Yoshihara (1976) established the weak invariance theorem of the generalized U-statistic for absolutely regular variables but only for the stationary case. In this paper we extend the results from the stationary case to the nonstationary case.

The joint asymptotic multinormality of certain linear signed-rank statistics introduced by Shane and Puri (1969) is established for the nonidentically distributed case; moreover, the usual restriction forbidding constant score generating functions is dropped. In addition, sufficient conditions...

An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models. Special cases yield Fisher-Yates, van der Waerden, and...

Let Fn(x) be the empirical distribution function based on n independent random variables X1,...,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm,...

In this note, we establish the convergence properties for a broad class of random variables of the form Sn = [integral operator]Fn(Tn - s)[nu]n(ds) where Tn is some random variable, Fn is an empirical distribution function based on an independent sample of size n, and [nu]n is some measure.

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.

K. I. Yoshihara (1990,Comput. Math. Appl.19, No. 1, 149-158) proved the weak invariance of the conditional nearest neighbor regression function estimator called the conditional empirical process based on[phi]-mixing observations. In this paper, we extend the result for nonstationary and...

Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrixf([lambda]). In this paper we consider the testing problemH: [integral operator][pi]-[pi] K{f([lambda])} d[lambda]=cagainstA: [integral operator][pi]-[pi] K{f([lambda])} d[lambda][not...