On the role played by the fixed bandwidth in the Bickel-Rosenblatt goodness-of-fit test.

• Autores: Carlos Tenreiro
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 29, Nº. 2, 2005, págs. 201-216
• Idioma: inglés
• Títulos paralelos:
  • Sobre el papel del ancho de banda fijo en el test de bondad de ajuste de Bickel-Rosenblatt.
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• Resumen

  • HolaFor the Bickel-Rosenblatt goodness-of-fit test with fixed bandwidth studied by Fan (1998) we derive its Bahadur exact slopes in a neighbourhood of a simple hypothesis f = f0 and we use them to get a better understanding on the role played by the smoothing parameter in the detection of departures from the null hypothesis. When f0 is a univariate normal distribution and we take for kernel the standard normal density function, we compute these slopes for a set of Edgeworth alternatives which give us a description of the test properties in terms of the bandwidth h. A simulation study is presented which indicates that finite sample properties are in good accordance with the theoretical properties based on Bahadur local efficiency. Comparisons with the quadratic classical EDF tests lead us to recommend a test based on a combination of bandwidths in alternative to Anderson-Darling or Cram¿er-von Mises tests.

    MSC: 62G10, 62G20 Keywords: goodness-of-fit test, kernel density estimator, Bahadur efficiency HolaPer al contrast de bondat d¿ajust de Bickel-Rosenblatt amb amplada de banda fixa, estudiat per Fan (1998), derivem la seva pendent exacta de Bahadur en un entorn d¿una hip`otesi simple f = f0 i la utilitzem per obtenir un coneixement millor del paper del par`ametre suavitzador en la detecci¿o de desviacions de la hip`otesi nul·la. Quan f0 ¿es una distribuci¿o normal univariant i agafem com a nucli la funci¿o de densitat de la normal est`andard, calculem aquestes pendents per a un conjunt d¿alternatives de Edgeworth les quals ens donen una descripci¿o de les propietats del contrast en termes de l¿amplada de banda, h. Es presenta un estudi de simulaci¿o que indica que les propietats de les mostres finites estan d¿acord amb les propietats te`oriques basades en l¿efici`encia local de Bahadur. Comparacions amb els contrastos quadr`atics EDF cl`assics ens porten a recomanar un contrast basat en una combinaci¿o d¿amplades de banda com alternativa als contrastos de Anderson-Darling o Cram¿er-Von Mises.

    Paraules clau: contrastos de bondat d¿ajust, estimadors de densitats amb nuclis, efici`encia de Bahadur

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