Semiparametric Structure Research Articles

The role of propensity score structure in asymptotic efficiency of estimated conditional quantile treatment effect

AbstractWhen a strict subset of covariates is given, we propose conditional quantile treatment effect () to offer, compared with the unconditional quantile treatment effect () and conditional average treatment effect (), a more complete and informative view of the heterogeneity of treatment effects via the quantile sheet that is a function of the given covariates and quantile levels. Even though either one or both and are not significant, could still show some impact of the treatment on the upper and lower tails of subpopulations' (defined by the covariates subset) distribution. To the best of our knowledge, this is the first to consider such a low‐dimensional conditional quantile treatment effect in the literature. We focus on deriving the asymptotic normality of propensity score‐based estimators under parametric, nonparametric, and semiparametric structure. We make a systematic study on the estimation efficiency to check the importance of propensity score structure and the essential differences from the unconditional counterparts. The derived unique properties can answer: what is the general ranking of these estimators? how does the affiliation of the given covariates to the set of covariates of the propensity score affect the efficiency? how does the convergence rate of the estimated propensity score affect the efficiency? and why would semiparametric estimation be worth of recommendation in practice? The simulation studies are conducted to examine the performances of these estimators. A real data example is analyzed for illustration and some new findings are acquired.

Constrained Varying-Coefficient Model for Time-Course Experiments in Soft Tissue Fabrication

In the fabrication of artificial soft tissues, novel biomaterials with the required properties are obtained by appropriately adjusting process parameters during material synthesis. One key step in finding the desired material is understanding the relationship between the process parameters and the material properties, and time-course experiments are typically conducted for this purpose. This article proposes a constrained varying-coefficient modeling method for such data in which expert knowledge is properly accommodated in the model estimation to make the modeling practically meaningful. The proposed model has a semiparametric structure and incorporates expert knowledge in the form of constraints on model coefficients. Estimation algorithms based on a smoothing spline and a weighted smoothing spline are also provided. Finally, the proposed method is compared with existing methods in a case study and a numerical study.

Predicting LGD distributions with mixed continuous and discrete ordinal outcomes

The loss given default (LGD) distribution is known to have a complex structure. Consequently, the parametric approach for its prediction by fitting a density function may suffer a loss of predictive power. To overcome this potential drawback, we use the cumulative probability model (CPM) to predict the LGD distribution. The CPM applies a transformed variable to model the LGD distribution. This transformed variable has a semiparametric structure. It models the predictor effects parametrically. The functional form of the transformation is unspecified. Thus, CPM provides more flexibility and simplicity in modeling the LGD distribution. To implement CPM, we collect a sample of defaulted debts from Moody’s Default and Recovery Database. Given this sample, we use an expanding rolling window approach to investigate the out-of-time performance of CPM and its alternatives. Our results confirm that CPM is better than its alternatives, in the sense of yielding more accurate LGD distribution predictions.

Likelihood Induced by Moment Functions using Particle Filter: A Comparison of Particle GMM and Standard MCMC Methods

Particle filtering is a useful statistical tool which can be used to make inference on the latent variables and the structural parameters of state space models by employing it inside MCMC algorithms (Flury and Shephard, 2011). It only relies on two assumptions (Gordon et al, 1993): a: The ability to simulate from the dynamic of the model; b: The predictive measurement density can be computed. In practice the second assumption may not be obvious and implementations of particle filter can become difficult to conduct. Gallant, Giacomini and Ragusa (2016) have recently developed a particle filter which does not rely on the structural form of the measurement equation. This method uses a set of moment conditions to induce the likelihood function of a structural model under a GMM criteria. The semiparametric structure allows to use particle filtering where the standard techniques are not applicable or difficult to implement. On the other hand, the GMM representation is less efficient than the standard technique and in some cases it can affect the proper functioning of particle lter and in turn deliver poor estimates. The contribution of this paper is to provide a comparison between the standard techniques, as Kalman filter and standard bootstrap particle filter, and the method proposed by Gallant et al (2016) in order to measure the performance of particle filter with GMM representation.

Modeling the density of US yield curve using Bayesian semiparametric dynamic Nelson-Siegel model

This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model for estimating the density of bond yields. Specifically, we model the distribution of the yield curve factors according to an infinite Markov mixture (iMM). The model allows for time variation in the mean and covariance matrix of factors in a discrete manner, as opposed to continuous changes in these parameters such as the Time Varying Parameter (TVP) models. Estimating the number of regimes using the iMM structure endogenously leads to an adaptive process that can generate newly emerging regimes over time in response to changing economic conditions in addition to existing regimes. The potential of the proposed framework is examined using US bond yields data. The semiparametric structure of the factors can handle various forms of non-normalities including fat tails and nonlinear dependence between factors using a unified approach by generating new clusters capturing these specific characteristics. We document that modeling parameter changes in a discrete manner increases the model fit as well as forecasting performance at both short and long horizons relative to models with fixed parameters as well as the TVP model with continuous parameter changes. This is mainly due to fact that the discrete changes in parameters suit the typical low frequency monthly bond yields data characteristics better.

Inverse-Probability-Weighted Estimation for Monotone and Nonmonotone Missing Data.

Missing data is a common occurrence in epidemiologic research. In this paper, 3 data sets with induced missing values from the Collaborative Perinatal Project, a multisite US study conducted from 1959 to 1974, are provided as examples of prototypical epidemiologic studies with missing data. Our goal was to estimate the association of maternal smoking behavior with spontaneous abortion while adjusting for numerous confounders. At the same time, we did not necessarily wish to evaluate the joint distribution among potentially unobserved covariates, which is seldom the subject of substantive scientific interest. The inverse probability weighting (IPW) approach preserves the semiparametric structure of the underlying model of substantive interest and clearly separates the model of substantive interest from the model used to account for the missing data. However, IPW often will not result in valid inference if the missing-data pattern is nonmonotone, even if the data are missing at random. We describe a recently proposed approach to modeling nonmonotone missing-data mechanisms under missingness at random to use in constructing the weights in IPW complete-case estimation, and we illustrate the approach using 3 data sets described in a companion article (Am J Epidemiol. 2018;187(3):568-575).

Empirical likelihood analysis of longitudinal data involving within-subject correlation

In this paper we use profile empirical likelihood to construct confidence regions for regression coefficients in partially linear model with longitudinal data. The main contribution is that the within-subject correlation is considered to improve estimation efficiency. We suppose a semi-parametric structure for the covariances of observation errors in each subject and employ both the first order and the second order moment conditions of the observation errors to construct the estimating equations. Although there are nonparametric estimators, the empirical log-likelihood ratio statistic still tends to a standard χ 2 variable in distribution after the nuisance parameters are profiled away. A data simulation is also conducted.

Estimation of medical costs by copula models with dynamic change of health status

This paper develops models aimed at more accurate estimation of the medical cost function based on the individual cost data. In our proposed models, the cost data are assumed to be dependent on the whole clinical evolution via Markov transition probabilities, and the accumulative rate of cost in a time period (sojourn) has a semiparametric structure. The medical costs are recurrent at different time points with different states under informative censoring, and the cost incurred in a sojourn at a state is correlated with that sojourn. A copula is used to model the relationship between a sojourn and its associated cost. The multivariate local likelihood method is employed to estimate model parameters and the asymptotic properties of the estimators are established as well. Our methods can be easily extended to model the total cost and to analyze the cost-effectiveness of the model. Simulations are performed to assess the proposed models and methodology, and comparisons with certain existing models are discussed.

Semiparametric hazard function estimation in meta-analysis for time to event data.

Meta-analyses have been widely used to combine information from survival data using estimated parameters in, for example, a Cox model. A number of approaches dealing with study level random effects have been developed. However, there are far fewer meta-analysis approaches for estimating survival or hazard functions. Typical approaches are based on the cumulative survival function using the generalized estimating equation. We propose an alternative approach following Efron's discrete logistic regression (Efron, 1988), but using generalized linear mixed models. We show that spline functions can be used in fitting the models to obtain smoothed estimates for hazard functions. The models also allow a semi-parametric structure to include factors such as random study effects and treatment groups. This approach models the hazard function based on which the survival function can be estimated too. We also propose a Bayesian bootstrap approach for statistical inference for both hazard and survival functions. This approach was applied to two meta-analysis data sets as examples to illustrate its use. Copyright © 2012 John Wiley & Sons, Ltd.

Hidden Regular Variation and Detection of Hidden Risks

Hidden regular variation requires regular variation on 𝔼 = [0, ∞] d \\ {(0, 0,…, 0)} and another regular variation on the sub-cone , where 𝕃 i is the ith axis. We extend this concept to sub-cones of 𝔼(2) as well. We suggest a procedure for detecting hidden regular variation, and when it exists, propose a method of estimating the limit measure exploiting its semi-parametric structure. We give an example where hidden regular variation yields improved estimates of probabilities of risk sets.

Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes

Abstract. Many time series in applied sciences obey a time‐varying spectral structure. In this article, we focus on locally stationary processes and develop tests of the hypothesis that the time‐varying spectral density has a semiparametric structure, including the interesting case of a time‐varying autoregressive moving‐average (tvARMA) model. The test introduced is based on a L2‐distance measure of a kernel smoothed version of the local periodogram rescaled by the time‐varying spectral density of the estimated semiparametric model. The asymptotic distribution of the test statistic under the null hypothesis is derived. As an interesting special case, we focus on the problem of testing for the presence of a tvAR model. A semiparametric bootstrap procedure to approximate more accurately the distribution of the test statistic under the null hypothesis is proposed. Some simulations illustrate the behaviour of our testing methodology in finite sample situations.

Semiparametric model for prediction of individual claim loss reserving

The estimation of loss reserves for incurred but not reported (IBNR) claims presents an important task for insurance companies to predict their liabilities. Conventional methods, such as ladder or separation methods based on aggregated or grouped claims of the so-called “run-off triangle”, have been illustrated to have some drawbacks. Recently, individual claim loss models have attracted a great deal of interest in actuarial literature, which can overcome the shortcomings of aggregated claim loss models. In this paper, we propose an alternative individual claim loss model, which has a semiparametric structure and can be used to fit flexibly the claim loss reserving. Local likelihood is employed to estimate the parametric and nonparametric components of the model, and their asymptotic properties are discussed. Then the prediction of the IBNR claim loss reserving is investigated. A simulation study is carried out to evaluate the performance of the proposed methods.

Social Experiments and Instrumental Variables with Duration Outcomes

This paper examines the empirical analysis of treatment effects on duration outcomes from data that contain instrumental variation. We focus on social experiments in which an intention to treat is randomized and compliance may be imperfect. We distinguish between cases where the treatment starts at the moment of randomization and cases where it starts at a later point in time. We derive exclusion restrictions under various informational and behavioral assumptions and we analyze identifiability under these restrictions. It turns out that randomization (and by implication, instrumental variation) by itself is often insufficient for inference on interesting effects, and needs to be augmented by a semi-parametric structure. We develop corresponding non- and semi-parametric tests and estimation methods.