Estimation in Linear Models

  • Wolfgang Karl Härdle
  • Vladimir Spokoiny
  • Vladimir Panov
  • Weining Wang
Part of the Springer Texts in Statistics book series (STS)

Exercise 4.1.

A company decides to compare the effect of three marketing strategies
  1. 1.

    Advertisement in local newspaper,

  2. 2.

    Presence of sales assistant,

  3. 3.

    Special presentation in shop windows,

on the sales of their portfolio in 30 shops. The 30 shops were divided into 3 groups of 10 shops. The sales using the strategies 1, 2, and 3 were y1= (9,11,10,12,7,11,12,10,11,13), y2= (10,15,11,15,15,13,7,15,13,10), and y3= (18,14,17,9,14,17,16,14,17,15), respectively. Define xias the index of the shop, i.e., xi= i,i = 1,2,…,30. Using this notation, the null hypothesis corresponds to a constant regression line, \(\mathbb{E}Y =\mu\)


Null Hypothesis Marketing Strategy Induction Step Spectral Norm Adaptivity Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Csiszár, I., & Tusnády, G. (1984). Information geometry and alternating minimization procedures. Statistics & Decisions, Supplement Issue, 1, 205–237.Google Scholar
  2. Härdle, W., & Simar, L. (2011). Applied multivariate statistical analysis (3rd ed.). Berlin: Springer.Google Scholar
  3. Spokoiny, V., & Dickhaus, T. (2014). Basics of modern parametric statistics. Berlin: Springer.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Wolfgang Karl Härdle
    • 1
  • Vladimir Spokoiny
    • 2
  • Vladimir Panov
    • 3
  • Weining Wang
    • 1
  1. 1.L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. and Econ.Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Weirstrass Institute for Applied Analysis and Stochastics (WIAS)BerlinGermany
  3. 3.Universität Duisburg-EssenEssenGermany

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