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An Introduction to Model-Based Survey Sampling with Applications
This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance
estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.
eBook
Modeling and analysis of compositional data
Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn's earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.
eBook
Stability selection
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis, is notoriously difficult, especially for high dimensional data. We introduce stability selection. It is based on subsampling in combination with (high dimensional) selection algorithms. As such, the method is extremely general and has a very wide range of applicability. Stability selection provides finite sample control for some error rates of false discoveries and hence a transparent principle to choose a proper amount of regularization for structure estimation. Variable selection and structure estimation improve markedly for a range of selection methods if stability selection is applied. We prove for the randomized lasso that stability selection will be variable selection consistent even if the necessary conditions for consistency of the original lasso method are violated. We demonstrate stability selection for variable selection and Gaussian graphical modelling, using real and simulated data.
Journal Article
Minimizing finite sums with the stochastic average gradient
We analyze the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method’s iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. The convergence rate is improved from
O
(
1
/
k
)
to
O
(1 /
k
) in general, and when the sum is strongly-convex the convergence rate is improved from the sub-linear
O
(1 /
k
) to a linear convergence rate of the form
O
(
ρ
k
)
for
ρ
<
1
. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. This extends our earlier work Le Roux et al. (Adv Neural Inf Process Syst,
2012
), which only lead to a faster rate for well-conditioned strongly-convex problems. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.
Journal Article
Ecological Niches and Geographic Distributions (MPB-49)
This book provides a first synthetic view of an emerging area of ecology and biogeography, linking individual- and population-level processes to geographic distributions and biodiversity patterns. Problems in evolutionary ecology, macroecology, and biogeography are illuminated by this integrative view. The book focuses on correlative approaches known as ecological niche modeling, species distribution modeling, or habitat suitability modeling, which use associations between known occurrences of species and environmental variables to identify environmental conditions under which populations can be maintained. The spatial distribution of environments suitable for the species can then be estimated: a potential distribution for the species. This approach has broad applicability to ecology, evolution, biogeography, and conservation biology, as well as to understanding the geographic potential of invasive species and infectious diseases, and the biological implications of climate change. The authors lay out conceptual foundations and general principles for understanding and interpreting species distributions with respect to geography and environment. Focus is on development of niche models. While serving as a guide for students and researchers, the book also provides a theoretical framework to support future progress in the field.
eBook
A dynamic bivariate Poisson model for analysing and forecasting match results in the English Premier League
We develop a statistical model for the analysis and forecasting of football match results which assumes a bivariate Poisson distribution with intensity coefficients that change stochastically over time. The dynamic model is a novelty in the statistical time series analysis of match results in team sports. Our treatment is based on state space and importance sampling methods which are computationally efficient. The out-of-sample performance of our methodology is verified in a betting strategy that is applied to the match outcomes from the 2010–2011 and 2011–2012 seasons of the English football Premier League. We show that our statistical modelling framework can produce a significant positive return over the bookmaker's odds.
Journal Article
SAMPLING-BASED VERSUS DESIGN-BASED UNCERTAINTY IN REGRESSION ANALYSIS
Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design-based. In a design-based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design-based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design-based uncertainty instead of, or in addition to, sampling-based uncertainty. We show that our standard errors in general are smaller than the usual infinite-population sampling-based standard errors and provide conditions under which they coincide.
Journal Article
SPARSE MODELS AND METHODS FOR OPTIMAL INSTRUMENTS WITH AN APPLICATION TO EMINENT DOMAIN
We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic \"beta-min\" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.
Journal Article
Complex Adaptive Systems
This book provides the first clear, comprehensive, and accessible account of complex adaptive social systems, by two of the field's leading authorities. Such systems--whether political parties, stock markets, or ant colonies--present some of the most intriguing theoretical and practical challenges confronting the social sciences. Engagingly written, and balancing technical detail with intuitive explanations, Complex Adaptive Systems focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It provides a detailed introduction to concepts such as emergence, self-organized criticality, automata, networks, diversity, adaptation, and feedback. It also demonstrates how complex adaptive systems can be explored using methods ranging from mathematics to computational models of adaptive agents. John Miller and Scott Page show how to combine ideas from economics, political science, biology, physics, and computer science to illuminate topics in organization, adaptation, decentralization, and robustness. They also demonstrate how the usual extremes used in modeling can be fruitfully transcended.
eBook