Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station

Abstract: One of the main assumptions in Clarke's classic channel model is isotropic scattering, i.e., uniform distribution for the angle of arrival (AOA) of multipath components at the mobile station. However, in many mobile radio channels we encounter nonisotropic scattering, which strongly affects the correlation function and power spectrum of the complex envelope at the mobile receiver. We propose the use of the versatile von Mises (1918) angular distribution, which includes and/or closely approximates important distributions like uniform, impulse, cardioid, Gaussian, and wrapped Gaussian, for modeling the nonuniform AOAs at the mobile. Based on this distribution, the associated correlation function and. power spectrum of the complex envelope at the mobile receiver are derived. The utility of the new results is demonstrated by comparison with the correlation function estimates of measured data.

A minimal parameter adaptive notch filter with constrained poles and zeros

Abstract: A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of infinite impulse response (IIR) with a minimal number of parameters. The convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the variances of the sine wave frequency estimates are of the same order of magnitude as the Cramer-Rao bound. Results from simulations illustrate the performance of the algorithm under a wide range of conditions.

Smoothing by Local Regression: Principles and Methods

Abstract: Local regression is an old method for smoothing data, having origins in the graduation of mortality data and the smoothing of time series in the late 19th century and the early 20th century. Still, new work in local regression continues at a rapid pace. We review the history of local regression. We discuss four of its basic components that must be chosen in using local regression in practice — the weight function, the parametric family that is fitted locally, the bandwidth, and the assumptions about the distribution of the response. A major theme of the paper is that these choices represent a modeling of the data; different data sets deserve different choices. We describe polynomial mixing, a method for enlarging polynomial parametric families. We introduce an approach to adaptive fitting,assessment of parametric localization. We describe the use of this approach to design two adaptive procedures: one automatically chooses the mixing degree of mixing polynomials at each x using cross-validation, and the other chooses the bandwidth at each x using C p . Finally, we comment on the efficacy of using asymptotics to provide guidance for methods of local regression.

Distribution-free and robust statistical methods: viable alternatives to parametric statistics?

Abstract: After making a case for the prevalence of nonnormality, this paper attempts to introduce some distribution-free and robust techniques to ecologists and to offer a critical appraisal of the potential advantages and drawbacks of these methods. The techniques presented fall into two distinct categories, methods based on ranks and "computer-inten- sive" techniques. Distribution-free rank tests have features that can be recommended. They free the practitioner from concern about the underlying distribution and are very robust to outliers. If the distribution underlying the observations is other than normal, rank tests tend to be more efficient than their parametric counterparts. The absence, in computing packages, of rank procedures for complex designs may, however, severely limit their use for ecological data. An entire body of novel distribution-free methods has been developed in parallel with the increasing capacities of today's computers to process large quantities of data. These techniques either reshuffle or resample a data set (i.e., sample with replacement) in order to perform their analyses. The former we shall refer to as "permutation" or "randomiza- tion" methods and the latter as "bootstrap" techniques. These computer-intensive methods provide new alternatives for the problem of a small and/or unbalanced data set, and they may be the solution for parameter estimation when the sampling distribution cannot be derived analytically. Caution must be exercised in the interpretation of these estimates because confidence limits may be too small.