Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters
Higher-order asymptotic methods for nonlinear models with nuisance parameters are developed. We allow for both one-step estimators, in which the nuisance and parameters of interest are jointly estimated; and also two-step (or iterated) estimators, in which the nuisance parameters are first estimated...
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2025-01-01
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| author | Paul Rilstone |
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| author_sort | Paul Rilstone |
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| description | Higher-order asymptotic methods for nonlinear models with nuisance parameters are developed. We allow for both one-step estimators, in which the nuisance and parameters of interest are jointly estimated; and also two-step (or iterated) estimators, in which the nuisance parameters are first estimated. The properties of the former, although in principle simpler to conceptualize, are more difficult to establish explicitly. The iterated estimators allow for a variety of scenarios. The results indicate when second-order considerations should be taken into account when conducting inferences with two-step estimators. The results in the paper accomplish three objectives: (i) provide simpler methods for deriving higher-order moments when nuisance parameters are present; (ii) indicate more explicitly the sources of deviations of estimators’ sampling distributions from that given by standard first-order asymptotic theory; and, in turn, (iii) indicate in which situations the corrections (either analytically or by a resampling method such as bootstrap or jackknife) should be made when making inferences. We illustrate using several popular examples in econometrics. We also provide a numerical example which highlights how a simple analytical bias correction can improve inferences. |
| format | Article |
| id | doaj-art-5186d08194f04e3987d142e585e62114 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5186d08194f04e3987d142e585e621142025-01-24T13:39:39ZengMDPI AGMathematics2227-73902025-01-0113217910.3390/math13020179Higher-Order Expansions for Estimators in the Presence of Nuisance ParametersPaul Rilstone0Department of Economics, York University, Toronto, ON M3J 1P3, CanadaHigher-order asymptotic methods for nonlinear models with nuisance parameters are developed. We allow for both one-step estimators, in which the nuisance and parameters of interest are jointly estimated; and also two-step (or iterated) estimators, in which the nuisance parameters are first estimated. The properties of the former, although in principle simpler to conceptualize, are more difficult to establish explicitly. The iterated estimators allow for a variety of scenarios. The results indicate when second-order considerations should be taken into account when conducting inferences with two-step estimators. The results in the paper accomplish three objectives: (i) provide simpler methods for deriving higher-order moments when nuisance parameters are present; (ii) indicate more explicitly the sources of deviations of estimators’ sampling distributions from that given by standard first-order asymptotic theory; and, in turn, (iii) indicate in which situations the corrections (either analytically or by a resampling method such as bootstrap or jackknife) should be made when making inferences. We illustrate using several popular examples in econometrics. We also provide a numerical example which highlights how a simple analytical bias correction can improve inferences.https://www.mdpi.com/2227-7390/13/2/179stochastic expansionsapproximate momentsnuisance parameterstwo-step estimatorsinstrumental variables |
| spellingShingle | Paul Rilstone Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters Mathematics stochastic expansions approximate moments nuisance parameters two-step estimators instrumental variables |
| title | Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters |
| title_full | Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters |
| title_fullStr | Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters |
| title_full_unstemmed | Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters |
| title_short | Higher-Order Expansions for Estimators in the Presence of Nuisance Parameters |
| title_sort | higher order expansions for estimators in the presence of nuisance parameters |
| topic | stochastic expansions approximate moments nuisance parameters two-step estimators instrumental variables |
| url | https://www.mdpi.com/2227-7390/13/2/179 |
| work_keys_str_mv | AT paulrilstone higherorderexpansionsforestimatorsinthepresenceofnuisanceparameters |