Journal of Inequalities and Applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1, pp. 1 - 14

Let {X,Xn}n∈N\(\{X, X_{n}\}_{n\in N}\) be a strictly stationary ρ−\(\rho^{-}\)-mixing sequence of positive random variables, under the suitable conditions, we...

Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables

Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 07/2014, Volume 19, pp. 1 - 14

We consider the probability that a weighted sum of n i.i.d. random variables X-j, j = 1,...,n, with stretched exponential tails is larger than its expectation...

Kernels | Self-normalized weights | Stretched exponential random variables | Nonparametric regression | Subexponential random variables | Large deviations | Quenched and annealed large deviations | Weighted sums | self-normalized weights | weighted sums | nonparametric regression | quenched and annealed large deviations | subexponential random variables | kernels | STATISTICS & PROBABILITY | stretched exponential random variables | Mathematics - Probability

Kernels | Self-normalized weights | Stretched exponential random variables | Nonparametric regression | Subexponential random variables | Large deviations | Quenched and annealed large deviations | Weighted sums | self-normalized weights | weighted sums | nonparametric regression | quenched and annealed large deviations | subexponential random variables | kernels | STATISTICS & PROBABILITY | stretched exponential random variables | Mathematics - Probability

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 3/2016, Volume 29, Issue 1, pp. 267 - 276

Let $$X, X_{1}, X_{2}, \ldots $$ X , X 1 , X 2 , … be i.i.d. random variables, and set $$S_{n}=X_{1}+\cdots +X_{n}$$ S n = X 1 + ⋯ + X n and $$...

Precise asymptotics | Self-normalized sums | Secondary 60F15 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Domain of attraction | Primary 60G50 | Stable law | LAWS | LARGE NUMBERS | STATISTICS & PROBABILITY

Precise asymptotics | Self-normalized sums | Secondary 60F15 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Domain of attraction | Primary 60G50 | Stable law | LAWS | LARGE NUMBERS | STATISTICS & PROBABILITY

Journal Article

Bernoulli, ISSN 1350-7265, 8/2013, Volume 19, Issue 3, pp. 1006 - 1027

Let X 1 , X 2 ,... be independent random variables with zero means and finite variances, and let S n = ${\mathrm{\Sigma }}_{\mathrm{i}=1}^{\mathrm{n}} \...

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

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, 2012, Volume 17, pp. 1 - 21

We consider the self-normalized sums T-n = Sigma(n)(i=1) XiYi/Sigma(n)(i=1) Y-i, where {Y-i : i >= 1} are non-negative i.i.d. random variables, and {X-i : i >=...

Self-normalized sums | Stable distributions | Feller class | stable distributions | STATISTICS & PROBABILITY | Mathematics - Probability

Self-normalized sums | Stable distributions | Feller class | stable distributions | STATISTICS & PROBABILITY | Mathematics - Probability

Journal Article

The Annals of Probability, ISSN 0091-1798, 7/2003, Volume 31, Issue 3, pp. 1228 - 1240

Let X,X ,X ,... be a sequence of nondegenerate i.i.d. random variables with zero means. In this paper we show that a self-normalized version of Donsker's...

Mathematical theorems | Central limit theorem | Statistical theories | Probability theory | Partial sums | Mathematical moments | Random variables | Probabilities | Law of sines | Self-normalized sums | Arc sine law | Donsker's theorem | arc sine law | STATISTICS & PROBABILITY | self-normalized sums | 60F17 | 60F05 | 62E20

Mathematical theorems | Central limit theorem | Statistical theories | Probability theory | Partial sums | Mathematical moments | Random variables | Probabilities | Law of sines | Self-normalized sums | Arc sine law | Donsker's theorem | arc sine law | STATISTICS & PROBABILITY | self-normalized sums | 60F17 | 60F05 | 62E20

Journal Article

Bernoulli, ISSN 1350-7265, 05/2015, Volume 21, Issue 2, pp. 1231 - 1237

Let epsilon(1) . . . . . epsilon(n) be independent identically distributed Rademacher random variables, that is P{epsilon(i) = +/- 1) = 1/2. Let S-n...

Tail comparison | Self-normalized sums | Weighted Rademachers | Random sign | Optimal constants | Student's statistic | Gaussian | Large deviations | Symmetric | Bounds for tail probabilities | large deviations | optimal constants | bounds for tail probabilities | STATISTICS & PROBABILITY | symmetric | random sign | self-normalized sums | tail comparison | weighted Rademachers | Mathematics - Probability | Student’s statistic

Tail comparison | Self-normalized sums | Weighted Rademachers | Random sign | Optimal constants | Student's statistic | Gaussian | Large deviations | Symmetric | Bounds for tail probabilities | large deviations | optimal constants | bounds for tail probabilities | STATISTICS & PROBABILITY | symmetric | random sign | self-normalized sums | tail comparison | weighted Rademachers | Mathematics - Probability | Student’s statistic

Journal Article

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 5, pp. 1413 - 1422

Let 𝑋,𝑋₁,𝑋₂, . . . be a stationary sequence of negatively associated random variables. A universal result in almost sure central limit theorem for the...

Partial sums | Central limit theorem | Random variables | Self-normalized partial sums | Almost sure central limit theorem | Negatively associated random variables | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-CONVERGENCE

Partial sums | Central limit theorem | Random variables | Self-normalized partial sums | Almost sure central limit theorem | Negatively associated random variables | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-CONVERGENCE

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2015, Volume 28, Issue 4, pp. 1556 - 1570

Let $$N$$ N be a Poisson distributed random variable (r.v.) with parameter $$\lambda $$ λ . Let $$\{X, X_i, i \ge 1\}$$ { X , X i , i ≥ 1 } be a sequence of...

Cramér large deviation | 62E20 | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Self-normalized compound Poisson sum | Studentized compound Poisson sum | LIMIT-THEOREMS | APPROXIMATIONS | RISK | STATISTICS & PROBABILITY | Cramer large deviation | RANDOM-VARIABLES

Cramér large deviation | 62E20 | 60G50 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Self-normalized compound Poisson sum | Studentized compound Poisson sum | LIMIT-THEOREMS | APPROXIMATIONS | RISK | STATISTICS & PROBABILITY | Cramer large deviation | RANDOM-VARIABLES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 376, Issue 1, pp. 29 - 41

Let X , X 1 , X 2 , … be a sequence of independent and identically distributed positive random variables with EX = μ > 0 . In this paper we show that the...

Domain of attraction of the normal law | Almost sure central limit theorem | Products of sums | Self-normalized | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTICS | ASSOCIATION

Domain of attraction of the normal law | Almost sure central limit theorem | Products of sums | Self-normalized | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTICS | ASSOCIATION

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 9, pp. 2639 - 2644

Let { X i , i ≥ 1 } be a sequence of i.i.d. random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite...

Central limit theorem | Domain of attraction of the normal law | Almost sure | Self-normalized | DEPENDENT RANDOM-VARIABLES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LARGE DEVIATIONS | Attraction | Theorems | Law | Mathematical models | Random variables | Variance | Sums

Central limit theorem | Domain of attraction of the normal law | Almost sure | Self-normalized | DEPENDENT RANDOM-VARIABLES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LARGE DEVIATIONS | Attraction | Theorems | Law | Mathematical models | Random variables | Variance | Sums

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2013, Volume 56, Issue 1, pp. 149 - 160

Let {X, Xn,n ≥ 1} be a sequence of independent identically distributed random variables with EX = 0 and assume that EX2I（｜X｜ ≤ x） is slowly varying as x → ∞,...

en型 | 独立同分布 | 标准化 | 强逼近 | 吸引力 | 慢变 | 随机变量 | strong approximation | 62E20 | domain of attraction of the normal law | Mathematics | Applications of Mathematics | 60F17 | self-normalized sums | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | Attraction | Law | Approximation | Infinity | Mathematical analysis | China | Random variables | Sums | Series (mathematics) | Astronomy

en型 | 独立同分布 | 标准化 | 强逼近 | 吸引力 | 慢变 | 随机变量 | strong approximation | 62E20 | domain of attraction of the normal law | Mathematics | Applications of Mathematics | 60F17 | self-normalized sums | 60F15 | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | Attraction | Law | Approximation | Infinity | Mathematical analysis | China | Random variables | Sums | Series (mathematics) | Astronomy

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 9/2016, Volume 110, Issue 2, pp. 699 - 710

Let $$X, X_1, X_2,\ldots $$ X , X 1 , X 2 , … be a sequence of independent and identically distributed random variables with zero mean and finite second...

Almost sure central limit theorem | Theoretical, Mathematical and Computational Physics | Self-normalized partial sums | Mathematics, general | Mathematics | Applications of Mathematics | Maxima | 60F15 | MATHEMATICS | GAUSSIAN SEQUENCES | PRODUCTS | RANDOM-VARIABLES | Theorems | Mathematical analysis | Texts | Random variables | Formulas (mathematics) | Sums

Almost sure central limit theorem | Theoretical, Mathematical and Computational Physics | Self-normalized partial sums | Mathematics, general | Mathematics | Applications of Mathematics | Maxima | 60F15 | MATHEMATICS | GAUSSIAN SEQUENCES | PRODUCTS | RANDOM-VARIABLES | Theorems | Mathematical analysis | Texts | Random variables | Formulas (mathematics) | Sums

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 12

Let be a sequence of independent and identically distributed random variables in the domain of attraction of the normal law. A universal result in an almost...

Analysis | self-normalized partial sums | domain of attraction of the normal law | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | MATHEMATICS | MATHEMATICS, APPLIED | I.I.D. RANDOM-VARIABLES | Attraction | Theorems | Law | Random variables | Inequalities | Sums

Analysis | self-normalized partial sums | domain of attraction of the normal law | Mathematics, general | Mathematics | Applications of Mathematics | almost sure central limit theorem | MATHEMATICS | MATHEMATICS, APPLIED | I.I.D. RANDOM-VARIABLES | Attraction | Theorems | Law | Random variables | Inequalities | Sums

Journal Article

15.
Full Text
Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

Econometrica, ISSN 0012-9682, 11/2012, Volume 80, Issue 6, pp. 2369 - 2429

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage predictions and estimate optimal instruments in linear instrumental...

imperfect model selection | instrumental variables | heteroscedasticity | non‐Gaussian errors | Lasso | data‐driven penalty | Inference on a low‐dimensional parameter after model selection | moderate deviations for self‐normalized sums | post‐Lasso | Data-driven penalty | Inference on a low-dimensional parameter after model selection | Non-Gaussian errors | Instrumental variables | Imperfect model selection | Moderate deviations for self-normalized sums | Post-Lasso | Heteroscedasticity | VARIABLE ESTIMATION | MOMENT | post-Lasso | non-Gaussian errors | INEQUALITIES | GMM | STATISTICS & PROBABILITY | QUANTILE REGRESSION | INFERENCE | data-driven penalty | RECOVERY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | moderate deviations for self-normalized sums | ECONOMICS | SELECTION | AGGREGATION | Methods | Eminent domain (Law)

imperfect model selection | instrumental variables | heteroscedasticity | non‐Gaussian errors | Lasso | data‐driven penalty | Inference on a low‐dimensional parameter after model selection | moderate deviations for self‐normalized sums | post‐Lasso | Data-driven penalty | Inference on a low-dimensional parameter after model selection | Non-Gaussian errors | Instrumental variables | Imperfect model selection | Moderate deviations for self-normalized sums | Post-Lasso | Heteroscedasticity | VARIABLE ESTIMATION | MOMENT | post-Lasso | non-Gaussian errors | INEQUALITIES | GMM | STATISTICS & PROBABILITY | QUANTILE REGRESSION | INFERENCE | data-driven penalty | RECOVERY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | moderate deviations for self-normalized sums | ECONOMICS | SELECTION | AGGREGATION | Methods | Eminent domain (Law)

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 6, pp. 1803 - 1809

Let { X , X n ; n ≥ 1 } be a sequence of independent and identically distributed (i.i.d.) random variables with X in the domain of attraction of the normal law...

Precise asymptotics | Self-normalized sums | Complete moment convergence | RATES | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | BAUM-KATZ | ITERATED LOGARITHM | RANDOM-VARIABLES | DEVIATIONS | Attraction | Mathematical models | Law | Random variables | Convergence | Sums

Precise asymptotics | Self-normalized sums | Complete moment convergence | RATES | MATHEMATICS, APPLIED | LARGE NUMBERS | LAW | BAUM-KATZ | ITERATED LOGARITHM | RANDOM-VARIABLES | DEVIATIONS | Attraction | Mathematical models | Law | Random variables | Convergence | Sums

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 56, Issue 7, pp. 1779 - 1786

Let X , X 1 , X 2 , … be a sequence of nondegenerate i.i.d. random variables with zero means, set S n = X 1 + ⋯ + X n and V n 2 = X 1 2 + ⋯ + X n 2 , E X 2 I (...

Precise asymptotics | Self-normalized sums | Complete moment convergence | SPACE | MATHEMATICS, APPLIED | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | precise asymptotics | complete moment convergence | LIMIT-THEOREMS | ITERATED LOGARITHM | LARGE DEVIATIONS | self-normalized sums | Asymptotic properties | Mathematical analysis | Mathematical models | Random variables | Standards | Convergence | Sums

Precise asymptotics | Self-normalized sums | Complete moment convergence | SPACE | MATHEMATICS, APPLIED | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | precise asymptotics | complete moment convergence | LIMIT-THEOREMS | ITERATED LOGARITHM | LARGE DEVIATIONS | self-normalized sums | Asymptotic properties | Mathematical analysis | Mathematical models | Random variables | Standards | Convergence | Sums

Journal Article

Journal of Mathematical Inequalities, ISSN 1846-579X, 03/2016, Volume 10, Issue 1, pp. 233 - 245

Journal Article

19.
Moment equalities for sums of random variables via integer partitions and Faà di Bruno's formula

Turkish Journal of Mathematics, ISSN 1300-0098, 2014, Volume 38, Issue 3, pp. 558 - 575

We give moment equalities for sums of independent and identically distributed random variables including, in particular, centered and specifically symmetric...

Bootstrap | Faà di bruno's chain rule | Integer partitions | Marcinkiewicz-Zygmund inequalities | Moments | Self-normalized sums | MATHEMATICS | Faa. di Bruno's chain rule | bootstrap | integer partitions | self-normalized sums

Bootstrap | Faà di bruno's chain rule | Integer partitions | Marcinkiewicz-Zygmund inequalities | Moments | Self-normalized sums | MATHEMATICS | Faa. di Bruno's chain rule | bootstrap | integer partitions | self-normalized sums

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2009, Volume 22, Issue 5, pp. 715 - 718

Let { Y , Y i ; i ≥ 1 } be a sequence of nondegenerate, independent and identically distributed random variables with zero mean, which is in the domain of...

Moderate deviation | PLDP | Slowly varying | Attracting domain | Self-normalized | MATHEMATICS, APPLIED | Questions and answers

Moderate deviation | PLDP | Slowly varying | Attracting domain | Self-normalized | MATHEMATICS, APPLIED | Questions and answers

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.