Cramér-type moderate deviation theorems for nonnormal approximation

Cramér Type Moderate Deviation Theorems for Self-Normalized Processes

Cramér type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new randomized concentration inequality and establish a Cramér type moderate deviation theorem for general self-normalized processes which include many well-known Studentiz...

Direct Approximation Theorems for Discrete Type Operators

In the present paper we prove direct approximation theorems for discrete type operators (Lnf)(x) = ∞ ∑ k=0 un,k(x)λn,k(f), f ∈ C[0,∞), x ∈ [0,∞) using a modified K−functional. As applications we give direct theorems for Baskakov type operators, Szász-Mirakjan type operators and Lupaş operator.

Approximate confidence interval for standard deviation of nonnormal distributions

The exact confidence interval for is hypersensitive tominor violations of the normality assumption and its performance does not improvewith increasing sample size.An approximate confidence interval for is proposed and is shown to be nearly exact under normality with excellent small-sample properties under moderate nonnormality. The small-sample performance of the proposed interval may be furthe...

Inverse Approximation Theorems for . . .

Approximation Theorems for Generalized Complex Kantorovich-Type Operators

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials q > 0 attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∈ C : |z| < R}, R > q, the rate of approximation by the q-Kantorovich operators q > 1 is of order q−n versus 1/n for the classical K...