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An Analysis for Menstrual Data with TimeVarying Covariates
, 1996
"... This paper concerns the analysis of menstrual data; in particular, methodology to identify variables that contribute to the variability of menstrual cycles both within and between women. The basis for the proposed methodology is a parameterization of the mean length of a menstrual cycle conditional ..."
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This paper concerns the analysis of menstrual data; in particular, methodology to identify variables that contribute to the variability of menstrual cycles both within and between women. The basis for the proposed methodology is a parameterization of the mean length of a menstrual cycle conditional upon the past cycles and covariates. This approach accommodates the lengthbias and censoring commonly found in menstrual data. Data from a longitudinal study of menstrual patterns and other variables among Lese women of the Ituri Forest, Zaire, illustrate the methodology. A small simulation illustrates the bias caused by incorrectly deleting the censored cycles.
A Central Limit Theorem for Local Martingales with Applications to the Analysis of Longitudinal Data
, 1996
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TRANSFORM MARTINGALE ESTIMATING FUNCTIONS
, 711
"... An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. ..."
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An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. This method involves the construction of classes of transformbased martingale estimating functions that fit into the general framework of quasilikelihood. In the parametric setting of a discrete time stochastic process, we obtain transform quasiscore functions by projecting the unavailable score function onto the special linear spaces formed by these classes. The specification of the process by any of the main integral transforms makes possible an arbitrarily close approximation of the score function in an infinitedimensional Hilbert space by optimally combining transform martingale quasiscore functions. It also allows an extension of the domain of application of quasilikelihood methodology to processes with infinite conditional second moment. 1. Introduction. Maximum
Asymptotic Behaviour of Estimation Equations With Functional Nuisance Or Working Parameter
"... INTRODUCTION The starting point of our investigations is an estimation equation of the form U n (`; ff) = 0. It contains a finite dimensional parameter ` being of primary interest and a functional parameter ff. The latter may play the role of a nuisance parameter (in the classical sense) or that o ..."
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INTRODUCTION The starting point of our investigations is an estimation equation of the form U n (`; ff) = 0. It contains a finite dimensional parameter ` being of primary interest and a functional parameter ff. The latter may play the role of a nuisance parameter (in the classical sense) or that of a working parameter (coming into statistical use with Liang and Zeger, 1986). A nonparametric estimator ff n Theresienstr.39, D80333 Munich, Germany 1 is assumed to be given showing a certain kind of limit behaviour, the special type of the estimator being of no regard. For estimators ` n of ` which solve (asymptotically) the estimation equation we will prove consistency and asymptotic normality. A special feature of the present paper is a consequent functionally orientated approach. The Taylor methodwell established for
Ignorable dropout in . . .
"... This paper provides a concise definition for ignorable dropout. This is done primarily from a frequentist perspective. The definition of ignorable dropout depends on both the population of inference and the type of statistical methodology used for inference. Different types of dropouts are described ..."
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This paper provides a concise definition for ignorable dropout. This is done primarily from a frequentist perspective. The definition of ignorable dropout depends on both the population of inference and the type of statistical methodology used for inference. Different types of dropouts are described and compared to those found in the literature. Ignorability conditions are then given for the following types of inference: Likelihoodbased