General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

Čı́žek, Pavel

doi:10.1017/s0266466608080596

Cited by 42 publications

(16 citation statements)

References 45 publications

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“…Also, it is interesting to analyze the breakdown point properties for other implied probabilities, such as the exponential tilting weights obtained from the information projection by the Boltzmann-Shannon entropy. 9 We also considered trimming more than two observations but the point estimatesβGMT M remain quite close to −0.1716.…”

Section: Resultsmentioning

confidence: 99%

Robustness of Bootstrap in Instrumental Variable Regression

Camponovo

Otsu

2014

Econometric Reviews

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This paper studies robustness of bootstrap inference methods for instrumental variable (IV) regression models. We consider test statistics for parameter hypotheses based on the IV estimator and generalized method of trimmed moments (GMTM) estimator introduced by Čížek (2009), and compare the pairs and implied probability bootstrap approximations for these statistics by applying the finite sample breakdown point theory. In particular, we study limiting behaviors of the bootstrap quantiles when the values of outliers diverge to infinity but the sample size is held fixed. The outliers are defined as anomalous observations that can arbitrarily change the value of the statistic of interest. We analyze both just-and over-identified cases and discuss implications of the breakdown point analysis to the size and power properties of bootstrap tests. We conclude that the implied probability bootstrap test using the statistic based on the GMTM estimator shows desirable robustness properties. Simulation studies endorse this conclusion. An empirical example based on Romer's (1993) study on the effect of openness of countries to inflation rates is presented. Several extensions including the analysis for the residual bootstrap are provided.

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Section: Resultsmentioning

confidence: 99%

Robustness of Bootstrap in Instrumental Variable Regression

Camponovo

Otsu

2014

Econometric Reviews

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“…This does not include only regression under heteroscedasticity, but also instrumental variable estimation proposed for LWS by [15], nonlinear regression using results of [2], or maximum likelihood estimation [3] as long as the response variable is continuous.…”

Section: Resultsmentioning

confidence: 99%

Efficient robust estimation of time-series regression models

Čı́žek

2008

Appl Math

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Abstract. The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.

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“…We exploit theory developed in Cizek [16], Lemma 2.1, page 29. By distribution continuity and linearity of the volatility process {σ…”

Section: Appendix: Proofs Of Main Theoremsmentioning

confidence: 99%

“…In fact, under distribution continuity arguments developed in Cizek J.B. Hill [16], Lemma 2.1, page 29, apply for almost sure twice differentiability of the otherwise non-differentiableQ n (θ). In particular, we have almost surely…”

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confidence: 99%

Robust Estimation and Inference for Heavy Tailed GARCH

Hill

2013

SSRN Journal

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We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming QML criterion equations according to error extremes. The second imbeds negligibly transformed errors into QML score equations for a Method of Moments estimator. In this case, we exploit a sub-class of redescending transforms that includes tail-trimming and functions popular in the robust estimation literature, and we re-center the transformed errors to minimize small sample bias. The negligible transforms allow both identification of the true parameter and asymptotic normality. We present a consistent estimator of the covariance matrix that permits classic inference without knowledge of the rate of convergence. A simulation study shows both of our estimators trump existing ones for sharpness and approximate normality including QML, Log-LAD, and two types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the tail-trimmed QML estimator to financial data.

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General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

Cited by 42 publications

References 45 publications

Robustness of Bootstrap in Instrumental Variable Regression

Robustness of Bootstrap in Instrumental Variable Regression

Efficient robust estimation of time-series regression models

Robust Estimation and Inference for Heavy Tailed GARCH

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