【latex版】水贴

(This article was first published on Ripples, and kindly contributed to R-bloggers)
Triangles are my favorite shape, three points where two lines meet (Tessellate, Alt-J)

Inspired by recurrence plots and by the Gauss error function, I have done the following plots. The first one represents the recurrence plot of where distance between points is measured by Gauss error function:

Earlier this week a press release from the Linux Foundation formally unveiled The R Consortium: “a group of businesses organized under an open source governance and foundation model to provide support to the R community, the R Foundation and groups and individuals, using, maintaining and distributing R software”.  Mango Solutions were announced as founding silver members alongside the R Foundation; Microsoft and RStudio (Platinum); TIBCO Software Inc. (Gold); and Alteryx, Google, HP, Ketchum Trading and Oracle (Silver).  Clearly we think The R Consortium is idea.  But what does it mean for ordinary R users?

In this paper, we are concerned with two common and related problems for generalized varying-coefficient models, variable selection and constant coefficient identification. Starting with a specification of generalized varying-coefficient models assuming possible nonlinear interactions between the index variable and all other predictors, we propose a polynomial-spline based procedure that simultaneously eliminates irrelevant predictors and identifies predictors that do not interact with the index variable. Our approach is based on a double-penalization strategy where two penalty functions are used for these two related purposes respectively, in a single functional. In a “large p, small n” setting, we demonstrate the convergence rates of the estimator under suitable regularity assumptions. Based on its previous success on parametric models, we use the extended Bayesian information criterion (eBIC) to automatically choose the regularization parameters. Finally, post-penalization estimator is proposed to further reduce the bias of the resulting estimator. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed procedures and an application to a leukemia dataset is presented.

In this paper, we are concerned with two common and related problems for generalized varying-coefficient models, variable selection and constant coefficient identification.

Starting with a specification of generalized varying-coefficient models assuming possible nonlinear interactions between the index variable and all other predictors, we propose a polynomial-spline based procedure that simultaneously eliminates irrelevant predictors and identifies predictors that do not interact with the index variable.

Generalized linear models (GLM) provide an extension of linear models in dealing with different types of responses, including for example binary data and count data  [24]. However, such parametric models are not flexible enough to capture the true underlying relationships between covariates and responses. Of particular interests to us in this paper is the generalized varying-coefficient models (GVCM)  [13] and [3]. Let Y be a response variable and (X,T) is the associated covariates where T is one dimensional and X=(X1,…,Xp)T

The (conditional) mean of the response, μ=E[Y|X,T], takes the form

equation(1)
g(μ)=XTα(T),
Turn MathJax on

where α(T)=(α1(T),…,αp(T))T. The index variable T is usually some variable related to time or age in many applications whose interactions with other predictors are believed to be of importance. Meanwhile, we assume the conditional variance View the MathML source only depends on the conditional mean.

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Outlier detection covers the wide range of methods aiming at identifying observations that are considered unusual. Novelty detection, on the other hand, seeks observations among newly generated test data that are exceptional compared with previously observed training data. In many applications, the general existence of novelty is of more interest than identifying the individual novel observations. For instance, in high-throughput cancer treatment screening experiments, it is meaningful to test whether any new treatment effects are seen compared with existing compounds. Here, we present hypothesis tests for such global level novelty. The problem is approached through a set of very general assumptions, making it innovative in relation to the current literature. We introduce test statistics capable of detecting novelty. They operate on local neighborhoods and their null distribution is obtained by the permutation principle. We show that they are valid and able to find different types of novelty, e.g. location and scale alternatives. The performance of the methods is assessed with simulations and with applications to real data sets.

Sample size justification is an important consideration when planning a clinical trial, not only for the main trial but also for any preliminary pilot trial. When the outcome is a continuous variable, the sample size calculation requires an accurate estimate of the standard deviation of the outcome measure. A pilot trial can be used to get an estimate of the standard deviation, which could then be used to anticipate what may be observed in the main trial. However, an important consideration is that pilot trials often estimate the standard deviation parameter imprecisely. This paper looks at how we can choose an external pilot trial sample size in order to minimise the sample size of the overall clinical trial programme, that is, the pilot and the main trial together. We produce a method of calculating the optimal solution to the required pilot trial sample size when the standardised effect size for the main trial is known. However, as it may not be possible to know the standardised effect size to be used prior to the pilot trial, approximate rules are also presented. For a main trial designed with 90% power and two-sided 5% significance, we recommend pilot trial sample sizes per treatment arm of 75, 25, 15 and 10 for standardised effect sizes that are extra small (≤0.1), small (0.2), medium (0.5) or large (0.8), respectively.