Let X be a unit vector random variable taking values on a k-dimensional sphere [Omega] with probability density function f(x). The problem considered is one of estimating f(x) based on n independent observation X1,...,Xn on X. The proposed estimator is of the form fn(x) = (nhk-1)-1C(h)...

Consider the nonparametric regression model Yi(n) = g(xi(n)) + [var epsilon]i(n), i = 1, ..., n, where g is an unknown function, the design points xi(n) are known and nonrandom, and [var epsilon]i(n)'s are independent random variables. The regressor is assumed to take values in A [subset of] Rp,...

In this paper the problem of slope-change point in linear regression model is discussed with the help of the theory of Gaussian process. The distribution of the estimators of the change point proposed in this paper can be approximated by the first type of extremal distribution. Based on this...

Let M be the regression subspace and [gamma] the set of possible covariances for a random vector Y. The linear model determined by M and [gamma] is regular if the identity is in [gamma] and if [Sigma](M)[subset, double equals]M for all [Sigma][set membership, variant][gamma]. For such models,...

For the linear growth curve model introduced by Potthoff and Roy (Biometrika 51 (1964), 313-326), various likelihood ratio tests and some ad hoc tests are available for the location and scale parameters on the basis of normally distributed error components. We study these tests under the...

To determine the order of an autoregressive model, a new method based on information theoretic criterion is proposed. This method is shown to be strongly consistent and the convergence rate of the probability of wrong determination is established.

A global lower estimate for the transition probability of the Brownian motion on a complete Riemannian manifold is given in the form of a comparison with the transition probability of the Brownian motion on a model. This estimate is applied to obtain the laws of the iterated logarithms in the...

In this paper we prove that the sum of two independent multivariate ARMA processes is also ARMA under certain regularity conditions.

The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form [integral operator]01 W dW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA...

Let (Xj, j = 1) be a strictly stationary sequence of uniformly mixing random variables with zero mean, unit variance and finite fourth moment. Form the vector Sn = [Sigma]j = 1n[alpha]njXj where [alpha]nj = ([alpha]nj1, [alpha]nj2)t, [alpha]nj1, [alpha]nj2 [set membership, variant] R1 and [short...