• Corpus ID: 53492374

A bound for the error in the normal approximation to the distribution of a sum of dependent random variables

@inproceedings{Stein1972ABF,
  title={A bound for the error in the normal approximation to the distribution of a sum of dependent random variables},
  author={Charles M. Stein},
  year={1972}
}
This paper has two aims, one fairly concrete and the other more abstract. In Section 3, bounds are obtained under certain conditions for the departure of the distribution of the sum of n terms of a stationary random sequence from a normal distribution. These bounds are derived from a more abstract normal approximation theorem proved in Section 2. I regret that, in order to complete this paper in time for publication, I have been forced to submit it with many defects remaining. In particular the… 

Recent Results on Refinements of the Central Limit Theorem

Let {X"} be a sequence of independent and identically distributed (i.i.d.) random vectors in Rk with zero mean vector and identity covariance matrix. The distribution Qn of the normalized sum

Zero biasing and a discrete central limit theorem

We introduce a new family of distributions to approximate P(W ∈ A) for A ⊂ {..., -2, -1, 0, 1, 2,...} and W a sum of independent integer-valued random variables ξ 1 , ξ 2 ,..., ξ n with finite second

Approximation of Sums of Locally Dependent Random Variables via Perturbation of Stein Operator

Let ( X i , i ∈ J ) be a family of locally dependent non-negative integer-valued random variables, and consider the sum W = P i ∈ J X i . We estab- lish general error upper bounds for d TV ( W,M )

On the rate of convergence in the central limit theorem for Markov-chains

All results concerning the accuracy of the normal approximation for sums of not necessarily independent random variables assume Doeblin's condition or the condition of (p-mixing (see e.g. [1, 3, 5,

Stein's method for normal approximation

Stein’s method originated in 1972 in a paper in the Proceedings of the Sixth Berkeley Symposium. In that paper, he introduced the method in order to determine the accuracy of the normal approximation

Exact and approximate runs distributions

Let R = Rn denote the total (and unconditional) number of runs of successes or failures in a sequence of n Bernoulll (p) trials, where p is assumed to be known throughout. The exact distribution of R

A non uniform bound for half-normal approximation of the number of returns to the origin of symmetric simple random walk

ABSTRACT Let (Xn) be a sequence of independent identically distributed random variables with . A symmetric simple random walk is a discrete-time stochastic process (Sn)n ⩾ 0 defined by S0 = 0 and Sn

On the discounted global CLT for some weakly dependent random variables

AbstractIn this paper, we consider L1 upper bounds in the global central limit theorem for the sequence of r.v.’s (not necessarily stationary) satisfying the ψ-mixing condition. In a particular case,

Multivariate normal approximations by Stein's method and size bias couplings

Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any non-negative random vector.
...

References

SHOWING 1-4 OF 4 REFERENCES

The accuracy of the Gaussian approximation to the sum of independent variates

The sum of finitely many variates possesses, under familiar conditions, an almost Gaussian probability distribution. This already much discussed "central limit theorem"(x) in the theory of

Probability Theory I

These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of

Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law

Distribution Funetions of One Variable. Chap. I. Functions of Bounded Variation m~d Their Fourier-Stieltjes Transforms . 8 i . F u n c t i o n s of b o u n d e d v a r i a t i o n . . . . . . . . . .