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BACKGROUND:There is little evidence to guide the care of over a million sepsis survivors following hospital discharge despite high rates of hospital readmission. OBJECTIVE:We examined whether early home health nursing (first visit within 2 days of hospital discharge and at least 1 additional visit in the first posthospital week) and early physician follow-up (an outpatient visit in the first posthospital week) reduce 30-day readmissions among Medicare sepsis survivors. DESIGN:A pragmatic, comparative effectiveness analysis of Medicare data from 2013 to 2014 using nonlinear instrumental variable analysis. SUBJECTS:Medicare beneficiaries in the 50 states and District of Columbia discharged alive after a sepsis hospitalization and received home health care. MEASURES:The outcomes, protocol parameters, and control variables were from Medicare administrative and claim files and the home health Outcome and Assessment Information Set (OASIS). The primary outcome was 30-day all-cause hospital readmission. RESULTS:Our sample consisted of 170,571 mostly non-Hispanic white (82.3%), female (57.5%), older adults (mean age, 76 y) with severe sepsis (86.9%) and a multitude of comorbid conditions and functional limitations. Among them, 44.7% received only the nursing protocol, 11.0% only the medical doctor protocol, 28.1% both protocols, and 16.2% neither. Although neither protocol by itself had a statistically significant effect on readmission, both together reduced the probability of 30-day all-cause readmission by 7 percentage points (P=0.006; 95% confidence interval=2, 12). CONCLUSIONS:Our findings suggest that, together, early postdischarge care by home health and medical providers can reduce hospital readmissions for sepsis survivors.

We propose a self-tuning $\\sqrt {Lasso} $ Lasso method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example, perfectly collinear regressors, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case, in contrast to Lasso. We establish various nonasymptotic bounds for $\\sqrt {Lasso} $ including prediction norm rate and sparsity. Our analysis is based on new impact factors that are tailored for bounding prediction norm. In order to cover heteroscedastic non-Gaussian noise, we rely on moderate deviation theory for self-normalized sums to achieve Gaussian-like results under weak conditions. Moreover, we derive bounds on the performance of ordinary least square (ols) applied to the model selected by $\\sqrt {Lasso} $ accounting for possible misspecification of the selected model. Under mild conditions, the rate of convergence of ols post $\\sqrt {Lasso} $ is as good as $\\sqrt {Lasso's} $ rate. As an application, we consider the use of $\\sqrt {Lasso} $ and ols post $\\sqrt {Lasso} $ as estimators of nuisance parameters in a generic semiparametric problem (nonlinear moment condition or Z-problem), resulting in a construction of $\\sqrt n - consistent$ and asymptotically normal estimators of the main parameters.

This paper considers inference on functional of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill-posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root-estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug-in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug-in PSMD estimator, and hence the asymptotic chi-square distribution of the sieve Wald statistic; (3) the asymptotic chi-square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non-optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.

The paper examines the behavior of a generalized version of the nonlinear IV unit root test proposed by Chang ( 2002 ) when the series’ errors exhibit nonstationary volatility. The leading case of such nonstationary volatility concerns structural breaks in the error variance. We show that the generalized test is not robust to variance changes in general, and illustrate the extent of the resulting size distortions in finite samples. More importantly, we show that pivotality is recovered when using Eicker-White heteroskedasticity-consistent standard errors. This contrasts with the case of Dickey-Fuller unit root tests, for which Eicker-White standard errors do not produce robustness and thus require computationally costly corrections such as the (wild) bootstrap or estimation of the so-called variance profile. The pivotal versions of the generalized IV tests – with or without the correct standard errors – do however have no power in -neighbourhoods of the null. We also study the validity of panel versions of the tests considered here.

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite-dimensional function parameter space. Some of the PSMD procedures use slowly growing finite-dimensional sieves with flexible penalties or without any penalty; others use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup-norm or a root mean squared norm), allowing for possibly noncompact infinite-dimensional parameter spaces. For both mildly and severely ill-posed nonlinear inverse problems, our convergence rates in Hubert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.

We propose a local measure of the relationship between parameter estimates and the moments of the data they depend on. Our measure can be computed at negligible cost even for complex structural models. We argue that reporting this measure can increase the transparency of structural estimates, making it easier for readers to predict the way violations of identifying assumptions would affect the results. When the key assumptions are orthogonality between error terms and excluded instruments, we show that our measure provides a natural extension of the omitted variables bias formula for nonlinear models. We illustrate with applications to published articles in several fields of economics.

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some \"measure of location\" of the distribution of the measurement error (e.g., its mean, mode, or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to \"index\" the eigenfunctions so that the decomposition is unique. We propose a convenient sievebased estimator, derive its asymptotic properties, and investigate its finite-sample behavior through Monte Carlo simulations.

This paper makes several important contributions to the literature about non- parametric instrumental variables (NPIV ) estimation and inference on a structural function h0 and functionals of h0 .First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series two-stage least squares) estimators of h0 and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating h0 and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when h0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean- squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence bands (UCBs) for collections of nonlinear functionals of h0 under primitive conditions, allowing for mildly and severely ill-posed problems. Fourth, as applications, we obtain the first asymptotic pointwise and uniform inference results for plug-in sieve t -statistics of exact consumer surplus (CS) and deadweight loss (DL) welfare functionals under low-level conditions when demand is estimated via sieve NPIV. Our real data application of UCBs for exact CS and DL functionals of gasoline demand reveals interesting patterns and is applicable to other goods markets.

Instrumental variables are widely used in applied econometrics to achieve identification and carry out estimation and inference in models that contain endogenous explanatory variables. In most applications, the function of interest (e. g., an Engel curve or demand function) is assumed to be known up to finitely many parameters (e.g., a linear model), and instrumental variables are used to identify and estimate these parameters. However, linear and other finite-dimensional parametric models make strong assumptions about the population being modeled that are rarely if ever justified by economic theory or other a priori reasoning and can lead to seriously erroneous conclusions if they are incorrect. This paper explores what can be learned when the function of interest is identified through an instrumental variable but is not assumed to be known up to finitely many parameters. The paper explains the differences between parametric and nonparametric estimators that are important for applied research, describes an easily implemented nonparametric instrumental variables estimator, and presents empirical examples in which nonparametric methods lead to substantive conclusions that are quite different from those obtained using standard, parametric estimators.