The problem of the goodness of-fit testing for inhomogeneous Poisson process with parametric basic hypothesis is considered. A test statistic of the Cramér–von Mises type with parameter replaced by the maximum likelihood estimator is proposed and its asymptotic behavior is studied. It is...

For an ARCH model, we propose a multistage weighted least squares (WLS) estimate which consists of repeated WLS procedures until the corresponding asymptotic variance equals that of the quasi-maximum likelihood estimate (QMLE). At every stage, the current estimate is of a WLS type weighted by...

We consider a diffusion process (X <Subscript> t </Subscript>)<Subscript> t ≥ 0</Subscript>, with drift b(x) and diffusion coefficient σ(x). At discrete times t <Subscript> k </Subscript> = k δ for k from 1 to M, we observe noisy data of the sample path, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${Y_{k\delta}=X_{k\delta}+\varepsilon_{k}}$$</EquationSource > </InlineEquation> . The random variables <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></subscript></subscript></subscript>

We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationary Gaussian processes. This result allows us to find explicitly the rates of exponential decay of the error probabilities of type I and type II for Neyman–Pearson tests....