Serial correlation and distributions on the shere

Estimation and tests for serial correlation in recation and regression models with normal error have been derive from various points of view; for example: Anderson (1948), Durbi for Watson (1950, 1951, 1971), Theil (1965), Durbin (1970), Haq (1970), Kadiyala (1970), Abrahamse & Louter (1971), Levenbac (1972), Berenblut & Webb (1973), Phillips & Harvey (1974), a Sims (1975). In this paper we derive likelihood functions and most powerful tests for serial correclation in Locationa and regression models with arbitrary but specificed error; the methods extend to include the determination of the likelihood for the parameter of the error distribution.

In Section 2, we survey the modthods that have been used in deriving the various tests and estimates in the literature. In Section 2, we introduce the stataistical model that directly describes the error distribution and we obtain the likelihood function for error correlation and determine locally and specifically kost powerful tests for correlation. In Section 3 we consider the case with normal error derive a normal distribution on the sphere by radial projection. The likelihood function and test are then specialized to the case of normal error in Section 4. The computational procedures for the tests and related power functions are examined in Section 5. Power comparisons for the textile data of Theil and Nagar (1961), the consumption data of Kelin (1950), and the plums and the wheat data of Hildreth & Lu (1960) are presented in Section 6, while the likelihood functions for correlation in these data are given in Section 7.     

Testing the association between health status amd an environmental index

The design and analysis of a study to examine the association between a time series response collected on n subjects and an index are presented. Applications of this methodology to environmental health studies such as investigations into the relationship between air pollution levels and daily respiratory symptoms are indicated     

Change-points in stochastic ordering

This article studies the problem of testing and locating changepoints in stochas¬tic ordering. We propose a sequential process to detect the changepoints from two multinomial distributions. We also obtain the maximum likelihood estimators of two multinomial probability vectors under the assumption that the cumulative distribu¬tions have a changepoint. Asymptotically unbiased Akaike's information criterion is used to estimate the changepoints of two discrete probability distributions. Finally. we demonstrate our procedure by studying a data set pertaining to average daily insulin dose from the Boston Collaborative Drug Surveillance Program and locate the changepoints in stochastic ordering.     

The use of covariate information in the sequential analysis of dichotomous response experiments

A method is presented for the sequential analysis of experiments involving two treatments to which response is dichotomous. Composite hypotheses about the difference in success probabilities are tested, and covariate information is utilized in the analysis. The method is based upon a generalization of Bartlett’s (1946) procedure for using the maximum likelihood estimate of a nuisance parameter in a Sequential Probability Ratio Test (SPRT). Treatment assignment rules studied include pure randomization, randomized blocks, and an adaptive rule which tends to assign the superior treatment to the majority of subjects. It is shown that the use of covariate information can result in important reductions in the expected sample size for specified error probabilities, and that the use of covariate information is essential for the elimination of bias when adaptive assignment rules are employed. Designs of the type presented are easily generated, as the termination criterion is the same as for a Wald SPRT of simple hypotheses.     

The distance between random points in rectangles

Since 1943, numerous papers have discussed the problem of the distribution of the distance between random points in rectangles, considering special cases such as two points in the same square, points in adjacent squares, two rectangles sharing a side and others. The problems arise in a variety of settings: operations research, population studies, urban planning, physical chemistry, chemical physics and materials science. Reported results are all of special cases with formulas specific to each case. It is possible to put such problems in a general setting with a single formula that handles all the particular cases. The method is well suited to computing and use of graphics. Now that computers and graphic output are commonplace it seems worthwhile to describe the general method and provide program outlines for computing and plotting the resulting distributions. We do that in this article.     

Some properties of the dirichlet-multinomial distribution and its use in prior elicitation

Two results on the unimodality of the Dirichlet-multinomial distribution are proved, and a further result is alos proved on the identifiability of mixtures of multinomial distributions. These properties are used in developing a method for eliciting a Dirchlet prior distribution. The elicitation method is based on the mode, and region around the mode, of the Dirichlet-multinomial predictive distribution.     

Compound adaptive GPU design for clinical trials

In clinical trials, several competing treatments are often carried out in the same trial period. The goal is to assess the performances of these different treatments according to some optimality criterion and minimize risks to the patients in the entire process of the study. For this, each coming patient is allocated sequentially to one of the treatments according to a mechanism defined by the optimality criterion. In practice, sometimes different optimality criteria, or the same criterion with different regimes, need to be considered to assess the treatments in the same study, so that each mechanism is also evaluated through the trail study. In this case, the question is how to allocate the treatments to the incoming patients so that the criteria/mechanisms of interest are assessed during the trail process, and the overall performance of the trial is optimized under the combined criteria or regimes. In this paper, we consider this problem by investigating a compound adaptive generalized Pólya urn design. Basic asymptotic properties of this design are also studied.     

Factor structure of the Mini-Maternal Behavior Q-Sort and associations with infant attachment: Informing precision in research and intervention

We examined the factor structure of parental sensitivity to infants as assessed by the Mini-Maternal Behavior Q-Sort (Mini-MBQS), a 25-item short-form of the original 90-item MBQS. We aimed to: (1) identify latent factors of the Mini-MBQS; and (2) validate each factor by testing associations with infant attachment classifications. Data on parent-infant dyads (n = 313; 222 mothers with 281 children, 29 fathers with 32 children) were drawn from a three-generation Australian cohort study. Exploratory Factor Analysis and Exploratory Structural Equation Modelling examined the structure of the Mini-MBQS. Two latent Mini-MBQS factors were identified, requiring 8 of 25 original items: (1) Attention and Responsiveness and (2) Contingency in Interactions. Infants with insecure attachment classifications had parents with lower sensitivity across both factors relative to infants classified secure. In particular, infants with resistant attachment classifications had parents with notably low Contingency in Interactions scores. Infants with disorganised attachment classifications had parents with the lowest relative sensitivity across both factors, and in these dyads Attention and Responsiveness scores were especially low. Results provide an empirically derived factor structure for the Mini-MBQS. Two subscales, each with significant infant attachment associations, may improve precision in clinical intervention and research translation.     

Social fields,subfields and social spaces at the scale of empires: explaining the colonial state and colonial sociology

This article develops a series of arguments about social fields, subfields, and social spaces that can help us understand empires and colonies. First, we have to assume that the scale of fields is not always coextensive with the boundaries of the national state but is often much larger, or smaller. Imperial fields are among the most spatially extensive ones, though they may not be as territorially extensive as truly global fields. Second, we need to make a distinction between imperial fields and imperial social spaces (based on Bourdieu's distinction between social fields and social spaces). The third argument is that colonies in modern empires were characterized by two different kinds of fields: fields that were simply extended into the overseas territories, versus completely separate fields unique to one or more of the colonies. The colonial state is an example of a field that is specific to the colony. By contrast, scientific fields were often simply extended from the metropole into the colonies, encompassing both. The fourth argument concerns subfields. Transported into imperial realms, this distinction suggests that some colonial offshoots of fielded metropolitan practices do not constitute separate fields but are nonetheless differentiated from their main overarching field. These four points are illustrated with examples from British, French and German imperial policy, colonial statecraft and colonial sociology.