 10/1973, Volume 1, Issue 5, pp. 788 - 809
If $X_i$ are i.i.d. and have zero mean and arbitrary finite variance the limiting probability distribution of $S_n(2) = (\sum^n_{i=1} X_i)/(\sum^n_{j=1} X_j^2... 
Statistical variance | Zero | Absolute convergence | Numerical analysis | Local maximum | Positive laws | Eigenfunctions | Laplace transformation | Random variables | Distribution functions | stable laws | Limit theorems | domains of attraction | 60F0F | 60G50 | maxima of i.i.d. characteristic function
Journal Article
by Yao, Mei and Lin, Lu
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 13
By using some inequalities and properties of martingale differences, we investigate the moment of maximum normed randomly weighted sums of martingale differences under some weakly conditions... 
60F25 | random weighted | Analysis | Mathematics, general | Mathematics | maximum normed | Applications of Mathematics | 60F15 | martingale differences | COMPLETE CONVERGENCE | MATHEMATICS | MATHEMATICS, APPLIED | TAIL PROBABILITIES | QUADRATIC FORMS | INDEPENDENT RANDOM-VARIABLES | Norms | Stochasticity | Martingales | Inequalities | Sums
Journal Article
The Annals of statistics, ISSN 0090-5364, 2015, Volume 43, Issue 6, pp. 2451 - 2483
Journal Article
Bernoulli, ISSN 1350-7265, 11/2016, Volume 22, Issue 4, pp. 2325 - 2371
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 6/2018, Volume 31, Issue 2, pp. 1142 - 1165
Journal Article
Journal of Statistical Computation and Simulation, ISSN 0094-9655, 05/2020, Volume 90, Issue 7, pp. 1251 - 1266
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 4/2003, Volume 16, Issue 2, pp. 377 - 389
Journal Article
Journal of Computational and Graphical Statistics, ISSN 1061-8600, 07/2015, Volume 24, Issue 3, pp. 846 - 865
We propose sequential Monte Carlo-based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable... 
Maximum likelihood estimation | Approximate Bayesian computation | STATISTICS & PROBABILITY | PARTICLE FILTER | STOCHASTIC VOLATILITY
Journal Article
IET Communications, ISSN 1751-8628, 8/2015, Volume 9, Issue 12, pp. 1501 - 1509
Journal Article
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