A note on generalized wald's method Academic Article uri icon


MeSH Major

  • Antibodies, Monoclonal
  • Antineoplastic Agents
  • Protein Kinase Inhibitors
  • Receptor, Epidermal Growth Factor
  • Skin Neoplasms


  • Let {vn(θ)} be a sequence of statistics such that when θ =θ0, vn(θ0) {Mathematical expression}Np(0, Σ), where Σ is of rank p and θ εRd. Suppose that under θ =θ0, {Σn} is a sequence of consistent estimators of Σ. Wald (1943) shows that vnT(θ0)Σn-1vn(θ0) {Mathematical expression}x2(p). It often happens that vn(θ0) {Mathematical expression}Np(0, Σ) holds but Σ is singular. Moore (1977) states that under certain assumptions vnT(θ0)Σn-vn(θ0) {Mathematical expression}x2(k), where k = rank (Σ) and Σn- is a generalized inverse of Σn. However, Moore's result as stated is incorrect. It needs the additional assumption that rank (Σn) =k for n sufficiently large. In this article, we show that Moore's result (as corrected) holds under somewhat different, but easier to verify, assumptions. © 1990 Physica-Verlag Ges.m.b.H.

publication date

  • December 1990



  • Academic Article


Digital Object Identifier (DOI)

  • 10.1007/BF02613538

Additional Document Info

start page

  • 309

end page

  • 315


  • 37


  • 1