We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the true (weakly) self-avoiding walk, loop-erased random walk, and annealed random walk in random environment. In this paper we show that the expansion gives rise to useful formulae for the speed and variance of the random walk, when these quantities are known to exist. The results and formulae of this paper have been used elsewhere by the authors to prove monotonicity properties for the speed (in high dimensions) of excited random walk and related models, and certain models of random walk in random environment. We also derive a law of large numbers and central limit theorem (with explicit error terms) directly from this expansion, under strong assumptions on the expansion coefficients. The assumptions are shown to be satisfied by excited random walk in high dimensions with small excitation parameter, a model of reinforced random walk with underlying drift and small reinforcement parameter, and certain models of random walk in random environment under strong ellipticity conditions.

Univariate analysis of variance of a good summary measure, or two, may provide a simple and effective way of analyzing repeated measurements. It is shown here that selection of a linear summary measure on the basis of inspection of the total sample of response curves, leads to valid F-tests in the subsequent analysis of variance. The selection may also be based on residuals from a base model, rather than on the raw data. The treatments should, however, be blinded in this summary measure selection step, that is, the inspection of the sample of curves (or residuals) and the selection of the summary measure may not rely on which responses stem from which treatment groups. It is advocated as a convenient and often effective method to use the first principal component from the total sample of curves as the first summary measure. The main mathematical result of the paper is a simple proof of the validity of the F-tests for linear summary measures selected in this way, provided data are multivariate normally distributed. Alternatively, permutation tests may be used to provide a distribution free reference distribution for the F-statistic. Two examples illustrate the method.

In this work, we propose a heteroscedastic Von Bertalanffy growth model considering a multiplicative heteroscedastic dispersion matrix. All estimates were obtained using a sampling based approach, which allows information to be input beforehand with lower computational effort. Simulations were carried out in order to verify some frequentist properties of the estimation procedure in the presence of small and moderate sample sizes.

The methodology is illustrated on a real Kubbard female chicken corporeal weight dataset.

It is established that if a time series satisfies the Berman condition, and another related (summability) condition, the result of filtering that series through a certain type of filter also satisfies the two conditions. In particular it follows that if X_t satisfies the two conditions and if X_t and a_t are related by an invertible ARMA model, then the a_t satisfy the two conditions.

The power distribution is defined as the inverse of the Pareto distribution. We study in full detail a distribution so-called the beta power distribution. We obtain analytical forms for its probability density and hazard rate functions. Explicit expressions are derived for the moments, probability weighted moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, moments of order statistics, entropy and reliability. We estimate the parameters by maximum likelihood. The practicability of the model is illustrated in two applications to real data.