TY - JOUR
T1 - Higher order asymptotic theory for normalizing transformations of maximum likelihood estimators
AU - Taniguchi, Masanobu
AU - Puri, Madan L.
PY - 1995/9
Y1 - 1995/9
N2 - Suppose that Xn=(X1,... Xn) is a collection of m-dimensional random vectors Xi forming a stochastic process with a parameter θ{symbol}. Let {Mathematical expression} be the MLE of θ{symbol}. We assume that a transformation A( {Mathematical expression}) of {Mathematical expression} has the k-thorder Edgeworth expansion (k=2,3). If A extinguishes the terms in the Edgeworth expansion up to k-th-order (k≥2), then we say that A is the k-th-order normalizing transformation. In this paper, we elucidate the k-th-order asymptotics of the normalizing transformations. Some conditions for A to be the k-th-order normalizing transformation will be given. Our results are very general, and can be applied to the i.i.d. case, multivariate analysis and time series analysis. Finally, we also study the k-th-order asymptotics of a modified signed log likelihood ratio in terms of the Edgeworth approximation.
AB - Suppose that Xn=(X1,... Xn) is a collection of m-dimensional random vectors Xi forming a stochastic process with a parameter θ{symbol}. Let {Mathematical expression} be the MLE of θ{symbol}. We assume that a transformation A( {Mathematical expression}) of {Mathematical expression} has the k-thorder Edgeworth expansion (k=2,3). If A extinguishes the terms in the Edgeworth expansion up to k-th-order (k≥2), then we say that A is the k-th-order normalizing transformation. In this paper, we elucidate the k-th-order asymptotics of the normalizing transformations. Some conditions for A to be the k-th-order normalizing transformation will be given. Our results are very general, and can be applied to the i.i.d. case, multivariate analysis and time series analysis. Finally, we also study the k-th-order asymptotics of a modified signed log likelihood ratio in terms of the Edgeworth approximation.
KW - Edgeworth expansion
KW - MLE
KW - Normalizing transformation
KW - higher-order asymptotic theory
KW - multivariate analysis
KW - observed information
KW - saddlepoint expansion
KW - signed log likelihood ratio
KW - time series analysis
KW - variance stabilizing transformation
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U2 - 10.1007/BF00773402
DO - 10.1007/BF00773402
M3 - Article
AN - SCOPUS:0042105991
VL - 47
SP - 581
EP - 600
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
SN - 0020-3157
IS - 3
ER -