https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

Statistical analysis of cointegration vectors

(1966). The Scree Test For The Number Of Factors. Multivariate Behavioral Research: Vol. 1, No. 2, pp. 245-276.

The scree test for the number of factors

Models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit. Multivariate models with general covariance structure are often difficult to apply to highly unbalanced data, whereas two-stage random-effects models can be used easily. In two-stage models, the probability distributions for the response vectors of different individuals belong to a single family, but some random-effects parameters vary across individuals, with a distribution specified at the second stage. A general family of models is discussed, which includes both growth models and repeated-measures models as special cases. A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed. Two examples are taken from a current epidemiological study of the health effects of air pollution.

Random-effects models for longitudinal data

Longitudinal data sets are comprised of repeated observations of an outcome and a set of covariates for each of many subjects. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject. This paper proposes a unifying approach to such analysis for a variety of discrete and continuous outcomes. A class of generalized estimating equations (GEEs) for the regression parameters is proposed. The equations are extensions of those used in quasi-likelihood (Wedderburn, 1974, Biometrika 61, 439-447) methods. The GEEs have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as we often expect. A consistent variance estimate is presented. We illustrate the use of the GEE approach with longitudinal data from a study of the effect of mothers' stress on children's morbidity.

Longitudinal data analysis for discrete and continuous outcomes.

http://traits-dgs.nceas.ucsb.edu/workspace/readings/Rao82TPB.pdf/attachment_download/file

Diversity and dissimilarity coefficients: A unified approach☆

The Utilization of Multiple Measurements in Problems of Biological Classification

If the probability differential of a set of stochastic variates contains k unknown parameters, the statistical hypotheses concerning them may be simple or composite. The hypothesis leading to a complete specification of the values of the k parameters is called a simple hypothesis, and the one leading to a collection of admissible sets a composite hypothesis. In this paper we shall be concerned with the testing of these two types of hypotheses on the basis of a large number of observations from any probability distribution satisfying some mild restrictions and their use in problems of estimation.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0305004100023987

Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation

In an earlier paper (Rao, 1959), the author discussed the method of least squares when the observations are dependent and the dispersion matrix is unknown but an independent estimate is available. The unknown dispersion matrix was, however, considered as an arbitrary positive definite matrix. In the present paper we shall consider a class of problems where the dispersion matrix has a known structure and discuss the appropriate statistical methods. More specifically the structure of the dispersion matrix results from considering the parameters in the well-known Gauss-Markoff linear model as random variables. Let Y be a vector random variable with the structure

C. Radhakrishna Rao

Papers

Diversity and dissimilarity coefficients: A unified approach☆

The Utilization of Multiple Measurements in Problems of Biological Classification

Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation

The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves

Estimation of variance and covariance components—MINQUE theory