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We provide a limit theory for a general class of kernel smoothed Ustatistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and is useful in other applications. Simulations examine the finite sample performance of the test.

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group least absolute shrinkage and selection operator (LASSO) techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in highdimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal nonparametric regressions. Since our approach actually requires no estimation, it is advantageous in scenarios such as the single-index models where even specification and identification of a marginal model is an issue. By automatically incorporating the level of variation of the nonparametric regression and directly assessing the strength of data evidence supporting local contribution from each explanatory variable, our approach provides a unique perspective for solving feature screening problems. Theoretical analysis shows that our approach can handle data dimensionality growing exponentially with the sample size. With extensive theoretical illustrations and numerical examples, we show that the local independence screening approach performs promisingly.

We present new identification results for nonparametric models of differentiated products markets, using only market level observables. We specify a nonparametric random utility discrete choice model of demand allowing rich preference heterogeneity, product/market unobservables, and endogenous prices. Our supply model posits nonparametric cost functions, allows latent cost shocks, and nests a range of standard oligopoly models. We consider identification of demand, identification of changes in aggregate consumer welfare, identification of marginal costs, identification of firms' marginal cost functions, and discrimination between alternative models of firm conduct. We explore two complementary approaches. The first demonstrates identification under the same nonparametric instrumental variables conditions required for identification of regression models. The second treats demand and supply in a system of nonparametric simultaneous equations, leading to constructive proofs exploiting exogenous variation in demand shifters and cost shifters. We also derive testable restrictions that provide the first general formalization of Bresnahan's (1982) intuition for empirically distinguishing between alternative models of oligopoly competition. From a practical perspective, our results clarify the types of instrumental variables needed with market level data, including tradeoffs between functional form and exclusion restrictions.

Choice models today are ubiquitous across a range of applications in operations and marketing. Real-world implementations of many of these models face the formidable stumbling block of simply identifying the \"right\" model of choice to use. Because models of choice are inherently high-dimensional objects, the typical approach to dealing with this problem is positing, a priori, a parametric model that one believes adequately captures choice behavior. This approach can be substantially suboptimal in scenarios where one cares about using the choice model learned to make fine-grained predictions; one must contend with the risks of mis-specification and overfitting/underfitting. Thus motivated, we visit the following problem: For a \"generic\" model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal information about these distributions), how may one predict revenues from offering a particular assortment of choices? An outcome of our investigation is a nonparametric approach in which the data automatically select the right choice model for revenue predictions. The approach is practical. Using a data set consisting of automobile sales transaction data from a major U.S. automaker, our method demonstrates a 20% improvement in prediction accuracy over state-of-the-art benchmark models; this improvement can translate into a 10% increase in revenues from optimizing the offer set. We also address a number of theoretical issues, among them a qualitative examination of the choice models implicitly learned by the approach. We believe that this paper takes a step toward \"automating\" the crucial task of choice model selection. This paper was accepted by Yossi Aviv, operations management.

A variable screening procedure via correlation learning was proposed by Fan and Lv (2008) to reduce dimensionality in sparse ultra-high-dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening (NIS) is a specific type of sure independence screening. We propose several closely related variable screening procedures. We show that with general nonparametric models, under some mild technical conditions, the proposed independence screening methods have a sure screening property. The extent to which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, we also propose a data-driven thresholding and an iterative nonparametric independence screening (INIS) method to enhance the finite- sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.

This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional assumption on the data generating process, we consider a quasilikelihood induced from the conditional moment restriction, and put priors on the function-valued parameter. We call the resulting posterior quasi-posterior, which corresponds to \"Gibbs posterior\" in the literature. Here we focus on priors constructed on slowly growing finite-dimensional sieves. We derive rates of contraction and a nonparametric Bernstein—von Mises type result for the quasi-posterior distribution, and rates of convergence for the quasi-Bayes estimator defined by the posterior expectation. We show that, with priors suitably chosen, the quasi-posterior distribution (the quasi-Bayes estimator) attains the minimax optimal rate of contraction (convergence, resp.). These results greatly sharpen the previous related work.

The generalizability of empirical findings to new environments, settings or populations, often called \"external validity,\" is essential in most scientific explorations. This paper treats a particular problem of generalizability, called \"transportability,\" defined as a license to transfer causal effects learned in experimental studies to a new population, in which only observational studies can be conducted. We introduce a formal representation called \"selection diagrams\" for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we reduce questions of transportability to symbolic derivations in the docalculus. This reduction yields graph-based procedures for deciding, prior to observing any data, whether causal effects in the target population can be inferred from experimental findings in the study population. When the answer is affirmative, the procedures identify what experimental and observational findings need be obtained from the two populations, and how they can be combined to ensure bias-free transport.

Germination and emergence assays represent the most notable examples of time-to-event data in agriculture and related disciplines. In spite of the peculiar characteristics of this type of data, there has been little effort to establish a specific and comprehensive framework for their analyses. Indeed, a brief survey of the literature shows that germination and emergence data, along with other phenological measurements such as flowering time, have been analyzed through myriad approaches, giving rise to confusion and uncertainty among scientists and practitioners as to what may represent the best statistical practice. This lack of coherence in statistical approach may reduce the efficiency of research, while making the communication of results and the cross-study comparisons extremely challenging. Here, we attempt to provide a coherent framework and protocol for the analyses of germination/emergence and other time-to-event data in weed science and related disciplines, together with a software implementation in the form of a new R package. We propose a similar approach to biological assays in ecotoxicology, based on: (1) fitting a time-to-event model to describe the whole time course of events; (2) comparing time-to-event curves across experimental treatments, and (3) deriving further information from the fitted model to better focus on some traits of interest. The most appropriate methods to accomplish this procedure were carefully selected from the framework of survival analysis and related sources and were modified to comply with the specific needs of weed, seed, and plant sciences. Finally, they were implemented in the new R package drcte. In this article, we describe the procedure and its limitations by way of providing examples of several types of germination/emergence assays. We highlight that our proposed procedure can also serve as the first step of data analyses, with its output subsequently submitted to traditional or meta-analytic approaches.

Researchers have long struggled to identify causal effects in nonexperimental settings. Many recently proposed strategies assume ignorability of the treatment assignment mechanism and require fitting two models-one for the assignment mechanism and one for the response surface. This article proposes a strategy that instead focuses on very flexibly modeling just the response surface using a Bayesian nonparametric modeling procedure, Bayesian Additive Regression Trees (BART). BART has several advantages: it is far simpler to use than many recent competitors, requires less guesswork in model fitting, handles a large number of predictors, yields coherent uncertainty intervals, and fluidly handles continuous treatment variables and missing data for the outcome variable. BART also naturally identifies heterogeneous treatment effects. BART produces more accurate estimates of average treatment effects compared to propensity score matching, propensity-weighted estimators, and regression adjustment in the nonlinear simulation situations examined. Further, it is highly competitive in linear settings with the \"correct\" model, linear regression. Supplemental materials including code and data to replicate simulations and examples from the article as well as methods for population inference are available online.