Semiparametric estimation for inverse density weighted expectations when responses are missing at random

In this article, we consider semiparametric estimation in a partially linear single-index panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross-section size and the time series length tend to infinity, we not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. The asymptotically normal distributions of the proposed estimators are similar to those obtained in the random effects case. In addition, we study several partially linear single-index dynamic panel data models. The methods and results are augmented by simulation studies and illustrated by application to two real data examples. This article has online supplementary materials.

In regression analysis, a parametric model is often assumed from prior information or a pilot study. If the model assumption is valid, the parametric method is useful. However, the efficiency of the estimator is not guaranteed when a poor model is selected. This article aims to check whether the model assumption is correct or not and to estimate the regression function. To achieve this, we propose a hybrid technique of parametrically guided method and group lasso. First, the parametric model is prepared. The parametrically guided estimator is constructed by summing the parametric estimator and nonparametric estimator. For the estimation of the nonparametric component, we use B‐splines and the group lasso method. If the nonparametric component is estimated to be a zero function, the parametrically guided estimator is reduced to the parametric estimator. Then, we can decide that the parametric model assumption is correct. If the nonparametric estimator is not zero, the semiparametric estimator is obtained. Thus, the proposed method discovers the model structure and estimates the regression function simultaneously. We investigate the asymptotic properties of the proposed estimator. A simulation study and real data example are presented. Copyright © 2016 John Wiley & Sons, Ltd.

Auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects. This article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data. We propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation-based inference procedure by treating both the error structure and random effects as nuisance parameters. This method is robust against misspecification of either error structure or random-effects distribution and allows for dependence between random effects and covariates. We show that the resulting estimators are consistent and asymptotically normal. Extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method. We illustrate the method with two real data examples.

Gene-gene interaction plays an important role in the etiology of complex diseases, which may exist without a genetic main effect. Most current statistical approaches, however, focus on assessing an interaction effect in the presence of the gene's main effects. It would be very helpful to develop methods that can detect not only the gene's main effects but also gene-gene interaction effects regardless of the existence of the gene's main effects while adjusting for confounding factors. In addition, when a disease variant is rare or when the sample size is quite limited, the statistical asymptotic properties are not applicable; therefore, approaches based on a reasonable and applicable computational framework would be practical and frequently applied. In this study, we have developed an extended support vector machine (SVM) method and an SVM-based pedigree-based generalized multifactor dimensionality reduction (PGMDR) method to study interactions in the presence or absence of main effects of genes with an adjustment for covariates using limited samples of families. A new test statistic is proposed for classifying the affected and the unaffected in the SVM-based PGMDR approach to improve performance in detecting gene-gene interactions. Simulation studies under various scenarios have been performed to compare the performances of the proposed and the original methods. The proposed and original approaches have been applied to a real data example for illustration and comparison. Both the simulation and real data studies show that the proposed SVM and SVM-based PGMDR methods have great prediction accuracies, consistencies, and power in detecting gene-gene interactions.

Extension of SO-PLS to multi-way arrays: SO-N-PLS

In this paper we investigate a broader semiparametric two‐sample density ratio model based on two groups of right‐censored data. A semiparametric maximum likelihood estimator for the unknown finite and infinite dimensional parameters of the model is proposed and obtained by an EM algorithm. By using empirical process theory, we establish the uniform consistency and asymptotic normality of the proposed estimator. We moreover employ a Kolmogorov–Smirnov type test statistic to evaluate the model validity and a likelihood ratio test statistic to examine the treatment effects between the two groups. Simulation studies are conducted to assess the finite sample performance of the proposed estimator and to compare it with its alternatives. Finally a real data example is analyzed to illustrate its application. The Canadian Journal of Statistics 44: 58–81; 2016 © 2015 Statistical Society of Canada

ABSTRACTThe paper presents 3D diffraction imaging based on the spectral decomposition of a different combination of selective or partial images. These images are obtained by the pre‐stack asymmetric migration procedure, which is weighted data summation. Spectral decomposition is done in the Fourier domain with respect to spatial dip and azimuth angles. Numerical examples with the application of different workflows for the synthetic and real data examples demonstrate detailed reliable reconstruction of the fractured zones and reliable reconstruction of fracture orientation on synthetic and real 3D data examples.

ABSTRACTA mixture model is proposed to analyze a bivariate interval censored data with cure rates. There exist two types of association related with bivariate failure times and bivariate cure rates, respectively. A correlation coefficient is adopted for the association of bivariate cure rates and a copula function is applied for bivariate survival times. The conditional expectation of unknown quantities attributable to interval censored data and cure rates are calculated in the E-step in ES (Expectation-Solving algorithm) and the marginal estimates and the association measures are estimated in the S-step through a two-stage procedure. A simulation study is performed to evaluate the suggested method and a real data from HIV patients is analyzed as a real data example.

The issue of multicollinearity has long been acknowledged in statistical modelling; however, it is often untreated in the most of published papers. Indeed, the use of methods for multicollinearity correction is still scarce. One important reason is that despite many proposed methods, little is known about their strength or performance. We compare the statistical properties and performance of four main techniques to correct multicollinearity, i.e., Ridge Regression (R-R), Principal Components Regression (PC-R), Partial Least Squares Regression (PLS-R), and Lasso Regression (L-R), in both a simulation study and two real data examples used for modelling volumes of heart and Thyroid as a function of clinical and anthropometric parameters. We find that when the statistical approaches were used to address different levels of collinearity, we observed that R-R, PC-R and PLS-R appeared to have a somewhat similar behavior, with a slight advantage for the PLS-R. Indeed, in all implemented cases, the PLS-R always provided the smallest value of root mean square error (RMSE). When the degree of collinearity was moderate, low or very low, the L-R method had also somewhat similar performance to other methods. Furthermore, correction methods allowed us to provide stable and trustworthy parameter estimates for predictors in the modelling of heart and Thyroid volumes. Therefore, this work will contribute to highlighting performances of methods used only for situations ranging from low to very high multicollinearity.

A novel distribution‐free k‐sample test of differences in location shifts based on the analysis of kernel density functional estimation is introduced and studied. The proposed test parallels one‐way analysis of variance and the Kruskal–Wallis (KW) test aiming at testing locations of unknown distributions. In contrast to the rank (score)‐transformed non‐parametric approach, such as the KW test, the proposed F‐test uses the measurement responses along with well‐known kernel density estimation (KDE) to estimate the locations and construct the test statistic. A practical optimal bandwidth selection procedure is also provided. Our simulation studies and real data example indicate that the proposed analysis of kernel density functional estimate (ANDFE) test is superior to existing competitors for fat‐tailed or heavy‐tailed distributions when the k groups differ mainly in location rather than shape, especially with unbalanced data. ANDFE is also highly recommended when it is unclear whether test groups differ mainly in shape or location. The Canadian Journal of Statistics 48: 167–186; 2020 © 2019 Statistical Society of Canada

We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.

The weighted least square based estimators with censoring indicators missing at random

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that remove an estimated seismic wavelet from seismic data. We assume that seismic trace subtle discontinuities are associated with acoustic impedance contrasts and can be characterized by wavelet transform spectral ridges, also called modulus maxima lines (WTMML), allowing us to improve seismic resolution by using the wavelet transform. Specifically, we apply the complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMMLs. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform from the computed WTMMLs with a broader band complex Morlet wavelet than that used in the forward CWT. Because the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result looks like a deconvolution method. Considering this high-resolution seismic representation as a reflectivity approximation, we estimate the relative acoustic impedance (RAI) by filtering and trace integrating it. Conventional deconvolution algorithms assume the seismic wavelet to be stochastic, while the CWT is implicitly time varying such that it can be applied to both depth and time-domain data. Using synthetic and real seismic data, we evaluated the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes. In the real data examples, time and in-depth RAI results, show good correlation with real P-impedance band-pass data computed using more rigorous commercial inversion software packages that require well logs and low-frequency velocity model information.

Chapter 12 - Specific Methods

In this paper we propose a longitudinal credit rating model which accounts for the serial correlation in the ratings. We achieve this by imposing an autoregressive structure of order one on the errors of a multivariate ordinal regression model. The longitudinal structure of the model improves significantly both the goodness-of-fit and predictive performance compared to static models. By modeling the joint distribution of the ratings over time, the framework allows us to obtain predictions conditional on the past rating history of a firm, which clearly out-perform the unconditional predictions both in- and out-of-sample. This shows the importance of incorporating past rating information in the prediction. Another upside lies in the framework’s ability to deal with missing rating observations. A real data example is provided by using a sample of US publicly traded corporates rated by S&P for the years 1985–2016. The determinants of corporate credit ratings are pre-selected using the ordinal version of the least absolute shrinkage and selection operator (LASSO). Additionally, as a model extension we allow the regression coefficients of the selected variables to vary over time in the longitudinal model. This allows us to gain a better understanding of the drivers and evolution of the rating behavior over the sample period. Finally, based on the longitudinal model with LASSO selected variables, we find evidence that S&P exhibits procyclical aspects in their rating behavior. • A credit rating model accounting for the serial correlation in the ratings. • A variable selection exercise is performed using ordinal LASSO. • Predictions conditional on the past rating history of a firm. • Longitudinal structure improves goodness-of-fit and predictive performance. • Real data example of US corporates rated by S&P for the years 1985–2016.