A Clt for Empirical Processes Involving Time-dependent Data by James Kuelbs,
نویسندگان
چکیده
converges in distribution in a sense described more completely below. Hence limit theorems for such processes, such as the law of large numbers and the central limit theorem (CLT), allow one to asymptotically get uniform estimates for the unknown cdf, F(y)= Pr(X ≤ y), via the sample data. A more general version of these processes is to replace the indicators of halflines in (1) by functions of a “random variable” taking values in some abstract space (S,S). More specifically, { 1 √ n n ∑
منابع مشابه
A CLT for Empirical Processes Involving Time Dependent Data
For stochastic processes {Xt : t ∈ E}, we establish sufficient conditions for the empirical process based on {IXt≤y − P (Xt ≤ y) : t ∈ E, y ∈ R} to satisfy the CLT uniformly in t ∈ E, y ∈ R. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and E = [0, 1]. ∗Research supported in part b...
متن کاملEmpirical Quantile CLTs for Time Dependent Data
We establish empirical quantile process CLTs based on n independent copies of a stochastic process {Xt : t ∈ E} that are uniform in t ∈ E and quantile levels α ∈ I, where I is a closed subinterval of (0, 1). Typically E = [0, T ], or a finite product of such intervals. Also included are CLT’s for the empirical process based on {IXt≤y − Pr(Xt ≤ y) : t ∈ E, y ∈ R} that are uniform in t ∈ E, y ∈ R...
متن کاملAn EMQ inventory model for defective products involving rework and sales team’s initiatives-dependent demand
This paper investigates the issue of an economic manufacturing quantity model for defective products involving imperfect production processes and rework. We consider that the demand is sensitive to promotional efforts/sales teams’ initiatives as well as the setup cost can be reduced through further investment. It also assumes that fixed quantity multiple installments of the finished batch are d...
متن کاملA sequential empirical CLT for multiple mixing processes with application to B - geometrically ergodic Markov chains ∗
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F . Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F . This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron–Frobenius or...
متن کاملA Functional Lil for Symmetric Stable Processes
A functional law of the iterated logarithm is obtained for symmetric stable processes with stationary independent increments. This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion. Proofs depend on small ball probability estimates and yield the small ball probabilities o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013