Date/heure
Date(s) - 19 septembre 2016

Catégories Pas de Catégories

$The\; talk\; deals\; with\; estimating\; unknown\; parameters\; \$a,b\backslash in\backslash mathbbR\$\; in\; the\; simple\; Errors-in-Variables\; (EiV)\; linear\; model\; \$Y\_i=a+bX\_i+\backslash epsilon\_n\backslash xi\_i\$\; ;\; \$\; Z\_i=X\_i+\backslash sigma\_n\backslash zeta\_i\$,\; where\; \$i=1,\backslash ldots,n\$,\; \$\backslash xi\_i,,\; \backslash zeta\_i\$\; are\; i.i.d.\; standard\; Gaussian\; random\; variables,\; \$X\_i\backslash in\backslash mathbbR\$\; are\; unknown\; nuisance\; variables,\; and\; \$\backslash epsilon\_n,\backslash sigma\_n\$\; are\; noise\; levels\; which\; are\; assumed\; to\; be\; known.It\; is\; well\; known\; that\; the\; standard\; maximum\; likelihood\; estimates\; of\; \$a,,\; b\$\; haven’t\; bounded\; moments.\; In\; order\; to\; improve\; these\; estimates,\; we\; study\; the\; EiV\; model\; in\; the\; so-called\; Large\; Noise\; Regime\; assuming\; that\; \$n\backslash rightarrow\; \backslash infty\$,\; but\; \$\backslash epsilon\_n^2=\backslash sqrtn\backslash epsilon\_\backslash circ^2\$,\; \$\backslash sigma\_n^2=\backslash sqrtn\backslash sigma\_\backslash circ^2\$\; with\; \$\backslash epsilon\_\backslash circ^2,\backslash sigma\_\backslash circ^2>0\$.\; Under\; these\; assumptions,\; the\; minimax\; approach\; to\; estimating\; \$a,b\$\; is\; developed.\; In\; particular,\; it\; is\; shown\; that\; the\; minimax\; estimate\; of\; \$b\$\; is\; a\; solution\; to\; a\; convex\; optimization\; problem\; and\; a\; fast\; algorithm\; for\; computing\; this\; estimate\; is\; proposed.[$