text: 62G05 Estimation
  62G09 Resampling methods
  62G10 Hypothesis testing
  62G20 Asymptotic properties
  62G86 Nonparametric inference and fuzziness
  62G99 None of the above, but in this section
  Displaying 1 – 20 of 75
  A note on orthogonal series regression function estimators
  Waldemar Popiński (1999)
  The problem of nonparametric estimation of the regression function f(x) = E(Y | X=x) using the orthonormal system of trigonometric functions or Legendre polynomials e k , k=0,1,2,..., is considered in the case where a sample of i.i.d. copies ( X i , Y i ) , i=1,...,n, of the random variable (X,Y) is available and the marginal distribution of X has density ϱ ∈ L 1 [a,b]. The constructed estimators are of the form f ^ n ( x ) = ∑ k = 0 N ( n ) c ^ k e k ( x ) , where the coefficients c ^ 0 , c ^ 1 , . . . , c ^ N are determined by minimizing the empirical risk n - 1 ∑ i = 1 n ( Y i - ∑ k = 0 N c k e k ( X i ) ) 2 . Sufficient conditions for...
  A note on the rate of convergence of local polynomial estimators in regression models
  Friedrich Liese, Ingo Steinke (2001)
  Local polynomials are used to construct estimators for the value m ( x 0 ) of the regression function m and the values of the derivatives D γ m ( x 0 ) in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established. The results...
  Adaptive hard-thresholding for linear inverse problems
  Paul Rochet (2013)
  A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....
  Aggregated estimators and empirical complexity for least square regression
  Jean-Yves Audibert (2004)
  An application of nonprarametric Cox regression model in reliability analysis: a case study
  Petr Volf (2004)
  The contribution deals with an application of the nonparametric version of Cox regression model to the analysis and modeling of the failure rate of technical devices. The objective is to recall the method of statistical analysis of such a model, to adapt it to the real–case study, and in such a way to demonstrate the flexibility of the Cox model. The goodness-of-fit of the model is tested, too, with the aid of the graphical test procedure based on generalized residuals.
  An ℓ1-oracle inequality for the Lasso in finite mixture gaussian regression models
  Caroline Meynet (2013)
  We consider a finite mixture of Gaussian regression models for high-dimensional heterogeneous data where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by an ℓ1-penalized maximum likelihood estimator. We shall provide an ℓ1-oracle inequality satisfied by this Lasso estimator with the Kullback–Leibler loss. In particular, we give a condition on the regularization parameter of the Lasso to obtain such an oracle inequality....
  Asymptotic distribution of robust k-nearest neighbour estimator for functional nonparametric models
  Mohammed Kadi Attouch, Tawfik Benchikh (2012)
  Asymptotic optimality of new adaptive test in regression model
  Tadeusz Inglot, Teresa Ledwina (2006)
  Asymptotically sufficient statistics in nonparametric regression experiments with correlated noise.
  Carter, Andrew V. (2009)
  Asymptotics of the regression quantile basic solution under misspecification
  Keith Knight (2008)
  We consider the asymptotic distribution of covariate values in the quantile regression basic solution under weak assumptions. A diagnostic procedure for assessing homogeneity of the conditional densities is also proposed.
  Beta-regression model for periodic data with a trend.
  Rydlewski, Jerzy P. (2007)
  Cécile Durot, Karelle Thiébot (2006)
  The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in...
  Convergence rates of orthogonal series regression estimators
  Waldemar Popiński (2000)
  General conditions for convergence rates of nonparametric orthogonal series estimators of the regression function f(x)=E(Y | X = x) are considered. The estimators are obtained by the least squares method on the basis of a random observation sample (Yi,Xi), i=1,...,n, where X i ∈ A ⊂ ℝ d have marginal distribution with density ϱ ∈ L 1 ( A ) and Var( Y | X = x) is bounded on A. Convergence rates of the errors E X ( f ( X ) - f ^ N ( X ) ) 2 and ∥ f - f ^ N ∥ ∞ for the estimator f ^ N ( x ) = ∑ k = 1 N c ^ k e k ( x ) , constructed using an orthonormal system e k , k=1,2,..., in L 2 ( A ) are obtained.
  Detecting atypical data in air pollution studies by using shorth intervals for regression
  Cécile Durot, Karelle Thiébot (2010)
  To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...
  Cécile Durot, Karelle Thiébot (2005)
  Victor Konev, Serguei Pergamenshchikov (2012)
  The paper considers the problem of robust estimating a periodic function in a continuous time regression model with the dependent disturbances given by a general square integrable semimartingale with an unknown distribution. An example of such a noise is a non-Gaussian Ornstein–Uhlenbeck process with jumps (see (J. R. Stat. Soc. Ser. B Stat. Methodol.63 (2001) 167–241), (Ann. Appl. Probab.18 (2008) 879–908)). An adaptive model selection procedure, based on the weighted least square estimates, is...