Showing 1 - 10 of 199
Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.
Persistent link: https://www.econbiz.de/10011064904
Trimming is a standard method to decrease the effect of large sample elements in statistical procedures, used, e.g., for constructing robust estimators and tests. Trimming also provides a profound insight into the partial sum behavior of i.i.d. sequences. There is a wide and nearly complete...
Persistent link: https://www.econbiz.de/10011065082
We prove a functional central limit theorem for modulus trimmed i.i.d. variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The...
Persistent link: https://www.econbiz.de/10011040037
We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X_k = (ϕ + b_k)X_k - 1 + e_k, where (ϕ, omega-super-2, σ-super-2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |ϕ + b_0| = 0 and show that σ-super-2...
Persistent link: https://www.econbiz.de/10005005181
Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as "X"<sub>"i"</sub>("t")&equals;"μ"("t")&plus;Σ<sub>1≤"l"&infin ;</sub>"η"<sub>"i", "l"</sub>&plus; "v"<sub>"l"</sub>("t "), where "μ" is the common mean, "v"<sub>"l"</sub> are the eigenfunctions of the covariance operator and the...</sub>
Persistent link: https://www.econbiz.de/10008479741
Let X1, X2,... be independent, identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn = [summation operator]k[less-than-or-equals, slant]n Xk. We give nearly optimal criteria for an (unbounded) measurable function f to satisfy the a.s. central limit theorem, i.e., a.s., where...
Persistent link: https://www.econbiz.de/10005137793
We obtain an approximation for the logarithmic averages of I{k1/2a(k) [less-than-or-equals, slant] S(k) [less-than-or-equals, slant] k1/2b(k)}, where a(k) --> 0, b(k) --> 0 (k --> [infinity]) and S(k) is partial sum of independent, identically distributed random variables.
Persistent link: https://www.econbiz.de/10005254600
We consider polynomial variables which define an important subclass of Duan's augmented processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM,...
Persistent link: https://www.econbiz.de/10005254988
Persistent link: https://www.econbiz.de/10009215456
We obtain a strong approximation for the logarithmic average of sample extremes. The central limit theorem and laws of the iterated logarithm are immediate consequences.
Persistent link: https://www.econbiz.de/10008873657