Journal articles: 'Semiparametric theory'

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Fokianos, Konstantinos. "Semiparametric Theory and Missing Data." Technometrics 49, no. 2 (May 2007): 228–29. http://dx.doi.org/10.1198/tech.2007.s488.

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Kaji, Tetsuya. "Theory of Weak Identification in Semiparametric Models." Econometrica 89, no. 2 (2021): 733–63. http://dx.doi.org/10.3982/ecta16413.

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We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, that is, when it is locally homogeneous of degree zero. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that there exists an underlying regular parameter that fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of sufficiency and minimality help pin down a desirable one. If estimation of minimal sufficient underlying parameters is inefficient, it introduces noise in the corresponding estimation of weakly regular parameters, whence we can improve the estimators by local asymptotic Rao–Blackwellization. We call an estimator weakly efficient if it does not admit such improvement. New weakly efficient estimators are presented in linear IV and nonlinear regression models. Simulation of a linear IV model demonstrates how 2SLS and optimal IV estimators are improved.

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Bouzebda, Salim, and Mohamed Cherfi. "General inference in semiparametric models through divergences and the duality technique with applications." Theory of Stochastic Processes 25(41), no. 1 (December 21, 2020): 1–24. http://dx.doi.org/10.37863/tsp-7370403638-47.

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In this paper, we extend the dual divergence approach to general semiparametric models and study dual divergence estimators for semiparametric models. Asymptotic properties such as consistency, asymptotic normality of the proposed estimators are deeply investigated by mean the sophisticated modern empirical theory. We investigate the exchangeably weighted estimators in this setting and establish the consistency. We finally consider the functional M-estimator and obtain its weak convergence result.

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Saart, Patrick W., Jiti Gao, and David E. Allen. "Semiparametric Autoregressive Conditional Duration Model: Theory and Practice." Econometric Reviews 34, no. 6-10 (December 17, 2014): 849–81. http://dx.doi.org/10.1080/07474938.2014.956594.

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XU, Fang-min, Xiao-dong XU, and Ping ZHANG. "Semiparametric theory based MIMO model and performance analysis." Journal of China Universities of Posts and Telecommunications 14, no. 4 (December 2007): 36–40. http://dx.doi.org/10.1016/s1005-8885(08)60035-7.

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Hall, Peter, and Joel L. Horowitz. "Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models." Econometric Theory 6, no. 2 (June 1990): 123–50. http://dx.doi.org/10.1017/s0266466600005089.

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Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the case of semiparametric M estimation. However, the resulting estimates of derivatives, as well as parameter estimates and inferences that depend on the derivatives, can be highly sensitive to the choice of the kernel and finite difference bandwidths. This paper discusses the theory of asymptotically optimal bandwidths for kernel and difference quotient estimation of the derivatives required for quantile and semiparametric M estimation, respectively. We do not present a fully automatic method for bandwidth selection.

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Breitung, Jörg, and Philip Hans Franses. "ON PHILLIPS–PERRON-TYPE TESTS FOR SEASONAL UNIT ROOTS." Econometric Theory 14, no. 2 (April 1998): 200–221. http://dx.doi.org/10.1017/s0266466698142032.

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In this paper we consider a semiparametric version of the test for seasonal unit roots suggested by Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238). The asymptotic theory is based on the analysis of a simple regression problem, and the results apply to tests at any given frequency in the range (0,π]. Monte Carlo simulations suggest that the test may have more power than the parametric test of Hylleberg et al. (1990). On the other hand, the semiparametric version suffers from severe size distortions in some situations.

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Hidayati, Lilik, Nur Chamidah, and I. Nyoman Budiantara. "ESTIMASI SELANG KEPERCAYAAN NILAI UJIAN NASIONAL BERBASIS KOMPETENSI BERDASARKAN MODEL REGRESI SEMIPARAMETRIK MULTIRESPON TRUNCATED SPLINE." MEDIA STATISTIKA 13, no. 1 (June 25, 2020): 92–103. http://dx.doi.org/10.14710/medstat.13.1.92-103.

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Confidence interval estimation is important in statistical inference for the parameters of the regression model, but the theory of confidence interval estimation for multi-response semiparametric regression model parameters based on the truncated spline estimator has not been examined. In this study, we estimate the confidence interval of the multi-response semiparametric regression model based on the truncated spline estimator by using pivotal quantity method with the central limit theorem approach. This confidence interval theory is applied to data of competency-based national exam (UNBK) scores in West Nusa Tenggara Province where its UNBK in the lowest position among other provinces in Indonesia. The method used for estimating parameters is weighted least square. The best model is determined based on the Generalized Cross Validation (GCV) minimum value. Based on the estimated 95% confidence interval of parameters of the multi-response truncated spline semiparametric regression model, the results showed that the insignificant factors affecting the UNBK scores were gender and parental education duration while the report card of scores and USBK scores had a positive effect on the UNBK scores but only the UNBK scores of mathematics that report card of scores factor has a negative effect on it.

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Chernozhukov, Victor, Juan Carlos Escanciano, Hidehiko Ichimura, Whitney K. Newey, and James M. Robins. "Locally Robust Semiparametric Estimation." Econometrica 90, no. 4 (2022): 1501–35. http://dx.doi.org/10.3982/ecta16294.

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Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross‐fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

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Harris, David, and Brendan McCabe. "SEMIPARAMETRIC INDEPENDENCE TESTING FOR TIME SERIES OF COUNTS AND THE ROLE OF THE SUPPORT." Econometric Theory 35, no. 6 (December 26, 2018): 1111–45. http://dx.doi.org/10.1017/s0266466618000403.

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This article considers testing for independence in a time series of small counts within an Integer Autoregressive (INAR) model, taking a semiparametric approach that avoids any distributional assumption on the arrivals process of the model. The nature of the testing problem is shown to differ depending on whether or not the support of the arrivals distribution is the full set of natural numbers (as would be the case for Poisson or Negative Binomial distributions for example) or some strict subset of the natural numbers (such as for a Binomial or Uniform distribution). The theory for these two cases is studied separately.For the case where the arrivals have support on the natural numbers, a new asymptotically efficient semiparametric test, the effective score (Neyman-Rao) test, is derived. The semiparametric Likelihood-Ratio, Wald and score tests are shown to be asymptotically equivalent to the effective score test, and hence also asymptotically efficient. Asymptotic relative efficiency calculations demonstrate that the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation coefficient, which is most commonly applied in practice.For the case where the arrivals have support that is a strict subset of the natural numbers, the theory is considerably altered because the support of the observations becomes different under the null and alternative hypotheses. The semiparametric Likelihood-Ratio, Wald and score tests become asymptotically degenerate in this case, while the effective score test remains valid. Remarkably, in this case the effective score test is also found to have power against local alternatives that shrink to the null at the rate T−1. In rare cases where the arrival support is partly or totally known, additional tests exploiting this information are considered.Finite sample properties of the tests in these various cases demonstrate the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation test implied by a parametric Poisson specification. The simulations also reveal situations in which the first order autocorrelation is preferable in finite samples, so a hybrid of the effective score and autocorrelation tests is proposed to capture most of the benefits of each test.

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11

Sun, Yiguo, Zongwu Cai, and Qi Li. "SEMIPARAMETRIC FUNCTIONAL COEFFICIENT MODELS WITH INTEGRATED COVARIATES." Econometric Theory 29, no. 3 (January 8, 2013): 659–72. http://dx.doi.org/10.1017/s0266466612000710.

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AbstractCai, Li, and Park (Journal of Econometrics, 2009) and Xiao (Journal of Econometrics, 2009) developed asymptotic theories for estimators of semiparametric varying coefficient models when regressors are integrated processes but the smooth coefficients are functionals of stationary processes. Using a recent result from Phillips (Econometric Theory, 2009), we extend this line of research by allowing for both the regressors and the covariates entering the smooth functionals to be integrated variables. We derive the asymptotic distribution for the proposed semiparametric estimator. An empirical application is presented to examine the purchasing power parity hypothesis between U.S. and Canadian dollars.

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Angrist, Joshua D., Òscar Jordà, and Guido M. Kuersteiner. "Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited." Journal of Business & Economic Statistics 36, no. 3 (May 10, 2017): 371–87. http://dx.doi.org/10.1080/07350015.2016.1204919.

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13

Rotnitzky, Andrea. "Semiparametric Theory and Missing Data by TSIATIS, A. A." Biometrics 65, no. 1 (March 2009): 326–28. http://dx.doi.org/10.1111/j.1541-0420.2009.01208_1.x.

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Szczepańska, Anna, and Ewa Bakinowska. "Detection of the change point in the winter wheat experiment." Biometrical Letters 49, no. 1 (June 1, 2012): 37–44. http://dx.doi.org/10.2478/bile-2013-0002.

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SummaryThis paper concerns detection of the change point, which is treated as an abrupt change in the response function or one of its derivatives. The change point is identified using the semiparametric model and the theory given by Speckman (1994). The theory is illustrated by a real experiment in wchich the dry biomass of winter wheat is studied.

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McVinish, R., and K. Mengersen. "Semiparametric Bayesian circular statistics." Computational Statistics & Data Analysis 52, no. 10 (June 2008): 4722–30. http://dx.doi.org/10.1016/j.csda.2008.03.016.

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Hernández-Lobato, José Miguel, and Alberto Suárez. "Semiparametric bivariate Archimedean copulas." Computational Statistics & Data Analysis 55, no. 6 (June 2011): 2038–58. http://dx.doi.org/10.1016/j.csda.2011.01.018.

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Farrell, Max H., Tengyuan Liang, and Sanjog Misra. "Deep Neural Networks for Estimation and Inference." Econometrica 89, no. 1 (2021): 181–213. http://dx.doi.org/10.3982/ecta16901.

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We study deep neural networks and their use in semiparametric inference. We establish novel nonasymptotic high probability bounds for deep feedforward neural nets. These deliver rates of convergence that are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second‐step inference after first‐step estimation with deep learning, a result also new to the literature. Our nonasymptotic high probability bounds, and the subsequent semiparametric inference, treat the current standard architecture: fully connected feedforward neural networks (multilayer perceptrons), with the now‐common rectified linear unit activation function, unbounded weights, and a depth explicitly diverging with the sample size. We discuss other architectures as well, including fixed‐width, very deep networks. We establish the nonasymptotic bounds for these deep nets for a general class of nonparametric regression‐type loss functions, which includes as special cases least squares, logistic regression, and other generalized linear models. We then apply our theory to develop semiparametric inference, focusing on causal parameters for concreteness, and demonstrate the effectiveness of deep learning with an empirical application to direct mail marketing.

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18

Hristache, Marian, and Valentin Patilea. "SEMIPARAMETRIC EFFICIENCY BOUNDS FOR CONDITIONAL MOMENT RESTRICTION MODELS WITH DIFFERENT CONDITIONING VARIABLES." Econometric Theory 32, no. 4 (April 15, 2015): 917–46. http://dx.doi.org/10.1017/s0266466615000080.

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This paper addresses the problem of semiparametric efficiency bounds for conditional moment restriction models with different conditioning variables. We characterize such an efficiency bound, that in general is not explicit, as a limit of explicit efficiency bounds for a decreasing sequence of unconditional (marginal) moment restriction models. An iterative procedure for approximating the efficient score when this is not explicit is provided. Our theoretical results provide new insight for the theory of semiparametric efficiency bounds literature and open the door to new applications. In particular, we investigate a class of regression-like (mean regression, quantile regression,…) models with missing data, an example of a supply and demand simultaneous equations model and a generalized bivariate dichotomous model.

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Liu, Jialuo, Tingjin Chu, Jun Zhu, and Haonan Wang. "Semiparametric method and theory for continuously indexed spatio-temporal processes." Journal of Multivariate Analysis 183 (May 2021): 104735. http://dx.doi.org/10.1016/j.jmva.2021.104735.

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Yang, Ying. "Penalized semiparametric density estimation." Statistics and Computing 19, no. 4 (September 23, 2008): 355–66. http://dx.doi.org/10.1007/s11222-008-9097-4.

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Deléamont, P. Y., and D. La Vecchia. "Semiparametric segment M-estimation for locally stationary diffusions." Biometrika 106, no. 4 (September 16, 2019): 941–56. http://dx.doi.org/10.1093/biomet/asz042.

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Summary We develop and implement a novel M-estimation method for locally stationary diffusions observed at discrete time-points. We give sufficient conditions for the local stationarity of general time-inhomogeneous diffusions. Then we focus on locally stationary diffusions with time-varying parameters, for which we define our M-estimators and derive their limit theory.

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Lawless, Jerald F., and Yildiz E. Yilmaz. "Comparison of semiparametric maximum likelihood estimation and two-stage semiparametric estimation in copula models." Computational Statistics & Data Analysis 55, no. 7 (July 2011): 2446–55. http://dx.doi.org/10.1016/j.csda.2011.02.008.

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Matsushita, Yukitoshi, and Taisuke Otsu. "LIKELIHOOD INFERENCE ON SEMIPARAMETRIC MODELS WITH GENERATED REGRESSORS." Econometric Theory 36, no. 4 (November 25, 2019): 626–57. http://dx.doi.org/10.1017/s026646661900029x.

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Hahn and Ridder (2013, Econometrica 81, 315–340) formulated influence functions of semiparametric three-step estimators where generated regressors are computed in the first step. This class of estimators covers several important examples for empirical analysis, such as production function estimators by Olley and Pakes (1996, Econometrica 64, 1263–1297) and propensity score matching estimators for treatment effects by Heckman, Ichimura, and Todd (1998, Review of Economic Studies 65, 261–294). The present article studies a nonparametric likelihood-based inference method for the parameters in such three-step estimation problems. In particular, we apply the general empirical likelihood theory of Bravo, Escanciano, and van Keilegom (2018, Annals of Statistics, forthcoming) to modify semiparametric moment functions to account for influences from plug-in estimates into the above important setup, and show that the resulting likelihood ratio statistic becomes asymptotically pivotal without undersmoothing in the first and second step nonparametric estimates.

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Shuangge Ma. "Book review: Tsiatis, A.A. 2006: Semiparametric Theory and Missing Data. Springer." Statistical Methods in Medical Research 17, no. 5 (February 19, 2008): 538–39. http://dx.doi.org/10.1177/09622802080170051002.

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Claeskens, G., and R. J. Carroll. "An asymptotic theory for model selection inference in general semiparametric problems." Biometrika 94, no. 2 (February 28, 2007): 249–65. http://dx.doi.org/10.1093/biomet/asm034.

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Burda, Michael C., Wolfgang Härdle, Marlene Müller, and Axel Werwatz. "Semiparametric analysis of German East-West migration intentions: facts and theory." Journal of Applied Econometrics 13, no. 5 (September 1998): 525–41. http://dx.doi.org/10.1002/(sici)1099-1255(1998090)13:5<525::aid-jae508>3.0.co;2-c.

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Xiang, Sijia, Weixin Yao, and Byungtae Seo. "Semiparametric mixture: Continuous scale mixture approach." Computational Statistics & Data Analysis 103 (November 2016): 413–25. http://dx.doi.org/10.1016/j.csda.2016.06.001.

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Liu, Jin, Yingying Ma, and Hansheng Wang. "Semiparametric model for covariance regression analysis." Computational Statistics & Data Analysis 142 (February 2020): 106815. http://dx.doi.org/10.1016/j.csda.2019.106815.

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Pendakur, Krishna, Michael Scholz, and Stefan Sperlich. "Semiparametric indirect utility and consumer demand." Computational Statistics & Data Analysis 54, no. 11 (November 2010): 2763–75. http://dx.doi.org/10.1016/j.csda.2010.04.004.

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Liu, Jinyuan, Ke Xu, Tsungchin Wu, Lydia Yao, Tanya T. Nguyen, Dilip Jeste, and Xinlian Zhang. "Deciphering the ‘gut–brain axis’ through microbiome diversity." General Psychiatry 36, no. 5 (October 2023): e101090. http://dx.doi.org/10.1136/gpsych-2023-101090.

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Incentivised by breakthroughs and data generated by the high-throughput sequencing technology, this paper proposes a distance-based framework to fulfil the emerging needs in elucidating insights from the high-dimensional microbiome data in psychiatric studies. By shifting focus from traditional methods that focus on the observations from each subject to the between-subject attributes that aggregate two or more subjects’ entire feature vectors, the described approach revolutionises the conventional prescription for high-dimensional observations via microbiome diversity. To this end, we enrich the classical generalised linear models to articulate the multivariable regression relationship between distance-based variables. We also discuss a robust and computationally feasible semiparametric inference technique. Benefitting from the latest advances in the semiparametric efficiency theory for such attributes, the proposed estimators enjoy robustness and good asymptotic properties that guarantee sensitivity in detecting signals between clinical outcomes and microbiome diversity. It offers a readily implementable and easily interpretable solution for deciphering the gut–brain axis in mental health research.

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Li, Kunming, and Liting Fang. "Bayesian Estimation of the Semiparametric Spatial Lag Model." Mathematics 12, no. 14 (July 22, 2024): 2289. http://dx.doi.org/10.3390/math12142289.

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This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results.

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Phillips, Peter C. B. "LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION." Econometric Theory 25, no. 6 (December 2009): 1466–97. http://dx.doi.org/10.1017/s0266466609990223.

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A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnostics are suggested for forensic analysis of such regresssions, including a localR2and a local Durbin–Watson (DW) ratio, and their asymptotic behavior is investigated. The most immediate findings extend the earlier work on linear spurious regression (Phillips, 1986,Journal of Econometrics33, 311–340) showing that the key behavioral characteristics of statistical significance, lowDWratios and moderate to highR2continue to apply locally in nonparametric spurious regression. Some further applications of the limit theory to models of nonlinear functional relations and cointegrating regressions are given. The methods are also shown to be applicable in partial linear semiparametric nonstationary regression.

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Ding, S., J. Shi, and W. Jiang. "Theory and method of hypothetical test for nonparameters in linear semiparametric model." Survey Review 49, no. 354 (March 4, 2016): 221–26. http://dx.doi.org/10.1179/1752270614y.0000000147.

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Nan, Bin, John D. Kalbfleisch, and Menggang Yu. "Asymptotic theory for the semiparametric accelerated failure time model with missing data." Annals of Statistics 37, no. 5A (October 2009): 2351–76. http://dx.doi.org/10.1214/08-aos657.

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Wang, Haoying. "The Spatial Structure of Farmland Values: A Semiparametric Approach." Agricultural and Resource Economics Review 47, no. 3 (February 26, 2018): 568–91. http://dx.doi.org/10.1017/age.2017.35.

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Controlling for spatial heterogeneity and spatial dependence in farmland valuation models has gained substantial attention in recent literature. This paper proposes to derive the spatial structure of farmland values endogenously and semiparametrically based on the spatial competition theory. The paper assembles panel data of Pennsylvania county level farmland values between 1982 and 2012. A spatial autoregressive panel data model with spatial weights matrix endogenously incorporated is estimated. Out of sample predictions and non-nested statistical tests for model selection suggest that the fit and the predictability of hedonic farmland valuation models can be greatly improved.

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List, Marit Kristine, Olaf Köller, and Gabriel Nagy. "A Semiparametric Approach for Modeling Not-Reached Items." Educational and Psychological Measurement 79, no. 1 (December 27, 2017): 170–99. http://dx.doi.org/10.1177/0013164417749679.

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Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel’s item response theory model for NRIs by (1) including a semiparametric representation of the distribution of the onset of NRIs, (2) modeling the relationships of NRIs with proficiency via a flexible multinomial logit regression, and (3) including additional covariates to predict NRIs. We show that Glas and Pimentel’s and our model have close connections to event history analysis, thereby making it possible to apply tools developed in this context to the analysis of NRIs. Our model was applied to a timed low-stakes test of mathematics achievement. Our model fitted the data better than Glas and Pimentel’s model, and allowed for a more fine-grained assessment of the onset of NRIs. The results of a simulation study showed that our model accurately recovered the relationships of proficiency and covariates with the onset of NRIs, and reduced bias in the estimates of item parameters, proficiency distributions, and covariate effects on proficiency.

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Donelli, Nicola, Stefano Peluso, and Antonietta Mira. "A Bayesian semiparametric vector Multiplicative Error Model." Computational Statistics & Data Analysis 161 (September 2021): 107242. http://dx.doi.org/10.1016/j.csda.2021.107242.

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Mahmoud, Hamdy F. F., and Inyoung Kim. "Semiparametric spatial mixed effects single index models." Computational Statistics & Data Analysis 136 (August 2019): 108–22. http://dx.doi.org/10.1016/j.csda.2019.01.008.

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Arteche, J. "Semiparametric estimation in perturbed long memory series." Computational Statistics & Data Analysis 51, no. 4 (December 2006): 2118–41. http://dx.doi.org/10.1016/j.csda.2006.07.023.

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Bellio, Ruggero, and Luca Grassetti. "Semiparametric stochastic frontier models for clustered data." Computational Statistics & Data Analysis 55, no. 1 (January 2011): 71–83. http://dx.doi.org/10.1016/j.csda.2010.04.028.

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Hazelton, Martin L., and Berwin A. Turlach. "Semiparametric regression with shape-constrained penalized splines." Computational Statistics & Data Analysis 55, no. 10 (October 2011): 2871–79. http://dx.doi.org/10.1016/j.csda.2011.04.018.

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Miao, Wang, Lan Liu, Yilin Li, Eric J. Tchetgen Tchetgen, and Zhi Geng. "Identification and Semiparametric Efficiency Theory of Nonignorable Missing Data with a Shadow Variable." ACM / IMS Journal of Data Science 1, no. 2 (April 8, 2024): 1–23. http://dx.doi.org/10.1145/3592389.

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We consider identification and estimation with an outcome missing not at random (MNAR). We study an identification strategy based on a so-called shadow variable . A shadow variable is assumed to be correlated with the outcome but independent of the missingness process conditional on the outcome and fully observed covariates. We describe a general condition for nonparametric identification of the full data law under MNAR using a valid shadow variable. Our condition is satisfied by many commonly used models; moreover, it is imposed on the complete cases, and therefore has testable implications with observed data only. We characterize the semiparametric efficiency bound for the class of regular and asymptotically linear estimators and derive a closed form for the efficient influence function. We describe a doubly robust and locally efficient estimation method and evaluate its performance on both simulation data and a real data example about home pricing.

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Wellner, Jon A., Brad McNeney, and Norman Breslow. "Large sample theory for semiparametric regression models with two-phase, outcome dependent sampling." Annals of Statistics 31, no. 4 (August 2003): 1110–39. http://dx.doi.org/10.1214/aos/1059655907.

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Tchetgen Tchetgen, Eric J., and Ilya Shpitser. "Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis." Annals of Statistics 40, no. 3 (June 2012): 1816–45. http://dx.doi.org/10.1214/12-aos990.

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Luts, Jan. "Real-Time Semiparametric Regression for Distributed Data Sets." IEEE Transactions on Knowledge and Data Engineering 27, no. 2 (February 1, 2015): 545–57. http://dx.doi.org/10.1109/tkde.2014.2334326.

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Caner, Mehmet. "Weak Convergence to a Matrix Stochastic Integral with Stable Processes." Econometric Theory 13, no. 4 (February 1997): 506–28. http://dx.doi.org/10.1017/s0266466600005983.

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This paper generalizes the univariate results of Chan and Tran (1989, Econometric Theory 5, 354–362) and Phillips (1990, Econometric Theory 6, 44–62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and identically distributed errors and for I(1) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. The limit laws are represented by functional of a stable process. A semiparametric correction is used in order to asymptotically eliminate the “bias” term in the limit law. These results are also an extension of the multivariate limit theory for square-integrable disturbances derived by Phillips and Durlauf (1986, Review of Economic Studies 53, 473–495). Potential applications include tests for multivariate unit roots and cointegration.

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Wei, Shaojie, Chao Zhang, Zhi Geng, and Shanshan Luo. "Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes." Mathematics 12, no. 18 (September 10, 2024): 2801. http://dx.doi.org/10.3390/math12182801.

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Potential outcomes play a fundamental and important role in many causal inference problems. If the potential-outcome means are identifiable, a series of causal effect measures, including the risk difference, the risk ratio, and the treatment benefit rate, among others, can also be identified. However, current identification and estimation methods for these means often implicitly assume that the collected data for analysis are measured precisely. In many fields such as medicine and economics, the collected variables may be subject to measurement errors, such as medical diagnostic results and individual wage data. Misclassification, as a non-classic measurement error, can lead to severely biased estimates in causal inference. In this paper, we leverage a combined sample to study the identifiability of potential-outcome means corresponding to different treatment levers under a plausible misclassification assumption for the outcome, allowing the misclassification probability to depend on not only the true outcome but also the covariates. Furthermore, we propose the multiply-robust and semiparametric efficient estimators for the means, consistent even under partial misspecification of the observed data law, based on the semiparametric theory framework. The simulation studies and real data analysis demonstrate the satisfactory performance of the proposed method.

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Leonelli, Manuele, and Dani Gamerman. "Semiparametric bivariate modelling with flexible extremal dependence." Statistics and Computing 30, no. 2 (May 28, 2019): 221–36. http://dx.doi.org/10.1007/s11222-019-09878-w.

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Gao, Jiti, Rodney Wolff, and Vo Anh. "Semiparametric Approximation Methods in Multivariate Model Selection." Journal of Complexity 17, no. 4 (December 2001): 754–72. http://dx.doi.org/10.1006/jcom.2001.0591.

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You, Jinhong, and Xian Zhou. "ASYMPTOTIC THEORY IN FIXED EFFECTS PANEL DATA SEEMINGLY UNRELATED PARTIALLY LINEAR REGRESSION MODELS." Econometric Theory 30, no. 2 (December 13, 2013): 407–35. http://dx.doi.org/10.1017/s0266466613000352.

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This paper deals with statistical inference for the fixed effects panel data seemingly unrelated partially linear regression model. The model naturally extends the traditional fixed effects panel data regression model to allow for semiparametric effects. Multiple regression equations are permitted, and the model includes the aggregated partially linear model as a special case. A weighted profile least squares estimator for the parametric components is proposed and shown to be asymptotically more efficient than those neglecting the contemporaneous correlation. Furthermore, a weighted two-stage estimator for the nonparametric components is also devised and shown to be asymptotically more efficient than those based on individual regression equations. The asymptotic normality is established for estimators of both parametric and nonparametric components. The finite-sample performance of the proposed methods is evaluated by simulation studies.

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Journal articles on the topic 'Semiparametric theory'

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