Abstract Linear rank statistics in nonparametric factorial designs are asymptotically normal and, general, heteroscedastic. In a comprehensive simulation study, the asymptotic chi-squared law of corresponding quadratic forms is shown to be rather poor approximation finite-sample distribution. Motivated by this problem, we propose simple size approximations for distribution under heteroscedastic error structure. These based on an F with estimated degrees freedom that generalizes ideas Patnaik...

Canonical Moments. Orthogonal Polynomials. Continued Fractions and the Stieltjes Transform. Special Sequences of Moments Optimal DesignFirst Applications. Discrimination Model Robust Designs. Applications in Approximation Theory. Random Walks. The Circle Trigonometric Functions. Further Bibliography. Indexes.

Summary We introduce a new class of ‘standardized' optimality criteria which depend on covariances the least squares estimators and provide an alternative to commonly used in design theory. Besides nice statistical interpretation satisfy extremely useful invariance property allows easy calculation optimal designs many linearly transformed spaces.

Summary Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, non-parametric conditional estimates yield crossing curves (calculated for various p ∈ (0, 1)). We propose a new estimate of quantiles that avoids this problem. The method uses an initial distribution function first step solves problem inversion monotonization with respect to 1) simultaneously. It is demonstrated are asymptotically normally distributed...

We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in autocovariance function multivariate (second-order) piecewise stationary process, which also identifies components series where occur. MuBreD is based on comparison estimated spectral distribution different segments observed time consists three steps: it starts with consistent test, allows us prove existence at controlled Type I error. Second, estimates sets...

Summary The exact mean-squared error (MSE) of estimators the variance in nonparametric regression based on quadratic forms is investigated. In particular, two classes are compared: Hall, Kay and Titterington's optimal difference-based a class ordinary which generalize methods proposed by Rice Gasser, Sroka Jennen-Steinmetz. For small sample sizes MSE first estimator essentially increased magnitude integrated squared derivatives function. It shown that many situations more appropriate for...

A new method for monotone estimation of a regression function is proposed, which potentially attractive to users conventional smoothing methods. The main idea the approach construct density estimate from estimated values m̂ (i/N) ( i =1,…,N ) and use these `data' calculation an inverse function. final then obtained by numerical inversion. Compared currently available techniques does not require constrained optimization. We prove asymptotic normality compare properties with unconstrained...

In this paper we study the problem of testing functional form a given regression model. A consistent test is proposed which based on difference least squares variance estimator in assumed model and nonparametric estimator. The corresponding statistic can be shown to asymptotically normal under null hypothesis fixed alternatives with different rates convergence both cases. This provides simple asymptotic test, where results also used for calculation type II error procedure at any particular...

We propose a new test for the comparison of two regression curves that is based on difference marked empirical processes residuals. The large sample behavior corresponding statistic studied to provide full nonparametric curves. In contrast most procedures suggested in literature, procedure applicable case different design points and heteroscedasticity. Moreover, it demonstrated proposed detects continuous alternatives converging null at rate $N^{-1/2}$ that, all other available processes,...

Abstract Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper, performance of nonuniform experimental locate more points neighborhood boundary design space, is investigated. These designs obtained by quantile transformation one-dimensional projections commonly space-filling designs. This motivated logarithmic potential theory, yields arc-sine measure as an equilibrium distribution. The methodology illustrated for maximin...

AbstractUnderstanding and properly characterizing the dose–response relationship is a fundamental step in investigation of new compound, be it herbicide or fertilizer, molecular entity, an environmental toxin, industrial chemical. In this article we investigate problem deriving efficient designs for estimation target doses context clinical dose finding. We propose methods to determine appropriate number actual levels administered patients, as well their relative sample size allocations. More...

Abstract. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept dependence order (RDO). In addition, we define new non‐parametric measure and study its properties. Besides being monotone in RDOs, takes on extreme values precisely at independence almost sure functional dependence, respectively. A consistent estimator is constructed asymptotic properties are investigated. Finally, finite...

In this paper, we present an alternative method for the spectral analysis of a univariate, strictly stationary time series $\{Y_t\}_{t\in \mathbb {Z}}$. We define "new" spectrum as Fourier transform differences between copulas pairs $(Y_t,Y_{t-k})$ and independence copula. This object is called copula density kernel allows to separate marginal serial aspects series. show that closely related concept quantile regression. Like regression, which provides much more information about conditional...

Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with pairs $(X_t,X_{t-k})$ process $(X_t)_{t\in\mathbb{Z}}$, account for important dynamic features, such as changes conditional shape (skewness, kurtosis), time-irreversibility, or dependence extremes that traditional counterparts cannot capture. Despite proposals estimation strategies, only...

–The plausibility of the "parallel trends assumption" in Difference-in-Differences estimation is usually assessed by a test null hypothesis that difference between average outcomes both groups constant over time before treatment. However, failure to reject does not imply absence differences groups. We provide equivalence tests allow researchers find evidence favor parallel assumption and thus increase credibility their treatment effect estimates. While we motivate our standard two-way fixed...

Most of the popular dependence measures for two random variables X and Y (such as Pearson's Spearman's correlation, Kendall's τ Gini's γ) vanish whenever are independent. However, neither does a vanishing measure necessarily imply independence, nor equal to 1 that one variable is measurable function other. Yet, both properties natural convincing measure. In this paper, we present general approach transforming given into new which exactly characterizes independence well functional dependence....

ABSTRACT We consider the problem of detecting gradual changes in sequence mean functions from a not necessarily stationary functional time series. Our approach is based on maximum deviation (calculated over given interval) between benchmark function and at different points. speak change size , if this quantity exceeds threshold . For example, could represent an average yearly temperature curves pre‐industrial time, we are interested question whether afterwards deviate by more than degrees...

In the problem of testing equalityof k regression curves from independent samples, we discuss three methods using nonparametric estimators function. The first test is based on a linear combination for integrated variance function in individual samples and combined sample. second approach transfers classical one-way analysis to situation comparing non-parametric curves, while third compares differences between estimates functions by means an $L^2$-distance.We prove asymptotic normality all...

Summary The importance of being able to detect heteroscedasticity in regression is widely recognized because efficient inference for the function requires that taken into account. In this paper a simple consistent test proposed nonparametric set-up. based on an estimator best L 2-approximation variance by constant. Under mild assumptions asymptotic normality corresponding statistic established even under arbitrary fixed alternatives. Confidence intervals are obtained measure...

In the class of polynomial regression models up to degree $n$ we determine design on $\lbrack -1, 1\rbrack$ that maximizes a product $n + 1$ determinants information matrices weighted with prior $\beta$, where $l$-th matrix corresponds model $l$, for $l = 0, 1, \cdots, n$. The designs are calculated using canonical moments. We identify special priors $\beta(z)$ depending one real parameter $z$ so analogous results obtained as in classical $D$- and $D_1$-optimal problems. interior support...

Abstract A key objective in the clinical development of a medicinal drug is determination an adequate dose level and, more broadly, characterization its response relationship. If set too high, safety and tolerability problems are likely to result, while selecting low makes it difficult establish efficacy confirmatory phase, possibly leading failed program. Hence, finding studies critical importance need be planned carefully. In this paper, we focus on practical considerations for...

We propose a new class of estimators for Pickands dependence function which is based on the concept minimum distance estimation. An explicit integral representation $A^*(t)$, minimizes weighted $L^2$-distance between logarithm copula $C(y^{1-t},y^t)$ and functions form $A(t)\log(y)$ derived. If unknown an extreme-value copula, $A^*(t)$ coincides with function. Moreover, even if this not case, always satisfies boundary conditions The are obtained by replacing its empirical counterpart weak...

In this article we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate L2-distance between spectral density process and its best approximation by process. An explicit expression minimal distance derived, which depends only integrals square. These can be estimated directly without estimating density, as consequence, estimation measure does not require specification smoothing bandwidth. We show weak...