Top PDF Tests in Censored Models when the Structural Parameters Are Not Identified

Tests in Censored Models when the Structural Parameters Are Not Identified

Tests in Censored Models when the Structural Parameters Are Not Identified

structural parameters. In the unrestricted model, the auxiliary parameters are well-identified inde- pendent of the presence of weak instruments. The auxiliary parameters can be estimated either by the two-stage conditional maximum likelihood method as proposed by Smith and Blundell (1986), or any other consistent estimators such as the symmetrically censored least square (Powell (1986)) and the winsorized mean estimator (Lee (1995)). Simple linear restrictions on the unrestricted parameters are enough to obtain the minimum distance objective function for the structural pa- rameter. Robust tests are derived from the minimum distance objective function following the same lines as Kleibergen (2005). The minimum distance approach allows the extension of the weak instrument robust tests to other classes of limited dependent variable models such as endogenous probit and endogenous ordered probit (see Magnusson (2006)).
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Identification-robust inference for endogeneity parameters in linear structural models

Identification-robust inference for endogeneity parameters in linear structural models

Dufour, J.-M., 1979. Methods for Specification Errors Analysis with Macroeconomic Applications PhD thesis University of Chicago. 257 + XIV pages. Thesis committee: Arnold Zellner (Chair- man), Robert E. Lucas and Nicholas Kiefer. Dufour, J.-M., 1987. Linear Wald methods for inference on covariances and weak exogeneity tests in structural equations. In: I. B. MacNeill , G. J. Umphrey, eds, Advances in the Statistical Sciences: Festschrift in Honour of Professor V.M. Joshi’s 70th Birthday. Volume III, Time Series and Econometric Modelling. D. Reidel, Dordrecht, The Netherlands, pp. 317–338. Dufour, J.-M., 1990. Exact tests and confidence sets in linear regressions with autocorrelated errors.
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Identification robust inference for endogeneity parameters in linear structural models

Identification robust inference for endogeneity parameters in linear structural models

We provide a generalization of the Anderson-Rubin (AR) procedure for inference on parameters which represent the dependence between possibly endogenous explanatory variables and distur- bances in a linear structural equation (endogeneity parameters). We focus on second-order depen- dence and stress the distinction between regression and covariance endogeneity parameters. Such parameters have intrinsic interest (because they measure the effect of “common factors” which induce simultaneity) and play a central role in selecting an estimation method (because they deter- mine “simultaneity biases” associated with least-squares methods). We observe that endogeneity parameters may not identifiable and we give the relevant identification conditions. We develop identification-robust finite-sample tests for joint hypotheses involving structural and regression en- dogeneity parameters, as well as marginal hypotheses on regression endogeneity parameters. For Gaussian errors, we provide tests and confidence sets based on standard-type Fisher critical val- ues. For a wide class of parametric non-Gaussian errors (possibly heavy-tailed), we also show that exact Monte Carlo procedures can be applied using the statistics considered. As a special case, this result also holds for usual AR-type tests on structural coefficients. For covariance endogeneity parameters, we supply an asymptotic (identification-robust) distributional theory. Tests for partial exogeneity hypotheses (for individual potentially endogenous explanatory variables) are covered as instances of the class of proposed procedures. The proposed procedures are applied to two empiri- cal examples: the relation between trade and economic growth, and the widely studied problem of returns to education.
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Identification-robust inference for endogeneity parameters in

linear structural models

Identification-robust inference for endogeneity parameters in linear structural models

// ABSTRACT We provide a generalization of the Anderson-Rubin (AR) procedure for inference on parameters which represent the dependence between possibly endogenous explanatory variables and distur- bances in a linear structural equation (endogeneity parameters). We focus on second-order depen- dence and stress the distinction between regression and covariance endogeneity parameters. Such parameters have intrinsic interest (because they measure the effect of “common factors” which induce simultaneity) and play a central role in selecting an estimation method (because they deter- mine “simultaneity biases” associated with least-squares methods). We observe that endogeneity parameters may not identifiable and we give the relevant identification conditions. We develop identification-robust finite-sample tests for joint hypotheses involving structural and regression en- dogeneity parameters, as well as marginal hypotheses on regression endogeneity parameters. For Gaussian errors, we provide tests and confidence sets based on standard-type Fisher critical val- ues. For a wide class of parametric non-Gaussian errors (possibly heavy-tailed), we also show that exact Monte Carlo procedures can be applied using the statistics considered. As a special case, this result also holds for usual AR-type tests on structural coefficients. For covariance endogeneity parameters, we supply an asymptotic (identification-robust) distributional theory. Tests for partial exogeneity hypotheses (for individual potentially endogenous explanatory variables) are covered as instances of the class of proposed procedures. The proposed procedures are applied to two empiri- cal examples: the relation between trade and economic growth, and the widely studied problem of returns to education.
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Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures

Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures

At first sight, the only practically important difference between AIC and CAIC is that the factor 2 in the penalty term of Equation 19 is replaced by the factor (1 + logN ), which implies that the weight of the number of estimates now depends on the sample size and that parsimonious models are rewarded more generously. These obvious features may however distract from a fundamental problem inherent in CAIC. The promise that the "true" model will be selected as N → ∞ rests on the assumption that the true model is contained in the set of competing models. As Burnham and Anderson (1998) pointed out, such an assumption would be rather unrealistic in the biological and social sciences. First, if "an investigator knew that a true model existed and that it was in the set of candidate models, would not he know which one it was?" (p. 69). Second, even if the true model could be identified for a certain finite number of cases, this model would hardly remain the true model as N → ∞, because in the biological and social sci- ences, increasing the number of cases usually increases the number of relevant variables, too.
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U-statistic Type Tests for Structural Breaks in Linear Regression Models

U-statistic Type Tests for Structural Breaks in Linear Regression Models

Another interesting feature of these tests is their explicit dependence on the third moment of the residuals of linear regression models. This characteristic idiosyncratic to our test implies significant improvements in terms of power when the distribution of the residuals shows some asymmetries about zero. The last contribution to the literature on change point detection and structural break tests is to show that simple modifications of the family of U-statistic type processes introduced in this paper given by suitable weight functions have more power against changes in the parameters in the linear regression model that occur early as well as later on in the sample. This is an important feature of this class of statistics not satisfied by CUSUM type tests which are unable to detect a change in parameters produced early/later on in the sample. It is also worth highlighting the good performance of both simultaneous and joint tests in small samples.
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Bootstrapping Structural Change Tests

Bootstrapping Structural Change Tests

Linear models with endogenous regressors are commonly employed in time series econometric analysis. 1 In many cases, the parameters of these models are assumed constant throughout the sample. However, given the span of many economic time series data sets, this assumption may be questionable and a more appropriate specification may involve parameters that change value during the sample period. Such parameter changes could reflect legislative, institutional or technological changes, shifts in governmental and economic policy, political conflicts, or could be due to large macroeconomic shocks such as the oil shocks experienced over the past decades and the productivity slowdown. It is therefore important to test for parameter – or structural – change. Various tests for structural change have been proposed with one difference between them being in the type of structural change against which the tests are designed to have
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The finite-sample properties of bootstrap tests in multiple structural change models

The finite-sample properties of bootstrap tests in multiple structural change models

The motivation for this paper lies in the fact that the asymptotic distribution theory of many of the break tests presented in the literature may not always be particularly useful in small sample situations. This is a practical difficulty because model selection problems such as the one of selecting the number of breaks in a time series is a small sample problem. The solution discussed in this paper is the one in which the asymptotic distribution is replaced by an empirical one, and the latter is obtained by a parametric or nonparametric bootstrap. We first show that the bootstrap methods allow yielding distributions independent of the minimal number of observations in each regime and the maximal possible number of breaks, unlike the asymptotic distributions which depend on these parameters as discussed by Bai and Perron (1998). We second show the accuracy of the bootstrap procedures and their ability to reduce or eliminate the error in rejection probability (size distortion) committed by the asymptotic tests.
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Confidence sets for some partially identified parameters

Confidence sets for some partially identified parameters

The simplicity of the CIs of IM and Stoye (2007) makes them appealing, but their dependence on the speci…c structure of interval identi…ed parameters and the asymptotic normality of estimators of the lower and upper bounds on the true parameter makes them hard to generalize to parameters de…ned by general moment equalities/inequalities. In a series of papers, Andrews and Guggen- berger (2005a, b, c, 2007, AG hereafter) developed several general methods of constructing uniform con…dence sets (CS) in non-regular models based on the duality between CSs and hypotheses tests. CHT …rst applied this idea to constructing CSs for partially identi…ed parameters in a very gen- eral set-up and referred to it as the criterion function approach. In AG (2007), they proposed a simple plug-in asymptotic CS (PA-CS) for parameters de…ned by moment equalities/inequalities and showed that the PA-CS may be asymptotically conservative when there are restrictions on moment inequalities such that if one moment inequality holds as an equality, then another moment inequality can not be satis…ed as an equality. A notable example of this is the interval identi…ed parameter case unless the true parameter is point identi…ed. In contrast, the CIs of IM and Stoye (2007) take into account such restriction and are not asymptotically conservative.
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Set identified linear models

Set identified linear models

Consequently the estimated variance of the support function is large and points are less likely to be rejected when there are outside the estimated set. 6 Conclusion We develop in this paper a class of models defined by incomplete linear moment conditions and we provide examples of how this set up can be applied to economic data. In the most prominent one, the dependent variable in a linear model is censored by intervals. We present simple ways that lead to a sharp characterization of the identified sets. We generalize previous results about estimating such sets and we construct asymptotic tests for null hypotheses concerning the true value of the parameter of interest. These procedures are easy to implement and we can invert them and derive confidence regions for the parameter of interest. We also generalize the sim- ple setting of linear prediction using explanatory variables to the case in which supernumerary moment conditions are available. Specifically, we provide an extension to the usual Sargan test that can be performed using the asymptotic tests that we develop. Asymptotic properties of these generalized estimates are derived.
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Generalized Likelihood Ratio Tests for Varying Coefficient Models with Censored Data

Generalized Likelihood Ratio Tests for Varying Coefficient Models with Censored Data

In an effort to derive a generally applicable testing approach, Fan et al (2001) proposed the generalized likelihood ratio (GLR) statistic for nonparametric models. Their motivation was as follows. The maximum likelihood ratio test statistic in general may not exist in nonparametric and semiparametric settings. Even if it does, it is hard to find and may not be optimal in the simplest nonparametric regression setting. These drawbacks can be avoided when the maximum likelihood estimator is replaced by other reasonable nonparametric estimators, resulting in a class of statistics called the GLR statistic. The GLR test is intuitively appealing. Fan et al (2001) showed that for a variety of models and a number of nonparametric versus nonparametric and parametric versus nonparametric testing problems, the null distribution of the GLR test statistic follows an asymptotically  2 distribution, independent of nuisance parameters. This property is called the Wilks phenome- non and facilitates the application of the GLR statistic. The critical value can be determined either by asymptotic distributions or by simulations. In this paper, we extend the generalized likelihood ratio test to the varying- coefficient models with censored data.
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Bayes Interval Estimation on the Parameters of the Weibull Distribution for Complete and Censored Tests

Bayes Interval Estimation on the Parameters of the Weibull Distribution for Complete and Censored Tests

2. By constructing the confidence interval, we have condition the uncertainty based on the observations. As a result, the stages involved in constructing a confidence interval are the same as those of the Bayesian estimation. This will lead to find a Bayesian based approach to construct a CI. First, a prior distribution should be identified to model the uncertainty, and then information from a given data is used to design the CI. The unknown parameter is treated as a random variable and the observed data are utilized to obtain the posterior distribution. To conduct the above two-step process, let f X ( ) x ; θ be the joint pdf
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Statistical models for censored point processes with cure fractions

Statistical models for censored point processes with cure fractions

When data consists of repetitions of the same event through time, there are essentially two possible time scales that may be of interest: the total time, measured from the start of the follow-up, to the occurrence of all the events, or the gap times, that is, the durations between two successive events. Analysis of the MESS data focusses on the analysis of the times from randomisation to first seizure, and the times from first to second seizure, with the overall follow- up time subject to right censoring. When dealing with gap time distributions of recurrent events in this censoring scenario, all the gap times, except the first one, may be subject to dependent censoring (Lin et al. 1999). We consider data where the duration of the time to first seizure will have an effect on the potential censoring value of the second duration. A long time to first seizure post-randomisation implies a short observation period for the time from first to second seizure post-randomisation, and vice versa.
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On Marginal Effects in Semiparametric Censored Regression Models

On Marginal Effects in Semiparametric Censored Regression Models

U is allowed to be ∞. This has the censored regression model with fixed one–sided censoring at 0 (equation (1)) as a special case, and in a panel data setting it does not matter whether one thinks of ε as including a “fixed” effect. In the model (6), we will be interested in lim

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When is a wh-in-situ question identified in Persian?

When is a wh-in-situ question identified in Persian?

Previous literature demonstrated the influential role of prediction in processing speech [Brazil, 1981. The place of intonation in a discourse model. In C. Malcolm & M. Montgomery (Eds.), Studies in discourse analysis (pp. 146 – 157). London: Routledge & Kegan Paul; Grosjean, 1983. How long is the sentence? Prediction and prosody in the on-line processing of language. Linguistics, 21, 501 – 529, 1996a. Using prosody to predict the end of sentences in English and French: Normal and brain damaged subjects. Language and Cognitive Processes, 11, 107 – 134; Snedeker & Trueswell, 2003. Using prosody to avoid ambiguity: Effects of speaker awareness and referential context. Journal of Memory and Language, 48, 103 – 130], and of prosody in predicting the eventual syntactic structure of ambiguous sentences [e.g. Snedeker & Trueswell, 2003. Using prosody to avoid ambiguity: Effects of speaker awareness and referential context. Journal of Memory and Language, 48, 103 – 130]. Wh-in- situ questions contain temporary syntactic ambiguity. One of the languages characterised by wh-in- situ questions is Persian. The current research adopted the gating paradigm [Grosjean, 1980. Spoken word recognition processes and the gating paradigm. Perception and Psychophysics, 28, 267 – 283] to investigate when distinctive prosodic cues of the pre-wh part enable correct identification of wh-in- situ questions in Persian. A perception experiment was designed in which gated stimuli were played to Persian native speakers in a forced-choice sentence identification task. In line with our expectation, correct identification responses were given from the beginning of the sentence. The result is discussed in the context of proposals regarding the need to integrate prosody and prediction into models of language and speech processing [Beach, 1991. The interpretation of prosodic patterns at points of syntactic structure ambiguity: Evidence for cue trading relations. Journal of Memory and Language, 30, 644 – 663; Grosjean, 1983. How long is the sentence? Prediction and prosody in the on-line processing of language. Linguistics, 21, 501 – 529, 1996a. Using prosody to predict the end of sentences in English and French: Normal and brain damaged subjects. Language and Cognitive Processes, 11, 107 – 134].
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Estimating Causal Parameters in Marginal Structural Models with Unmeasured Confounders Using Instrumental Variables

Estimating Causal Parameters in Marginal Structural Models with Unmeasured Confounders Using Instrumental Variables

Causal inference methodology contains a framework designed to estimate parameters with a causal interpretation. Rubin [22] introduced the assumption that each subject carries with them a range of potential outcomes, one for each type of treatment or exposure being studied. At most one such outcome is observed, the rest are counterfactual outcomes. Robins [21] built upon this idea of modeling counterfactual outcomes to create a class of marginal structural models (MSM). MSMs make use of data with measured confounders, however, situations can arise in which differences between treatment and control groups are due in part to unmeasured confounding variables. For measured confounders the inverse probability of treatment weighted estimator can be used to construct consistent and asymptotically linear estimates of treatment effect [21]. A different approach is needed when unmeasured confounders are present.
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Measuring Precision of Statistical Inference on Partially Identified Parameters

Measuring Precision of Statistical Inference on Partially Identified Parameters

6 Conclusion I have compared what di¤erent measures of inferential precision for partially identi…ed parame- ters about optimal economic trade o¤ between reducing sampling error and reducing the extent of partial identi…cation in the data when the researcher could control both (for example, when choosing the size of a study and the level of e¤ort to reduce non-response). The length of con…- dence intervals for the identi…ed interval is the most apparent measure of precision, but it turns out to be an outlier. When the extent of partial identi…cation is relatively important, all other measures of precision considered here (mean sqaured error, mean absolute deviation, regret loss for treatment choice) would lead the researcher to reallocate the budget more strongly towards reducing the identi…cation problem at the expense of sampling error.
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Semiparametric Estimation and Inference for Censored Regression Models.

Semiparametric Estimation and Inference for Censored Regression Models.

For the simplest Scenario 1 with homoscedastic error and covariate-independent censoring, all three methods give essentially unbiased estimation. The resampling procedure for the LBJ method works reasonably well. The resampling standard errors are close to the Monte Carlo standard deviations, and the confidence intervals have coverage probabilities close to the 95% nominal level. Not surprisingly, BJ is slightly more e ffi cient than LBJ as the i . i . d . error as- sumption is satisfied. Both BJ and LBJ estimators tend to be more e ffi cient than WLS. One possible explanation is that the imputation procedure in LBJ utilizes the information from the censored data more e ffi ciently than WLS, which is partly dependent on the inverse probability weighting principle.
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Pairwise Comparison Estimation of Censored Transformation Models

Pairwise Comparison Estimation of Censored Transformation Models

The assumption of independence between the censoring variable and the covariates is often considered too restrictive. For example it rules out all competing risks models where the researcher only observes the minimum of two dependent variables depending on covari- ates and having some common covariates. Thus we feel that an estimator for the regression coefficients in a transformation model with covariate dependent censoring that is simple to implement, in the sense that it does not require smoothing parameters or trimming proce- dures, is something that is lacking in the literature. In this paper we propose an estimator which aims to address this problem.
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Proportional mean regression models for censored data

Proportional mean regression models for censored data

Among the various extensions of the traditional linear model, the AFT mod- els and the least squares method to accommodate the censored data seems most appealing, simply because the model is well known, widely used, well understood and well tested (see Wei, 1992). Some early attempts of such extensions are due to Miller (1976) and Buckley and James (1979). However, no rigorous proof of consistency was presented and the iterations in the computation of the estimate may not converge. Koul et al. (1981) developed a simple least square estimation method based on “synthetic data”, as termed by Leurgans (1987). The main idea of this approach is to replace the censored observations by a set of estimated “re- sponses” and then obtain the usual least square estimate for regression parameters based on the such estimated responses. Using a U-statistic representation, Koul et al. (1981) showed that their estimates are consistent and asymptotically normal under some regularity conditions. Following on this simple idea of using synthetic data several extensions of the method have appeared in the literature that uses a more efficient way to obtain estimated responses (see Zeng, 1984, Lai et al., 1995, Zhou, 1992 and references therein). These developments have been very exciting but generally lacks stability of the estimators and hence are not as widely used as the PH model.
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