We examine a consistent test for the correct specification of a regression function with dependent data. The test is based on the supremum of the difference between the parametric and nonparametric estimates of the re...
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We examine a consistent test for the correct specification of a regression function with dependent data. The test is based on the supremum of the difference between the parametric and nonparametric estimates of the regression model. Rather surprisingly, the behaviour of the test depends on whether the regressors are deterministic or stochastic. In the former situation, the normalization constants necessary to obtain the limiting Gumbel distribution are data dependent and difficult to estimate, so it may be difficult to obtain valid critical values, whereas, in the latter, the asymptotic distribution may not be even known. Because of that, under very mild regularity conditions, we describe a bootstrap analogue for the test, showing its asymptotic validity and finite sample behaviour in a small Monte-Carlo experiment. (c) 2007 Elsevier B.V. All rights reserved.
When estimating the marginal mean response with missing observations, a critical issue is robustness to model misspecification. In this article, we propose a semiparametric estimation method with extended double robus...
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When estimating the marginal mean response with missing observations, a critical issue is robustness to model misspecification. In this article, we propose a semiparametric estimation method with extended double robustness that attains the optimal efficiency under less stringent requirement for model specifications than the doubly robust estimators. In this semiparametric estimation, covariate information is collapsed into a two-dimensional score S. with one dimension for (i) the pattern of missingness and the other for (ii) the pattern of response, both estimated from some working parametric models. The mean response E(Y) is then estimated by the sample mean of E(Y vertical bar S), which is estimated via nonparametricregression. The semiparametric estimator is consistent if either the "core" of (i) or the "core" of (ii) is captured by S, and attains the optimal efficiency if both are captured by S. As the "cores" can be obtained without correctly specifying the full parametric models for (i) or (ii), the proposed estimator can be more robust than other doubly robust estimators. As S contains the propensity score as one component, the proposed estimator avoids the use and the shortcomings of inverse propensity weighting. This semiparametric estimator is most appealing for high-dimensional covariates, where fully correct model specification is challenging and nonparametric estimation is not feasible due to the problem of dimensionality. Numerical performance is investigated by simulation studies.
Suppose we want to estimate the response curve using a kernel estimator. When we perform an experiment to estimate the response curve, we usually decide on the location of all the design points in advance of the exper...
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Suppose we want to estimate the response curve using a kernel estimator. When we perform an experiment to estimate the response curve, we usually decide on the location of all the design points in advance of the experiment. Muller and Schmitt (1988) propose the optimal design, but in practice, we need some prior information about response curve to construct such a design. Park and Faraway (1998) present the sequential design for the global bandwidth estimator and show that their sequential design is asymptotically equivalent to the optimal design and is more efficient than the evenly spaced design. However, the sequential design points will be unequally spaced and so using a global bandwidth may not be appropriate. In this paper, we present the sequential design for the local bandwidth response curve estimator.
We studied the predictability of intraday stock market returns using both linear and nonlinear time series models. For the S&P 500 index we compared simple autoregressive and random walk linear models with a range...
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We studied the predictability of intraday stock market returns using both linear and nonlinear time series models. For the S&P 500 index we compared simple autoregressive and random walk linear models with a range of nonlinear models, including smooth transition, Markov switching, artificial neural network, nonparametric kernel regression and support vector machine models for horizons of 5, 10, 20, 30 and 60 minutes. The empirical results indicate that nonlinear models outperformed linear models on the basis of both statistical and economic criteria. Specifically, although return serial correlation receded by around 10 minutes, return predictability still persisted for up to 60?minutes according to nonlinear models, even though profitability decreases as time elapses. More flexible nonlinear models such as support vector machines and artificial neural network did not clearly outperform other nonlinear models. Copyright (C) 2011 John Wiley & Sons, Ltd.
We introduce a nonparametric smoothing procedure for nonparametric factor analysis of multivariate time series. Our main objective is to develop an adaptive method for estimating a time-varying covariance matrix. The ...
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We introduce a nonparametric smoothing procedure for nonparametric factor analysis of multivariate time series. Our main objective is to develop an adaptive method for estimating a time-varying covariance matrix. The asymptotic properties of the proposed procedures are derived. We present an application based on the residuals from the Fair macromodel of the U.S. economy. We find substantial evidence of time varying second moments and breaks in the contemporaneous correlation structure during the mid 1970's to the early 1980's.
We introduce the effective balancing score for estimation of the mean response under a missing-at-random mechanism. Unlike conventional balancing scores, the proposed score is constructed via dimension reduction free....
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We introduce the effective balancing score for estimation of the mean response under a missing-at-random mechanism. Unlike conventional balancing scores, the proposed score is constructed via dimension reduction free. of model specification. Three types of such scores are introduced, distinguished by whether they carry the covariate information about the missingness, the response, or both. The effective balancing score leads to consistent estimation with little or no loss in efficiency. Compared to existing estimators, it reduces the burden of model specification and is more robust. It is a near-automatic procedure which is most appealing when high-dimensional covariates are involved. We investigate its asymptotic and numerical properties, and illustrate its application with an HIV disease study.
Consider a response variable subject to nonignorable nonresponse and a fully observed covariate vector. The purpose of our study is threefold. First, we study how to extend nonparametric sufficient dimension reduction...
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Consider a response variable subject to nonignorable nonresponse and a fully observed covariate vector. The purpose of our study is threefold. First, we study how to extend nonparametric sufficient dimension reduction to data with nonignorable nonresponse. Second, we utilize sufficient dimension reduction to search an instrument, a linear function of covariates that is related to the response variable but can be excluded from the propensity of nonignorable nonresponse, for the purpose of identifying unknown parameters in a semiparametric propensity and a nonparametric distribution of response variable and covariates. Third, we establish asymptotic results for parameter estimators based on sufficient dimension reduction and instrument search, and investigate the effect on the limiting distribution of parameter estimators due to instrument search. We evaluate the performance of proposed estimators in a Monte Carlo study and illustrate our method in an application to AIDS Clinical Trials Group Protocol 175 data.
Causal inference from observational data is an ambitious but highly relevant task, with diverse applications ranging from natural to social sciences. Within the scope of non-parametric time series, causal inference de...
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Causal inference from observational data is an ambitious but highly relevant task, with diverse applications ranging from natural to social sciences. Within the scope of non-parametric time series, causal inference defined through interventions is largely unexplored, although time order simplifies the problem substantially. A marginal integration scheme is considered for inferring causal effects from observational time series data, MINT-T (marginal integration in time series), which is an adaptation for time series of a previously proposed method for the case of independent data. This approach for stationary stochastic processes is fully nonparametric and, assuming no instantaneous effects consistently recovers the total causal effect of a single intervention with optimal one-dimensional nonparametric convergence rate n(-2/5) assuming regularity conditions and twice differentiability of a certain corresponding regression function. Therefore, MINT-T remains largely unaffected by the curse of dimensionality as long as smoothness conditions hold in higher dimensions and it is feasible for a large class of stationary time series, including nonlinear and multivariate processes. For the case with instantaneous effects, we provide a procedure which guards against false positive causal statements. (c) 2016 EcoSta Econometrics and Statistics. Published by Elsevier B.V. All rights reserved.
This paper uses panel data and the Local Linear kernel Estimator (LLKE), to investigate the effects of aid on physical capital investment in developing countries. Specifically, we investigate the robustness of the rel...
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This paper uses panel data and the Local Linear kernel Estimator (LLKE), to investigate the effects of aid on physical capital investment in developing countries. Specifically, we investigate the robustness of the relationship between aid and physical capital investment in Less Developed countries (LDCs) using two different measures of aid and five measures of the policy environment. We find that external aid has a positive and significant impact on physical capital investment given the support of the sample data we use. This effect is robust to the measurement of aid as well as the policy environment. However, the character of the positive relationship between aid and investment varies with the combination of the aid measure and the policy environment. We find that conditional on inflows, the better the policy environment, the higher the investment rate, all things being equal. The results have implications for aid research and aid policy.
PurposeThis study aims to highlight potential savings in advertising budgets. Design/methodology/approachThis study uses modern computer-based tools including stochastic dominance to check if advertising expenses are ...
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PurposeThis study aims to highlight potential savings in advertising budgets. Design/methodology/approachThis study uses modern computer-based tools including stochastic dominance to check if advertising expenses are increasing sales by using modern causality assessment tools which allow for nonlinearities and use sophisticated assessment of causal impact of ads on sales. FindingsThis study identifies specific media spots where ad budget savings are possible. The marketing managers can take the next step to make small-scale local experiments to reassess this study's findings. Research limitations/implicationsThis study is a statistical observational assessment not based on controlled experiments. Practical implicationsThe authors have tools to identify ineffective advertising which can produce huge savings for the organization. The over-the-counter cold remedies have become important due to the pandemic. The tools have wider applicability in marketing research. Social implicationsLess wasteful expenses always benefit the society. Originality/valueTo the best of the authors' knowledge, this may be the first such attempt to use sophisticated causal identification tools. Remedies for the common cold sold by seven major US retailers help identify specific retailers and specific media with negative returns on investment.
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