Valid Asymptotic Expansions for the Maximum Likelihood Estimator of the Parameter of a Stationary, Gaussian, Strongly Dependent Process

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin's (1980) general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood derivatives; (ii) appeal to a simple result of Skovgaard (1986) to obtain from this an Edgeworth expansion for the joint distribution of the log-likelihood derivatives; (iii) appeal to and extension of arguments of Bhattacharya and Ghosh (1978) to accomplish the passage from the result on the log-likelihood derivatives to the result for the maximum likelihood estimators. We develop and make extensive use of a uniform version of Dahlhaus's (1989) Theorem 5.1 on products of Toeplitz matrices; the extension of Dahlhaus's result is of interest in its own right. A small numerical study of the efficacy of the Edgeworth expansion is presented for the case of fractional Gaussian noise.Edgeworth expansions, long memory processes, ARFIMA models

Case-control survival analysis with a general semiparametric shared frailty model--a pseudo full likelihood approach

In this work we deal with correlated failure time (age at onset) data arising from population-based case-control studies, where case and control probands are selected by population-based sampling and an array of risk factor measures is collected for both cases and con- trols and their relatives. Parameters of interest are e®ects of risk factors on the failure time hazard function and within-family depen- dencies among failure times after adjusting for the risk factors. Due to the retrospective sampling scheme, large sample theory for existing methods has not been established. We develop a novel technique for estimating the parameters of interest under a general semiparamet- ric shared frailty model. We also present a simple, easily computed, and non-iterative nonparametric estimator for the cumulative base- line hazard function. We provide rigorous large sample theory for the proposed method. We also present simulation results and a real data example for illustrating the utility of the proposed method

Valid Asymptotic Expansions for the Maximum Likelihood Estimator of the Parameter of a Stationary, Gaussian, Strongly Dependent Process

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin’s (1980) general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood derivatives; (ii) appeal to a simple result of Skovgaard (1986) to obtain from this an Edgeworth expansion for the joint distribution of the log-likelihood derivatives; (iii) appeal to and extension of arguments of Bhattacharya and Ghosh (1978) to accomplish the passage from the result on the log-likelihood derivatives to the result for the maximum likelihood estimators. We develop and make extensive use of a uniform version of Dahlhaus’s (1989) Theorem~5.1 on products of Toeplitz matrices; the extension of Dahlhaus’s result is of interest in its own right. A small numerical study of the efficacy of the Edgeworth expansion is presented for the case of fractional Gaussian noise

Same-Sex Social Behavior in Meadow Voles: Multiple and Rapid Formation of Attachments

Adult meadow voles (Microtus pennsylvanicus) are solitary in the spring–summer reproductive season, but during winter months, females and males are socially tolerant and aggregate in groups. This behavioral difference is triggered by day length: female meadow voles housed in short, winterlike day lengths form same-sex partner preferences, whereas those housed in long, summer-like day lengths are less social. The present study demonstrates that same-sex social attachments in short day lengths are not exclusive; females formed concurrent attachments with more than one individual, and with non-kin as well as siblings. Partner preferences between females were established within one day of cohousing and did not intensify with greater durations of cohabitation. Males also formed same-sex social attachments, but unlike female affiliative behavior, male partner preferences were not significantly affected by day length. These data are discussed in the context of field behavior and the physiological mechanisms supporting social behavior in voles