Parameter estimation in cosine regression
Parameter estimation of S-distributions with alternating regression.
We propose a novel 3-way alternating regression (3-AR) method as an effective strategy for the estimation of parameter values in S-distributions from frequency data. The 3-AR algorithm is very fast and performs well for error-free distributions and artificial noisy data obtained as random samples generated from S-distributions, as well as for traditional statistical distributions and for actual observation data. In rare cases where the algorithm does not immediately converge, its enormous speed...
Polynomials associated with exponential regression
Fitting exponentials to data by the least squares method is discussed. It is shown how the polynomials associated with this problem can be factored. The closure of the set of this type of functions defined on a finite domain is characterized and an existence theorem derived.
Predictions in nonlinear regression models.
Probability distribution of the multivariate nonlinear least squares estimates
Projection pursuit quadratic regression - the normal case
The model of quadratic regression is studied by means of the projection pursuit method. This method leads to a decomposition of the matrix of quadratic regression, which can be used for an estimation of this matrix from the data observed.
Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model
The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.
Properties of the generalized nonlinear least squares method applied for fitting distribution to data
We introduce and analyze a class of estimators for distribution parameters based on the relationship between the distribution function and the empirical distribution function. This class includes the nonlinear least squares estimator and the weighted nonlinear least squares estimator which has been used in parameter estimation for lifetime data (see e.g. [6, 8]) as well as the generalized nonlinear least squares estimator proposed in [3]. Sufficient conditions for consistency and asymptotic normality...