Asymptotic Normality of Sum-Functions of Spacings
نویسندگان
چکیده
منابع مشابه
Asymptotic Normality of Scaling Functions
The Gaussian function G(x) = 1 p 21⁄4 e¡x 2=2; which has been a classical choice for multiscale representation, is the solution of the scaling equation G(x) = Z R ®G(®x¡ y)dg(y); x 2 R; with scale ® > 1 and absolutely continuous measure dg(y) = 1 p 21⁄4(®2 ¡ 1) e¡y 2=2(®2¡1)dy: It is known that the sequence of normalized B-splines (Bn); where Bn is the solution of the scaling equation Á(x) = n ...
متن کاملThe Probability of Large Deviations Forthe Sum Functions of Spacings
Let 0= U0,n ≤ U1,n ≤ ··· ≤ Un−1,n ≤ Un,n = 1 be an ordered sample from uniform [0,1] distribution, and Din = Ui,n −Ui−1,n, i = 1,2, . . . ,n; n = 1,2, . . . , be their spacings, and let f1n, . . . , fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)= f1n(nD1n) + ···+ fnn(nDnn) are proved. Applicati...
متن کاملAsymptotic Normality of Graph Statistics
Various types of graph statistics for Bernoulli graphs are represented as numerators of incomplete U-statistics. Asymptotic normality of these statistics is proved for Bernoulli graphs in which the edge probability is constant. In addition it is shown that subgraph counts asymptotically are linear functions of the number of edges in the graph. AMS Subject Classification: Primary 05C99; Secondar...
متن کاملThe probability of large deviations for the sum functions of spacings
Let 0= U0,n ≤ U1,n ≤ ··· ≤ Un−1,n ≤ Un,n = 1 be an ordered sample from uniform [0,1] distribution, and Din = Ui,n −Ui−1,n, i = 1,2, . . . ,n; n = 1,2, . . . , be their spacings, and let f1n, . . . , fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)= f1n(nD1n) + ···+ fnn(nDnn) are proved. Applicati...
متن کاملOn asymptotic normality of sequential
For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1979
ISSN: 0091-1798
DOI: 10.1214/aop/1176994901