More flexible sequential and non-sequential designs in long-term clinical trial

In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.     

Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method

The stochastic volatility model has no closed form for its likelihood and hence the maximum likelihood estimation method is difficult to implement. However, it can be shown that the model has a known characteristic function. As a consequence, the model is estimable via the empirical characteristic function. In this paper, the characteristic function of the model is derived and the estimation procedure is discussed. An application is considered for daily returns of Australian/New Zealand dollar exchange rate. Model checking suggests that the stochastic volatility model together with the empirical characteristic function estimates fit the data well.     

A stochastic approximation algorithm for maximum-likelihood estimation with incomplete data

We propose a new stochastic approximation (SA) algorithm for maximum-likelihood estimation (MLE) in the incomplete-data setting. This algorithm is most useful for problems when the EM algorithm is not possible due to an intractable E-step or M-step. Compared to other algorithm that have been proposed for intractable EM problems, such as the MCEM algorithm of Wei and Tanner (1990), our proposed algorithm appears more generally applicable and efficient. The approach we adopt is inspired by the Robbins-Monro (1951) stochastic approximation procedure, and we show that the proposed algorithm can be used to solve some of the long-standing problems in computing an MLE with incomplete data. We prove that in general O(n) simulation steps are required in computing the MLE with the SA algorithm and O(n log n) simulation steps are required in computing the MLE using the MCEM and/or the MCNR algorithm, where n is the sample size of the observations. Examples include computing the MLE in the nonlinear error-in-variable model and nonlinear regression model with random effects.     

Nonlinear programming solutions to the nonstationary markov model

A nonstationary Markov process model with embedded explanatory variables offers a means to account for underlying causal factors while retaining unrestrictive assumptions and the predictive ability of a stochastic framework. We find that a direct search algorithm requiring minimal user preparation is a feasible computational procedure for estimating such a model. We compare this method with several others using factorially designed Monte Carlo simulations and find evidence that a small state space and a long time series lead to better algorithmic performance.     

A stochastic variant of the EM algorithm to fit mixed (discrete and continuous) longitudinal data with nonignorable missingness

Abstract

In longitudinal studies data are collected on the same set of units for more than one occasion. In medical studies it is very common to have mixed Poisson and continuous longitudinal data. In such studies, for different reasons, some intended measurements might not be available resulting in a missing data setting. When the probability of missingness is related to the missing values, the missingness mechanism is termed nonrandom. The stochastic expectation-maximization (SEM) algorithm and the parametric fractional imputation (PFI) method are developed to handle nonrandom missingness in mixed discrete and continuous longitudinal data assuming different covariance structures for the continuous outcome. The proposed techniques are evaluated using simulation studies. Also, the proposed techniques are applied to the interstitial cystitis data base (ICDB) data.     

Nonparametric regression for threshold data

Consider a detector which records the times at which the endogenous variable of a nonparametric regression model exceeds a certain threshold. If the error distribution is known, the regression function can still be identified from these threshold data. The author constructs estimators for the regression function that are transformations of kernel estimators. She determines the bandwidth that minimizes the asymptotic mean average squared error. Her investigation was motivated by recent work on stochastic resonance in neuroscience and signal detection theory, where it was observed that detection of a subthreshold signal is enhanced by the addition of noise. The author compares her model with several others that have been proposed in the recent past.     

Scalable statistical inference for averaged implicit stochastic gradient descent

Stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates in applications involving large‐scale data or streaming data. As an alternative version, averaged implicit SGD (AI‐SGD) has been shown to be more stable and more efficient. Although the asymptotic properties of AI‐SGD have been well established, statistical inferences based on it such as interval estimation remain unexplored. The bootstrap method is not computationally feasible because it requires to repeatedly resample from the entire data set. In addition, the plug‐in method is not applicable when there is no explicit covariance matrix formula. In this paper, we propose a scalable statistical inference procedure, which can be used for conducting inferences based on the AI‐SGD estimator. The proposed procedure updates the AI‐SGD estimate as well as many randomly perturbed AI‐SGD estimates, upon the arrival of each observation. We derive some large‐sample theoretical properties of the proposed procedure and examine its performance via simulation studies.     

Bandwidth selector for nonparametric recursive density estimation for spatial data defined by stochastic approximation method

Abstract

In this article we propose an automatic selection of the bandwidth of the recursive kernel density estimators for spatial data defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the MWISE (Mean Weighted Integrated Squared Error), the recursive estimator will be quite similar to the nonrecursive one in terms of estimation error and much better in terms of computational costs. In addition, we obtain the central limit theorem for the nonparametric recursive density estimator under some mild conditions.     

空间误差自相关随机前沿模型及其估计

将空间计量经济学的思想引入随机前沿分析，构建了基于横截面数据的空间误差自相关随机前沿模型，推导出模型的似然函数以求得参数估计，并给出了各生产单元技术效率的估计。     

On nonlinear random effects models for repeated measurements

Linear random effects models for longitudinal data discussed by Laird and Ware (1982), Jennrich and Schluchter (1986), Lange and Laird (1989), and others are extended in a straight forward manner to nonlinear random effects models. This results in a simple computational approach which accommodates patterned covariance matrices and data insufficient for fitting each subject separately. The technique is demonstrated with an interesting medical data set, and a short, simple SAS PROC IML program based on the EM algorithm is presented.     

Peter Schmidt: Econometrician and consummate professional

Peter Schmidt has been one of its best-known and most respected econometricians in the profession for four decades. He has brought his talents to many scholarly outlets and societies, and has played a foundational and constructive role in the development of the field of econometrics. Peter Schmidt has also served and led the development of Econometric Reviews since its inception in 1982. His judgment has always been fair, informed, clear, decisive, and constructive. Respect for ideas and scholarship of others, young and old, is second nature to him. This is the best of traits, and Peter serves as an uncommon example to us all. The seventeen articles that make up this Econometric Reviews Special Issue in Honor of Peter Schmidt represent the work of fifty of the very best econometricians in our profession. They honor Professor Schmidt's lifelong accomplishments by providing fundamental research work that reflects many of the broad research themes that have distinguished his long and productive career. These include time series econometrics, panel data econometrics, and stochastic frontier production analysis.     

Some applications of nonlinear and non-Gaussian state–space modelling by means of hidden Markov models

Nonlinear and non-Gaussian state–space models (SSMs) are fitted to different types of time series. The applications include homogeneous and seasonal time series, in particular earthquake counts, polio counts, rainfall occurrence data, glacial varve data and daily returns on a share. The considered SSMs comprise Poisson, Bernoulli, gamma and Student-t distributions at the observation level. Parameter estimations for the SSMs are carried out using a likelihood approximation that is obtained after discretization of the state space. The approximation can be made arbitrarily accurate, and the approximated likelihood is precisely that of a finite-state hidden Markov model (HMM). The proposed method enables us to apply standard HMM techniques. It is easy to implement and can be extended to all kinds of SSMs in a straightforward manner.     

Cross-validation approximation in functional linear regression

Cross-validation has been widely used in the context of statistical linear models and multivariate data analysis. Recently, technological advancements give possibility of collecting new types of data that are in the form of curves. Statistical procedures for analysing these data, which are of infinite dimension, have been provided by functional data analysis. In functional linear regression, using statistical smoothing, estimation of slope and intercept parameters is generally based on functional principal components analysis (FPCA), that allows for finite-dimensional analysis of the problem. The estimators of the slope and intercept parameters in this context, proposed by Hall and Hosseini-Nasab [On properties of functional principal components analysis, J. R. Stat. Soc. Ser. B: Stat. Methodol. 68 (2006), pp. 109–126], are based on FPCA, and depend on a smoothing parameter that can be chosen by cross-validation. The cross-validation criterion, given there, is time-consuming and hard to compute. In this work, we approximate this cross-validation criterion by such another criterion so that we can turn to a multivariate data analysis tool in some sense. Then, we evaluate its performance numerically. We also treat a real dataset, consisting of two variables; temperature and the amount of precipitation, and estimate the regression coefficients for the former variable in a model predicting the latter one.     

Two‐Sample Test Against One‐Sided Alternatives

Abstract. This paper proposes, implements and investigates a new non‐parametric two‐sample test for detecting stochastic dominance. We pose the question of detecting the stochastic dominance in a non‐standard way. This is motivated by existing evidence showing that standard formulations and pertaining procedures may lead to serious errors in inference. The procedure that we introduce matches testing and model selection. More precisely, we reparametrize the testing problem in terms of Fourier coefficients of well‐known comparison densities. Next, the estimated Fourier coefficients are used to form a kind of signed smooth rank statistic. In such a setting, the number of Fourier coefficients incorporated into the statistic is a smoothing parameter. We determine this parameter via some flexible selection rule. We establish the asymptotic properties of the new test under null and alternative hypotheses. The finite sample performance of the new solution is demonstrated through Monte Carlo studies and an application to a set of survival times.     

The analysis of transition times in multistate stochastic processes using proportional hazard regression models

Extensions to Cox's proportional hazards regression model (Cox, 1972) for the analysis of survival data are considered for a more general multistate framework. This framework allows several transient disease states between initial entry state and death as well as incorporating possible competing causes of death. Methods for parameter and function estimation within this extension are presented and applied to the analysis of data from the Stanford Heart Transplantation Program (Crowley and Hu,1977).     

Error analysis of stochastic flight trajectory prediction models

This paper focuses on the analysis of errors between a flight trajectory prediction model and flight data. A novel stochastic prediction flight model is compared with the popular fly-by and fly-over turn models. The propagated error is measured using either spatial coordinates or angles. Depending on the case, the distribution of error is estimated and confidence bounds for the linear and directional mean are provided for all three stochastic flight models.     

Nonparametric Estimation of Bounded Survival Functions with Censored Observations

Stochastic ordering of survival functions is a useful concept in many areas of statistics, especially in nonparametric and order restricted inferences. In this paper we introduce an algorithm to compute maximum likelihood estimates of survival functions where both upper and lower bounds are given. The algorithm allows censored survival data. In a simulation study, we found that the proposed estimates are more efficient than the unrestricted Kaplan-Meier product limit estimates both with and without censored observations.     

Sparse Bayesian variable selection in multinomial probit regression model with application to high-dimensional data classification

Here we consider a multinomial probit regression model where the number of variables substantially exceeds the sample size and only a subset of the available variables is associated with the response. Thus selecting a small number of relevant variables for classification has received a great deal of attention. Generally when the number of variables is substantial, sparsity-enforcing priors for the regression coefficients are called for on grounds of predictive generalization and computational ease. In this paper, we propose a sparse Bayesian variable selection method in multinomial probit regression model for multi-class classification. The performance of our proposed method is demonstrated with one simulated data and three well-known gene expression profiling data: breast cancer data, leukemia data, and small round blue-cell tumors. The results show that compared with other methods, our method is able to select the relevant variables and can obtain competitive classification accuracy with a small subset of relevant genes.     

A nonlinear mixed-effects model for multivariate longitudinal data with partially observed outcomes with application to HIV disease dynamics

The measurable multiple bio-markers for a disease are used as indicators for studying the response variable of interest in order to monitor and model disease progression. However, it is common for subjects to drop out of the studies prematurely resulting in unbalanced data and hence complicating the inferences involving such data. In this paper we consider a case where data are unbalanced among subjects and also within a subject because for some reason only a subset of the multiple outcomes of the response variable are observed at any one occasion. We propose a nonlinear mixed-effects model for the multivariate response variable data and derive a joint likelihood function that takes into account the partial dropout of the outcomes of the response variable. We further show how the methodology can be used in the estimation of the parameters that characterise HIV disease dynamics. An approximation technique of the parameters is also given and illustrated using a routine observational HIV dataset.