Assessing additivity in nonparametric models —A kernel‐based method

In this article, we address the testing problem for additivity in nonparametric regression models. We develop a kernel‐based consistent test of a hypothesis of additivity in nonparametric regression, and establish its asymptotic distribution under a sequence of local alternatives. Compared to other existing kernel‐based tests, the proposed test is shown to effectively ameliorate the influence from estimation bias of the additive component of the nonparametric regression, and hence increase its efficiency. Most importantly, it avoids the tuning difficulties by using estimation‐based optimal criteria, while there is no direct tuning strategy for other existing kernel‐based testing methods. We discuss the usage of the new test and give numerical examples to demonstrate the practical performance of the test. The Canadian Journal of Statistics 39: 632–655; 2011. © 2011 Statistical Society of Canada     

SMOOTH TRANSITION AUTOREGRESSIVE MODELS — A SURVEY OF RECENT DEVELOPMENTS

This paper surveys recent developments related to the smooth transition autoregressive (STAR) time series model and several of its variants. We put emphasis on new methods for testing for STAR nonlinearity, model evaluation, and forecasting. Several useful extensions of the basic STAR model, which concern multiple regimes, time-varying non-linear properties, and models for vector time series, are also reviewed.     

MMCTest—A Safe Algorithm for Implementing Multiple Monte Carlo Tests

Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest , a sequential algorithm that gives, with arbitrarily high probability, the same classification as a specific multiple testing procedure applied to ideal p‐values. The method can be used with a class of multiple testing procedures that include the Benjamini and Hochberg false discovery rate procedure and the Bonferroni correction controlling the familywise error rate. One of the key features of the algorithm is that it stops sampling for all the hypotheses that can already be decided as being rejected or non‐rejected. MMCTest can be interrupted at any stage and then returns three sets of hypotheses: the rejected, the non‐rejected and the undecided hypotheses. A simulation study motivated by actual biological data shows that MMCTest is usable in practice and that, despite the additional guarantee, it can be computationally more efficient than other methods.     

Small sample properties of isotonic estimators — bias and mean squared error of linear combinations under normality

Bias and mean squared error for linear combinations of the isotonic regression estimators are computed. The case of sampling three distinct populations and the case of sampling seven or fewer populations having common mean are studied in detail. Numerical results are given, and comparisons between isotonic and unbiased estimation procedures are made.     

SAMPLE SURVEYS VERSUS EXPERIMENTS,CONTROLLED OBSERVATIONS,CENSUSES, REGISTERS,AND LOCAL STUDIES1 2

Can we find some common principle in the three comparisons? Lacking adequate time for a thorough exploration, let me suggest that representation is that common principle. I suggested (section 4) that judgment selection of spatial versus temporal extensions distinguish “longitudinal” local studies from “cross-section” population sampling. We had noted (section 3) that censuses are taken for detailed representation of the spatial dimension but they depend on judgmental selection of the temporal. Survey sampling lacks spatial detail but is spatially representative with randomization, and it can be made timely. Periodic samples can be designed that are representative of temporal extension. Furthermore, spatial and temporal detail can be obtained either through estimation or through cumulated samples [Purcell and Kish 1979, 1980; Kish 1979b, 1981, 1986 6.6]. Registers and administrative records can have good spatial and temporal representation, but representation may be lacking in population content, and surely in representation of variables. Representation of variables and of the relations between variables and over the population are the issues in conflict between surveys, experiments, and observations. This is a deep subject, and too deep to be explored again, as it was in section 2. A final point about limits for randomization to achieve representation through sampling: randomization for selecting samples of variables is beyond me generally, because I cannot conceive of frames for defined populations of variables. Yet we can find attempts at randomized selection of variables: in the selection of items for the consumer price index, also of items for tests of IQ or of achievements. Generally I believe that randomization is the way to achieve representation without complete coverage, and that it can be applied and practised in many dimensions.