Journal of Theoretical Probability, ISSN 0894-9840, 6/2018, Volume 31, Issue 2, pp. 1142 - 1165

We provide an improved version of the Darling–Erdős theorem for sums of i.i.d. random variables with mean zero and finite variance...

Multidimensional version | Darling–Erdős theorem | Extreme value distribution | Strong invariance principle | Probability Theory and Stochastic Processes | Mathematics | Integral test | Statistics, general | Hartman–Wintner LIL | Double truncation | 60F17 | 60F15 | LAW | MAXIMUM | STATISTICS & PROBABILITY | NORMALIZED SUMS | Darling-Erdos theorem | IID RANDOM-VARIABLES | Hartman-Wintner LIL | HILBERT-SPACE

Multidimensional version | Darling–Erdős theorem | Extreme value distribution | Strong invariance principle | Probability Theory and Stochastic Processes | Mathematics | Integral test | Statistics, general | Hartman–Wintner LIL | Double truncation | 60F17 | 60F15 | LAW | MAXIMUM | STATISTICS & PROBABILITY | NORMALIZED SUMS | Darling-Erdos theorem | IID RANDOM-VARIABLES | Hartman-Wintner LIL | HILBERT-SPACE

Journal Article

The Annals of probability, ISSN 0091-1798, 4/2003, Volume 31, Issue 2, pp. 676 - 692

... to the domain of attraction of the normal law. In this context, we establish a Darling-Erdős-type theorem as well...

Mathematics | Mathematical theorems | Random variables | Logarithms | Statistical theories | Self-normalized sums | Erdos-Feller-Kolmogorov-Petrovski test | Darling-Erdos theorem | STATISTICS & PROBABILITY | self-normalized sums | RANDOM-VARIABLES | Darling--Erdős theorem | Erdős--Feller--Kolmogorov--Petrovski test | 60F05 | 62E20 | 60F15

Mathematics | Mathematical theorems | Random variables | Logarithms | Statistical theories | Self-normalized sums | Erdos-Feller-Kolmogorov-Petrovski test | Darling-Erdos theorem | STATISTICS & PROBABILITY | self-normalized sums | RANDOM-VARIABLES | Darling--Erdős theorem | Erdős--Feller--Kolmogorov--Petrovski test | 60F05 | 62E20 | 60F15

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 6/2011, Volume 24, Issue 2, pp. 376 - 396

We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes...

Functional CLT | Extremal distributions | 60B12 | 60J80 | Darling–Erdös theorem | 60B10 | Probability Theory and Stochastic Processes | Weighted c 0 spaces | Mathematics | Statistics, general | Branching processes | 60F17 | spaces | Darling-Erdös theorem | Weighted c | STATISTICS & PROBABILITY | Darling-Erdos theorem | Weighted c spaces

Functional CLT | Extremal distributions | 60B12 | 60J80 | Darling–Erdös theorem | 60B10 | Probability Theory and Stochastic Processes | Weighted c 0 spaces | Mathematics | Statistics, general | Branching processes | 60F17 | spaces | Darling-Erdös theorem | Weighted c | STATISTICS & PROBABILITY | Darling-Erdos theorem | Weighted c spaces

Journal Article

Probability surveys, ISSN 1549-5787, 2013, Volume 10, Issue 1, pp. 69 - 93

Cramer moderate deviation | Invariance principle | Hotelling's T2 statistic | Self-normalized sum | Large deviation | Absolute error | Darling-Erdos theorem | Central limit theorem | Saddle-point approximation | Student t statistic | Convergence rate | Laws of the iterated logarithm | Relative error

Journal Article

Brazilian Journal of Probability and Statistics, ISSN 0103-0752, 2014, Volume 28, Issue 4, pp. 538 - 560

Journal Article

Extremes, ISSN 1386-1999, 6/2008, Volume 11, Issue 2, pp. 135 - 166

... by an illustrative simulation study. Keywords Augmented GARCH processes · Darling–Erd os limit theorems · Linear models · Recursive residuals · Sequential testing AMS 2000...

Civil Engineering | Darling–Erdős limit theorems | Statistics, general | Sequential testing | Statistics | Linear models | Primary– 62J05 | Secondary– 62L10 | Augmented GARCH processes | Hydrogeology | Statistics for Business/Economics/Mathematical Finance/Insurance | Quality Control, Reliability, Safety and Risk | Recursive residuals | Environmental Management | Darling-Erdos limit theorems | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATISTICS & PROBABILITY | Analysis | Models | Detectors | Studies | Linear programming | Mathematical models | Stochastic models

Civil Engineering | Darling–Erdős limit theorems | Statistics, general | Sequential testing | Statistics | Linear models | Primary– 62J05 | Secondary– 62L10 | Augmented GARCH processes | Hydrogeology | Statistics for Business/Economics/Mathematical Finance/Insurance | Quality Control, Reliability, Safety and Risk | Recursive residuals | Environmental Management | Darling-Erdos limit theorems | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATISTICS & PROBABILITY | Analysis | Models | Detectors | Studies | Linear programming | Mathematical models | Stochastic models

Journal Article

Brazilian journal of probability and statistics, ISSN 0103-0752, 11/2014, Volume 28, Issue 4, pp. 538 - 560

This paper studies the problem of testing the null assumption of no-change in the mean of chronologically ordered independent observations on a random variable...

Statistical variance | Null hypothesis | Mathematical theorems | Approximation | Statistical theories | Sample mean | Random variables | Statistics | Probabilities | Brownian bridge | CHANGE-POINT MODELS | Change in the mean | weighted metrics | domain of attraction of the normal law | Darling-Erdos theorems | Gumbel distribution | STATISTICS & PROBABILITY | WEIGHTED APPROXIMATIONS | SUMS

Statistical variance | Null hypothesis | Mathematical theorems | Approximation | Statistical theories | Sample mean | Random variables | Statistics | Probabilities | Brownian bridge | CHANGE-POINT MODELS | Change in the mean | weighted metrics | domain of attraction of the normal law | Darling-Erdos theorems | Gumbel distribution | STATISTICS & PROBABILITY | WEIGHTED APPROXIMATIONS | SUMS

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 4/2003, Volume 16, Issue 2, pp. 377 - 389

.... The results are then applied to derive the law of the iterated logarithm and Darling–Erdős type theorem for long memory processes under ideal conditions.

strong approximation | the law of the iterated logarithm | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | long memory process | Darling–Erdős type theorem | Strong approximation | The law of the iterated logarithm | Long memory process | Darling-Erd″os type theorem | GAUSSIAN VARIABLES | LAW | MAXIMUM | ERDOS THEOREM | STATISTICS & PROBABILITY | ITERATED LOGARITHM | EMPIRICAL PROCESS | Darling-Erdos type theorem | PARTIAL SUMS | RANGE DEPENDENCE | MOVING AVERAGES | LIMIT-THEOREMS

strong approximation | the law of the iterated logarithm | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | long memory process | Darling–Erdős type theorem | Strong approximation | The law of the iterated logarithm | Long memory process | Darling-Erd″os type theorem | GAUSSIAN VARIABLES | LAW | MAXIMUM | ERDOS THEOREM | STATISTICS & PROBABILITY | ITERATED LOGARITHM | EMPIRICAL PROCESS | Darling-Erdos type theorem | PARTIAL SUMS | RANGE DEPENDENCE | MOVING AVERAGES | LIMIT-THEOREMS

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 2007, Volume 77, Issue 9, pp. 885 - 895

...–Erdős type limit theorem.

Darling–Erdős limit theorem | Linear regression model | Sequential monitoring | Darling-Erdo{combining double acute accent}s limit theorem | sequential monitoring | INDEPENDENT RVS | linear regression model | PARTIAL SUMS | APPROXIMATION | MODELS | Darling-Erdos limit theorem | STATISTICS & PROBABILITY | Darling-Erdös limit theorem Linear regression model Sequential monitoring | Analysis | Regression analysis

Darling–Erdős limit theorem | Linear regression model | Sequential monitoring | Darling-Erdo{combining double acute accent}s limit theorem | sequential monitoring | INDEPENDENT RVS | linear regression model | PARTIAL SUMS | APPROXIMATION | MODELS | Darling-Erdos limit theorem | STATISTICS & PROBABILITY | Darling-Erdös limit theorem Linear regression model Sequential monitoring | Analysis | Regression analysis

Journal Article

Ann. Probab, 1998, Volume 26, Issue no. 2, pp. 832 - 852

..., \max_{k=1,\dots,n} k^{-1/\alpha}S_k. This completes the Darling-Erdös limit theorem for the case \alpha = 2.

normalized maximum | 60J30 | Stable Lévy process | 60G10 | Darling-Erdös theorem | 60F05

normalized maximum | 60J30 | Stable Lévy process | 60G10 | Darling-Erdös theorem | 60F05

Journal Article

11.
Full Text
The Maximum Likelihood Method for Testing Changes in the Parameters of Normal Observations

The Annals of statistics, ISSN 0090-5364, 1993, Volume 21, Issue 2, pp. 671 - 680

We compute the asymptotic distribution of the maximum likelihood ratio test when we want to check whether the parameters of normal observations have changed at...

Monte Carlo methods | Random variables | Logarithms | Change-Point Problems | STRONG APPROXIMATION | STATISTICS & PROBABILITY | MAXIMUM LIKELIHOOD | CHANGE-POINT | DARLING-ERDOS TYPE LIMIT THEOREMS | SEQUENCE | Darling-Erdos-type limit theorems | 62F03 | maximum likelihood | strong approximation | 62F05

Monte Carlo methods | Random variables | Logarithms | Change-Point Problems | STRONG APPROXIMATION | STATISTICS & PROBABILITY | MAXIMUM LIKELIHOOD | CHANGE-POINT | DARLING-ERDOS TYPE LIMIT THEOREMS | SEQUENCE | Darling-Erdos-type limit theorems | 62F03 | maximum likelihood | strong approximation | 62F05

Journal Article

The Annals of probability, ISSN 0091-1798, 4/1998, Volume 26, Issue 2, pp. 832 - 852

... S . This completes the Darling-Erdos limit theorem for the case α = 2.

Mathematical theorems | Real numbers | Logical proofs | Markov processes | Partial sums | Spectral index | Ornstein Uhlenbeck process | Random variables | Distribution functions | Darling-Erdos theorem | Normalized maximum | Stable Lévy process | STATISTICS & PROBABILITY | normalized maximum | stable Levy process | STATIONARY

Mathematical theorems | Real numbers | Logical proofs | Markov processes | Partial sums | Spectral index | Ornstein Uhlenbeck process | Random variables | Distribution functions | Darling-Erdos theorem | Normalized maximum | Stable Lévy process | STATISTICS & PROBABILITY | normalized maximum | stable Levy process | STATIONARY

Journal Article

Canadian journal of statistics, ISSN 0319-5724, 12/2002, Volume 30, Issue 4, pp. 493 - 556

The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdős's contributions per...

Brownian motion | Mathematical theorems | Approximation | Statistical theories | Random walk | Partial sums | Random variables | Statistics | Probabilities | Change-point analysis | Erdos-Rényi laws | Arc sine laws | Erdos-Kac invariance principle | Complete convergence | Erdos numbers | Darling-Erdos theorems | CLT | Donsker's functional CLT | Erdos-Feller-Kolmogorov-Petrovski integral tests | arc sine laws | APPROXIMATION | Hungarian construction | Wiener process | random graphs | Erdos-Feller-Kolmogorov-Petrovski integral | Erdos-Renyi laws | probabilistic number theory | complete convergence | MOTION | moduli of continuity and nondifferentiability of a Wiener process | Skorohod embedding scheme | CONVERGENCE | large increments of partial sums and Wiener processes | weak convergence | STRASSEN TYPE LAWS | random walks | functional LIL | Ornstein-Uhlenbeck process | random walks local time | strong approximations-strong invariance | sampling from finite populations | STATISTICS & PROBABILITY | random walks and self-normalized sums | RENYI | change-point analysis | INCREMENTS | WIENER | tests | invariance in probability | prime number theorem | KINETIC-THEORY | partial sums | LIMIT-THEOREMS | PARTIAL-SUMS | Erdos series test for symmetric | Riemann hypothesis | probabilistic method | self-normalized Darling-Erdos and Donsker theorems

Brownian motion | Mathematical theorems | Approximation | Statistical theories | Random walk | Partial sums | Random variables | Statistics | Probabilities | Change-point analysis | Erdos-Rényi laws | Arc sine laws | Erdos-Kac invariance principle | Complete convergence | Erdos numbers | Darling-Erdos theorems | CLT | Donsker's functional CLT | Erdos-Feller-Kolmogorov-Petrovski integral tests | arc sine laws | APPROXIMATION | Hungarian construction | Wiener process | random graphs | Erdos-Feller-Kolmogorov-Petrovski integral | Erdos-Renyi laws | probabilistic number theory | complete convergence | MOTION | moduli of continuity and nondifferentiability of a Wiener process | Skorohod embedding scheme | CONVERGENCE | large increments of partial sums and Wiener processes | weak convergence | STRASSEN TYPE LAWS | random walks | functional LIL | Ornstein-Uhlenbeck process | random walks local time | strong approximations-strong invariance | sampling from finite populations | STATISTICS & PROBABILITY | random walks and self-normalized sums | RENYI | change-point analysis | INCREMENTS | WIENER | tests | invariance in probability | prime number theorem | KINETIC-THEORY | partial sums | LIMIT-THEOREMS | PARTIAL-SUMS | Erdos series test for symmetric | Riemann hypothesis | probabilistic method | self-normalized Darling-Erdos and Donsker theorems

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 08/2005, Volume 10, pp. 196 - 206

We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL...

Brownian motion | The law of the iterated logarithm | Darling-Erdos theorems | Extreme values | Darling-Erdós theorems | NORMALIZED SUMS | RATES | LAW | extreme values | MAXIMUM | ERDOS THEOREM | the law of the iterated logarithm | CONVERGENCE | STATISTICS & PROBABILITY | EXCEEDANCES

Brownian motion | The law of the iterated logarithm | Darling-Erdos theorems | Extreme values | Darling-Erdós theorems | NORMALIZED SUMS | RATES | LAW | extreme values | MAXIMUM | ERDOS THEOREM | the law of the iterated logarithm | CONVERGENCE | STATISTICS & PROBABILITY | EXCEEDANCES

Journal Article

Canadian Journal of Statistics, ISSN 0319-5724, 12/2002, Volume 30, Issue 4, pp. 493 - 556

The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdõs's contributions per...

Arc sine laws | Hungarian construction | Wiener process | change‐point analysis | CLT | random graphs | Donsker's functional CLT | Omstein‐Uhlenbeck process | Erdõs numbers | probabilistic number theory | complete convergence | moduli of continuity and nondifferentiability of a Wiener process | Skorohod embedding scheme | large increments of partial sums and Wiener processes | weak convergence | random walks | functional LIL | Erdõs‐Rényi laws | random walks local time | strong approximations‐strong invariance | sampling from finite populations | self‐normalized Darling‐Erdõs and Donsker theorems | Brownian motion | invariance in probability | prime number theorem | partial sums | Erdõs‐Feller‐Kolmogorov‐Petrovski integral tests | Erdõs series test for symmetric random walks and self‐normalized sums | Erdös‐Kac invariance principle | Riemann hypothesis | Darling‐Erdõs theorems | probabilistic method

Arc sine laws | Hungarian construction | Wiener process | change‐point analysis | CLT | random graphs | Donsker's functional CLT | Omstein‐Uhlenbeck process | Erdõs numbers | probabilistic number theory | complete convergence | moduli of continuity and nondifferentiability of a Wiener process | Skorohod embedding scheme | large increments of partial sums and Wiener processes | weak convergence | random walks | functional LIL | Erdõs‐Rényi laws | random walks local time | strong approximations‐strong invariance | sampling from finite populations | self‐normalized Darling‐Erdõs and Donsker theorems | Brownian motion | invariance in probability | prime number theorem | partial sums | Erdõs‐Feller‐Kolmogorov‐Petrovski integral tests | Erdõs series test for symmetric random walks and self‐normalized sums | Erdös‐Kac invariance principle | Riemann hypothesis | Darling‐Erdõs theorems | probabilistic method

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 10/1989, Volume 2, Issue 4, pp. 437 - 460

Journal Article

Metrika, ISSN 0026-1335, 1/2015, Volume 78, Issue 1, pp. 1 - 27

...–Erdős-type limit theorem. Under mild moment assumptions we investigate the asymptotic properties under the null hypothesis and show consistency under the alternatives of either an abrupt or a gradual change in the mean...

CUSUM | Nonparametric | Statistics for Business/Economics/Mathematical Finance/Insurance | Change-point test | Darling–Erdős | Probability Theory and Stochastic Processes | Economic Theory | Statistics, general | Statistics | Functional data analysis | Darling-Erdos | STATISTICS & PROBABILITY

CUSUM | Nonparametric | Statistics for Business/Economics/Mathematical Finance/Insurance | Change-point test | Darling–Erdős | Probability Theory and Stochastic Processes | Economic Theory | Statistics, general | Statistics | Functional data analysis | Darling-Erdos | STATISTICS & PROBABILITY

Journal Article

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