593,598 research outputs found
Bounds on Quantiles in the Presence of Full and Partial Item Nonresponse
Microeconomic surveys are usually subject to the problem of item nonresponse, typically associated with variables like income and wealth, where confidentiality and/or lack of accurate information can affect the response behavior of the individual. Follow up categorical questions can reduce item nonresponse and provide additional partial information on the missing value, hence improving the quality of the data. In this paper we allow item nonresponse to be non-random and extend Manski’s approach of estimating bounds to identify an upper and lower limit for the parameter of interest (the distribution function or its quantiles). Our extension consists of deriving bounding intervals taking into account all three types of response behavior: full response, partial (categorical) response and full nonresponse. We illustrate the theory by estimating bounds for the quantiles of the distribution of amounts held in savings accounts. We consider worst case bounds which cannot be improved upon without additional assumptions, as well as bounds that follow from different assumptions of monotonicity.item nonresponse;bracket response;bounds and identification
Generation interval contraction and epidemic data analysis
The generation interval is the time between the infection time of an infected
person and the infection time of his or her infector. Probability density
functions for generation intervals have been an important input for epidemic
models and epidemic data analysis. In this paper, we specify a general
stochastic SIR epidemic model and prove that the mean generation interval
decreases when susceptible persons are at risk of infectious contact from
multiple sources. The intuition behind this is that when a susceptible person
has multiple potential infectors, there is a ``race'' to infect him or her in
which only the first infectious contact leads to infection. In an epidemic, the
mean generation interval contracts as the prevalence of infection increases. We
call this global competition among potential infectors. When there is rapid
transmission within clusters of contacts, generation interval contraction can
be caused by a high local prevalence of infection even when the global
prevalence is low. We call this local competition among potential infectors.
Using simulations, we illustrate both types of competition.
Finally, we show that hazards of infectious contact can be used instead of
generation intervals to estimate the time course of the effective reproductive
number in an epidemic. This approach leads naturally to partial likelihoods for
epidemic data that are very similar to those that arise in survival analysis,
opening a promising avenue of methodological research in infectious disease
epidemiology.Comment: 20 pages, 5 figures; to appear in Mathematical Bioscience
Bounds on Quantiles in the Presence of Full and Partial Item Nonresponse
Microeconomic surveys are usually subject to the problem of item nonresponse, typically associated with variables like income and wealth, where confidentiality and/or lack of accurate information can affect the response behavior of the individual. Follow up categorical questions can reduce item nonresponse and provide additional partial information on the missing value, hence improving the quality of the data. In this paper we allow item nonresponse to be non-random and extend Manski’s approach of estimating bounds to identify an upper and lower limit for the parameter of interest (the distribution function or its quantiles). Our extension consists of deriving bounding intervals taking into account all three types of response behavior: full response, partial (categorical) response and full nonresponse. We illustrate the theory by estimating bounds for the quantiles of the distribution of amounts held in savings accounts. We consider worst case bounds which cannot be improved upon without additional assumptions, as well as bounds that follow from different assumptions of monotonicity
Countable locally 2-arc-transitive bipartite graphs
We present an order-theoretic approach to the study of countably infinite
locally 2-arc-transitive bipartite graphs. Our approach is motivated by
techniques developed by Warren and others during the study of cycle-free
partial orders. We give several new families of previously unknown countably
infinite locally-2-arc-transitive graphs, each family containing continuum many
members. These examples are obtained by gluing together copies of incidence
graphs of semilinear spaces, satisfying a certain symmetry property, in a
tree-like way. In one case we show how the classification problem for that
family relates to the problem of determining a certain family of highly
arc-transitive digraphs. Numerous illustrative examples are given.Comment: 29 page
Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach
The focus of modern biomedical studies has gradually shifted to explanation
and estimation of joint effects of high dimensional predictors on disease
risks. Quantifying uncertainty in these estimates may provide valuable insight
into prevention strategies or treatment decisions for both patients and
physicians. High dimensional inference, including confidence intervals and
hypothesis testing, has sparked much interest. While much work has been done in
the linear regression setting, there is lack of literature on inference for
high dimensional generalized linear models. We propose a novel and
computationally feasible method, which accommodates a variety of outcome types,
including normal, binomial, and Poisson data. We use a "splitting and
smoothing" approach, which splits samples into two parts, performs variable
selection using one part and conducts partial regression with the other part.
Averaging the estimates over multiple random splits, we obtain the smoothed
estimates, which are numerically stable. We show that the estimates are
consistent, asymptotically normal, and construct confidence intervals with
proper coverage probabilities for all predictors. We examine the finite sample
performance of our method by comparing it with the existing methods and
applying it to analyze a lung cancer cohort study
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