Limit theorems for empirical processes based on dependent data

Limit Theorems for Empirical Processes Based on Dependent Data

Empirical processes for non ergodic data are investigated under uniform distance. Some CLT’s, both uniform and non uniform, are proved. In particular, conditions for the empirical process Bn = √ n(μn − bn) to converge in distribution are given, where μn is the empirical measure and bn the arithmetic mean of the first n predictive measures. Such conditions apply under various assumptions on the ...

Ratio Limit Theorems for Empirical Processes

Concentration inequalities are used to derive some new inequalities for ratio-type suprema of empirical processes. These general inequalities are used to prove several new limit theorems for ratio-type suprema and to recover a number of the results from [1] and [2]. As a statistical application, an oracle inequality for nonparametric regression is obtained via ratio bounds.

Limit Theorems for Empirical Processes of Cluster Functionals

Let (Xn,i)1≤i≤n,n∈N be a triangular array of row-wise stationary R-valued random variables. We use a “blocks method” to define clusters of extreme values: the rows of (Xn,i) are divided into mn blocks (Yn,j), and if a block contains at least one extreme value the block is considered to contain a cluster. The cluster starts at the first extreme value in the block and ends at the last one. The ma...

Central Limit Theorems For Dependent, Heterogeneous Processes With Trending Moments

Limit Theorems for Competitive Density Dependent Population Processes

∣ = 0 respectively. We also use Hardy notation: f(N) ≪ g(N) if f(N) = o(g(N)). • Throughout, I will use ∂i to indicate the partial derivative with respect to the i th cooordinate and D to denote the total derivative operator: if F : R → R, (DF) = (∂jFi)ij • R+ = {x ∈ R K : xi ≥ 0, i = 1, . . . ,K}. • If x,y ∈ R , we write x ≤ y if xi ≤ yi for all i, x < y if x ≤ y and xi < yi for at least one i...