On estimation of linear transformation models with nested case–control sampling

Nested case–control (NCC) sampling is widely used in large epidemiological cohort studies for its cost effectiveness, but its data analysis primarily relies on the Cox proportional hazards model. In this paper, we consider a family of linear transformation models for analyzing NCC data and propose an inverse selection probability weighted estimating equation method for inference. Consistency and asymptotic normality of our estimators for regression coefficients are established. We show that the asymptotic variance has a closed analytic form and can be easily estimated. Numerical studies are conducted to support the theory and an application to the Wilms’ Tumor Study is also given to illustrate the methodology.     

A two-stage estimation in the Clayton–Oakes model with marginal linear transformation models for multivariate failure time data

This paper considers the analysis of multivariate survival data where the marginal distributions are specified by semiparametric transformation models, a general class including the Cox model and the proportional odds model as special cases. First, consideration is given to the situation where the joint distribution of all failure times within the same cluster is specified by the Clayton–Oakes model (Clayton, Biometrika 65:141–151, l978; Oakes, J R Stat Soc B 44:412–422, 1982). A two-stage estimation procedure is adopted by first estimating the marginal parameters under the independence working assumption, and then the association parameter is estimated from the maximization of the full likelihood function with the estimators of the marginal parameters plugged in. The asymptotic properties of all estimators in the semiparametric model are derived. For the second situation, the third and higher order dependency structures are left unspecified, and interest focuses on the pairwise correlation between any two failure times. Thus, the pairwise association estimate can be obtained in the second stage by maximizing the pairwise likelihood function. Large sample properties for the pairwise association are also derived. Simulation studies show that the proposed approach is appropriate for practical use. To illustrate, a subset of the data from the Diabetic Retinopathy Study is used.     

Dynamic semiparametric factor models in risk neutral density estimation

Dynamic semiparametric factor models (DSFM) simultaneously smooth in space and are parametric in time, approximating complex dynamic structures by time invariant basis functions and low dimensional time series. In contrast to traditional dimension reduction techniques, DSFM allows the access of the dynamics embedded in high dimensional data through the lower dimensional time series. In this paper, we study the time behavior of risk assessments from investors facing random financial payoffs. We use DSFM to estimate risk neutral densities from a dataset of option prices on the German stock index DAX. The dynamics and term structure of risk neutral densities are investigated by Vector Autoregressive (VAR) methods applied on the estimated lower dimensional time series.     

Reliability estimation in stress–strength models: an MCMC approach

In this paper, we consider the estimation of the stress–strength parameter R=P(Y<X) when X and Y are independent and both are modified Weibull distributions with the common two shape parameters but different scale parameters. The Markov Chain Monte Carlo sampling method is used for posterior inference of the reliability of the stress–strength model. The maximum-likelihood estimator of R and its asymptotic distribution are obtained. Based on the asymptotic distribution, the confidence interval of R can be obtained using the delta method. We also propose a bootstrap confidence interval of R. The Bayesian estimators with balanced loss function, using informative and non-informative priors, are derived. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulations.     

Stein-type estimation in logistic regression models based on minimum ϕ-divergence estimators

In this paper we present a study of Stein-type estimators for the unknown parameters in logistic regression models when it is suspected that the parameters may be restricted to a subspace of the parameter space. The Stein-type estimators studied are based on the minimum phi-divergence estimator instead on the maximum likelihood estimator as well as on phi-divergence test statistics.     

Identification of fractional differencing autoregressive models †

This paper proposes an identification method to fractional differencing autoregressive models, and this method gives a consistent estimator for fractional differencing order and efficient estimates for parameters in fractional differencing autoregressive models.     

A monte carlo study of collinearity in linear simultaneous equation models ∗

Although the collinearity issue has been studied in previous simulation studies with a simultaneous system of equations, alternative estimators to circumvent this problem have received little attention. Monte Carlo techniques are used to examine the performance of several estimators under a squared error loss criterion. In particular, this study considers the Vinod–Ullah ridge-type estimators at the first and/or second stage of 2SLS. Ridge regression in the second stage only of 2SLS but not the first stage only, seems to be a practical alternative to 2SLS, especially in situations of strong collinearity. The OLS estimator and the ordinary ridge regression estimator also yield favorable results in situations of moderate to strong collinearity.     

Estimation and testing in generalized partial linear models—A comparative study

A particular semiparametric model of interest is the generalized partial linear model (GPLM) which extends the generalized linear model (GLM) by a nonparametric component.The paper reviews different estimation procedures based on kernel methods as well as test procedures on the correct specification of this model (vs. a parametric generalized linear model). Simulations and an application to a data set on East–West German migration illustrate similarities and dissimilarities of the estimators and test statistics.     

Markov-switching BILINEAR − GARCH models: Structure and estimation

Markov-switching (MS) models are becoming increasingly popular as efficient tools of modeling various phenomena in different disciplines, in particular for non Gaussian time series. In this articlept", we propose a broad class of Markov-switching BILINEAR–GARCH processes (MS ? BLGARCH hereafter) obtained by adding to a MS ? GARCH model one or more interaction components between the observed series and its volatility process. This parameterization offers remarkably rich dynamics and complex behavior for modeling and forecasting financial time-series data which exhibit structural changes. In these models, the parameters of conditional variance are allowed to vary according to some latent time-homogeneous Markov chain with finite state space or “regimes.” The main aim of this new model is to capture asymmetric and hence purported to be able to capture leverage effect characterized by the negativity of the correlation between returns shocks and subsequent shocks in volatility patterns in different regimes. So, first, some basic structural properties of this new model including sufficient conditions ensuring the existence of stationary, causal, ergodic solutions, and moments properties are given. Second, since the second-order structure provides a useful information to identify an appropriate time-series model, we derive the expression of the covariance function of for MS ? BLGARCH and for its powers. As a consequence, we find that the second (resp. higher)-order structure is similar to some linear processes, and hence MS ? BLGARCH (resp. its powers) admit an ARMA representation. This finding allows us for parameter estimation via GMM procedure proved by a Monte Carlo study and applied to foreign exchange rate of the Algerian Dinar against the single European currency.     

Ranking and estimation of related means in two—way models—a Bayesian approach

A hierarchical Bayesian approach to ranking and selection as well as estimation of related means in two—way models is considered. Using the method of Monte Carlo simulation with importance sampling, we are able to carry out efficiently the three or four dimensional integrations as needed. An example is included to illustrate the methodology.     

Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

Joint mean–covariance model in generalized partially linear varying coefficient models for longitudinal data

In longitudinal data analysis, efficient estimation of regression coefficients requires a correct specification of certain covariance structure, and efficient estimation of covariance matrix requires a correct specification of mean regression model. In this article, we propose a general semiparametric model for the mean and the covariance simultaneously using the modified Cholesky decomposition. A regression spline-based approach within the framework of generalized estimating equations is proposed to estimate the parameters in the mean and the covariance. Under regularity conditions, asymptotic properties of the resulting estimators are established. Extensive simulation is conducted to investigate the performance of the proposed estimator and in the end a real data set is analysed using the proposed approach.     

A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists of coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption concerning the PPZ. It can be easily adapted to many versions of EM.     

Bayesian estimation and stochastic model specification search for dynamic survival models

Dynamic survival models are a useful extension of the popular Cox model as the effects of explanatory variables are allowed to change over time. In this paper a new auxiliary mixture sampler for Bayesian estimation of the model parameters is introduced. This sampler forms the basis of a model space MCMC method for stochastic model specification search in dynamic survival models, which involves selection of covariates to include in the model as well as specification of effects as time-varying or constant. The method is applied to two well-known data sets from the literature.     

Bayesian covariance matrix estimation using a mixture of decomposable graphical models

We present a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs in more efficiently estimating the covariance matrix. The prior requires knowing the number of decomposable graphs for each graph size and we give a simulation method for estimating these counts. We also present a Markov chain Monte Carlo method for estimating the posterior distribution of the covariance matrix that is much more efficient than current methods. Both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.     

Wavelets and estimation of long memory in nonstationary models: Does anything beat the exact local whittle estimator?

In this article, we analyze the performance of five estimation methods for the long memory parameter d. The goal of our article is to construct a wavelet estimate for the fractional differencing parameter in nonstationary long memory processes that dominate the well-known estimate of Shimotsu and Phillips (2005) Shimotsu, K., Phillips, P. (2005). Exact local whittle estimation of fractional integration. Annals of statistics 20:87–127. [Google Scholar]. The simulation results show that the wavelet estimation method of Lee (2005) Lee, J. (2005). Estimating memory parameter in the US inflation rate. Economics Letters 87:207–210. [Google Scholar] with several tapering techniques performs better under most cases in nonstationary long memory. The comparison is based on the empirical root mean squared error of each estimate.     

Adaptive quasi-maximum likelihood estimation of GARCH models with Student’s t likelihood

ABSTRACT

This paper proposes an adaptive quasi-maximum likelihood estimation (QMLE) when forecasting the volatility of financial data with the generalized autoregressive conditional heteroscedasticity (GARCH) model. When the distribution of volatility data is unspecified or heavy-tailed, we worked out adaptive QMLE based on data by using the scale parameter η_f to identify the discrepancy between wrongly specified innovation density and the true innovation density. With only a few assumptions, this adaptive approach is consistent and asymptotically normal. Moreover, it gains better efficiency under the condition that innovation error is heavy-tailed. Finally, simulation studies and an application show its advantage.     

A new local estimation method for single index models for longitudinal data

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They are very useful for longitudinal data analysis. In this paper, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonparametric parts will be established. Monte Carlo simulation studies show excellent finite sample performance. Furthermore, we illustrate our methods with a real data example.