Oracle Inequalities for Convex Loss Functions with Nonlinear Targets

This article considers penalized empirical loss minimization of convex loss functions with unknown target functions. Using the elastic net penalty, of which the Least Absolute Shrinkage and Selection Operator (Lasso) is a special case, we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear, this inequality also provides an upper bound of the estimation error of the estimated parameter vector. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically of the same order as that of the oracle. If the target is linear, we give sufficient conditions for consistency of the estimated parameter vector. We briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions covered by our framework.     

Model selection consistency of U-statistics with convex loss and weighted lasso penalty

In the paper we consider minimisation of U-statistics with the weighted Lasso penalty and investigate their asymptotic properties in model selection and estimation. We prove that the use of appropriate weights in the penalty leads to the procedure that behaves like the oracle that knows the true model in advance, i.e. it is model selection consistent and estimates nonzero parameters with the standard rate. For the unweighted Lasso penalty, we obtain sufficient and necessary conditions for model selection consistency of estimators. The obtained results strongly based on the convexity of the loss function that is the main assumption of the paper. Our theorems can be applied to the ranking problem as well as generalised regression models. Thus, using U-statistics we can study more complex models (better describing real problems) than usually investigated linear or generalised linear models.     

Adaptive phase I/II clinical trials for drug combination assessment in oncology using the outcomes of each cycle

Many new anticancer agents can be combined with existing drugs, as combining a number of drugs may be expected to have a better therapeutic effect than monotherapy owing to synergistic effects. Furthermore, to drive drug development and to reduce the associated cost, there has been a growing tendency to combine these as phase I/II trials. With respect to phase I/II oncology trials for the assessment of dose combinations, in the existing methodologies in which efficacy based on tumor response and safety based on toxicity are modeled as binary outcomes, it is not possible to enroll and treat the next cohort of patients unless the best overall response has been determined in the current cohort. Thus, the trial duration might be potentially extended to an unacceptable degree. In this study, we proposed a method that randomizes the next cohort of patients in the phase II part to the dose combination based on the estimated response rate using all the available observed data upon determination of the overall response in the current cohort. We compared the proposed method to the existing method using simulation studies. These demonstrated that the percentage of optimal dose combinations selected in the proposed method is not less than that in the existing method and that the trial duration in the proposed method is shortened compared to that in the existing method. The proposed method meets both ethical and financial requirements, and we believe it has the potential to contribute to expedite drug development.     

Confidence interval estimation of the difference between paired AUCs based on combined biomarkers

In many diagnostic studies, multiple diagnostic tests are performed on each subject or multiple disease markers are available. Commonly, the information should be combined to improve the diagnostic accuracy. We consider the problem of comparing the discriminatory abilities between two groups of biomarkers. Specifically, this article focuses on confidence interval estimation of the difference between paired AUCs based on optimally combined markers under the assumption of multivariate normality. Simulation studies demonstrate that the proposed generalized variable approach provides confidence intervals with satisfying coverage probabilities at finite sample sizes. The proposed method can also easily provide P-values for hypothesis testing. Application to analysis of a subset of data from a study on coronary heart disease illustrates the utility of the method in practice.     

Jensen's Inequality for General Location Parameter

A wide class of location parameters is shown to satisfy Jensen's inequality. When the expectation EX exists and l is a convex function, Jensen's inequality states that El(x) ≥ l(EX). It is shown that for μ, a properly defined location parameter, μ(l(x)) μ l(μ(x)).     

Time Series Models for Count or Qualitative Observations

Time series sometimes consist of count data in which the number of events occurring in a given time interval is recorded. Such data are necessarily nonnegative integers, and an assumption of a Poisson or negative binomial distribution is often appropriate. This article sets ups a model in which the level of the process generating the observations changes over time. A recursion analogous to the Kalman filter is used to construct the likelihood function and to make predictions of future observations. Qualitative variables, based on a binomial or multinomial distribution, may be handled in a similar way. The model for count data may be extended to include explanatory variables. This enables nonstochastic slope and seasonal components to be included in the model, as well as permitting intervention analysis. The techniques are illustrated with a number of applications, and an attempt is made to develop a model-selection strategy along the lines of that used for Gaussian structural time series models. The applications include an analysis of the results of international football matches played between England and Scotland and an assessment of the effect of the British seat-belt law on the drivers of light-goods vehicles.     

Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

Rank test statistics for umbrella alternatives

This paper proposes an optimal rank test procedure for testing an umbrella alternative when the peak of the umbrella is known. It is referred to as maximin efficient linear rank test. Also when the peak of the umbrella is unknown, a test procedure is proposed and its performance is discussed.     

论计划生育“三结合”模式的科学性

计划生育“三结合”由吉林省率先提出近十年,并已被国家充分肯定。十年来的实践已证实了计划生育“三结合”的正确与可行,尚缺少理论上的深入研究,经在国家计生委立项的“计划生育三结合之路研究”的软课题中找到了计划生育三结合提出的理论依据,进一步论证了计划生育三结合的科学性。     

Optimal experimental design criterion for discriminating semiparametric models

This paper studies the optimal experimental design problem to discriminate two regression models. Recently, López-Fidalgo et al. [2007. An optimal experimental design criterion for discriminating between non-normal models. J. Roy. Statist. Soc. B 69, 231–242] extended the conventional T-optimality criterion by Atkinson and Fedorov [1975a. The designs of experiments for discriminating between two rival models. Biometrika 62, 57–70; 1975b. Optimal design: experiments for discriminating between several models. Biometrika 62, 289–303] to deal with non-normal parametric regression models, and proposed a new optimal experimental design criterion based on the Kullback–Leibler information divergence. In this paper, we extend their parametric optimality criterion to a semiparametric setup, where we only need to specify some moment conditions for the null or alternative regression model. Our criteria, called the semiparametric Kullback–Leibler optimality criteria, can be implemented by applying a convex duality result of partially finite convex programming. The proposed method is illustrated by a simple numerical example.