Covariance matrix

About: Covariance matrix is a research topic. Over the lifetime, 24441 publications have been published within this topic receiving 653214 citations.

A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix

Abstract: This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.

Principles and Procedures of Statistics: A Biometrical Approach

Abstract: Observations probability sampling from a normal distribution comparisons involving two sample means principles of experimental design analysis of variance I - the one-way classification mutiple comparisons analysis of variance II - multiway classification linear regression linear correlation matrix notation linear regression in matrix notation multiple and partial regression and correlation analysis of variance III - factorial experiments analysis of variance analysis of covariance IV analysis of covariance analysis of variance V - unequal subclass numbers some uses of chi-square enumeration data I - one-way classifications enumeration data II - contingency tables categorical models some discrete distributions nonparametric statistics sampling finite populations.

A New Approach to Linear Filtering and Prediction Problems

Abstract: The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self-contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.

A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix

Abstract: This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.

Approximate inference in generalized linear mixed models

Abstract: Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior weights and a scale factor. The random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components. For problems involving time series, spatial aggregation and smoothing, the dispersion may be specified in terms of a rank deficient inverse covariance matrix. Approximation of the marginal quasi-likelihood using Laplace's method leads eventually to estimating equations based on penalized quasilikelihood or PQL for the mean parameters and pseudo-likelihood for the variances. Im...