Heteroscedastic semiparametric transformation models: estimation and testing for validity

In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is independent of the multidimensional covariates. In this model, we first consider the estimation of the unknown components of the model, namely the transformation parameter, regression and variance function and the distribution of the error. We show the asymptotic normality of the proposed estimators. Second, we propose tests for the validity of the model, and establish the limiting distribution of the test statistics under the null hypothesis. A bootstrap procedure is proposed to approximate the critical values of the tests. Finally, we carry out a simulation study to verify the small sample behavior of the proposed estimators and tests.Comment: 33 pages, 1 figur

Quantile Regression in the Presence of Sample Selection

Most sample selection models assume that the errors are independent of the regressors. Under this assumption, all quantile and mean functions are parallel, which implies that quantile estimators cannot reveal any (per definition non-existing) heterogeneity. However, quantile estimators are useful for testing the independence assumption, because they are consistent under the null hypothesis. We propose tests for this crucial restriction that are based on the entire conditional quantile regression process after correcting for sample selection bias. Monte Carlo simulations demonstrate that they are powerful and two empirical illustrations indicate that violations of this assumption are likely to be ubiquitous in labor economics.Sample selection, quantile regression, independence, test

Shortcomings of a parametric VaR approach and nonparametric improvements based on a non-stationary return series model

A non-stationary regression model for financial returns is examined theoretically in this paper. Volatility dynamics are modelled both exogenously and deterministic, captured by a nonparametric curve estimation on equidistant centered returns. We prove consistency and asymptotic normality of a symmetric variance estimator and of a one-sided variance estimator analytically, and derive remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, implemented by an asymmetric version of the Pearson type VII distribution for random innovations. By providing a method of moments for its parameter estimation and a connection to the Student-t distribution we offer the framework for a factor-based VaR approach. The approximation quality of the non-stationary model is supported by simulation studies. --heteroscedastic asset returns,non-stationarity,nonparametric regression,volatility,innovation modelling,asymmetric heavy-tails,distributional forecast,Value at Risk (VaR)

Asymptotic inference in some heteroscedastic regression models with long memory design and errors

This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple linear regression model, the first-order asymptotic distribution of the least square estimator of the slope parameter is observed to be degenerate. However, in the second order, this estimator is $n^{1/2}$-consistent and asymptotically normal for $h+H<3/2$; nonnormal otherwise, where $h$ and $H$ are LM parameters of design and error processes, respectively. The finite-dimensional asymptotic distributions of a class of kernel type estimators of the conditional variance function $\sigma^2(x)$ in a more general heteroscedastic regression model are found to be normal whenever $H<(1+h)/2$, and non-normal otherwise. In addition, in this general model, $\log(n)$-consistency of the local Whittle estimator of $H$ based on pseudo residuals and consistency of a cross validation type estimator of $\sigma^2(x)$ are established. All of these findings are then used to propose a lack-of-fit test of a parametric regression model, with an application to some currency exchange rate data which exhibit LM.Comment: Published in at http://dx.doi.org/10.1214/009053607000000686 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Endogenous semiparametric binary choice models with heteroscedasticity

In this paper we consider endogenous regressors in the binary choice model under a weak median exclusion restriction, but without further specification of the distribution of the unobserved random components. Our reduced form specification with heteroscedastic residuals covers various heterogeneous structural binary choice models. As a particularly relevant example of a structural model where no semiparametric estimator has of yet been analyzed, we consider the binary random utility model with endogenous regressors and heterogeneous parameters. We employ a control function IV assumption to establish identification of a slope parameter 'â' by the mean ratio of derivatives of two functions of the instruments. We propose an estimator based on direct sample counterparts, and discuss the large sample behavior of this estimator. In particular, we show '√'n consistency and derive the asymptotic distribution. In the same framework, we propose tests for heteroscedasticity, overidentification and endogeneity. We analyze the small sample performance through a simulation study. An application of the model to discrete choice demand data concludes this paper.

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

We study the drift of stationary diffusion processes in a time series analysis of the autoregression function. A marked empirical process measures the difference between the nonparametric regression functions of two time series. We bootstrap the distribution of a Kolmogorov-Smirnov-type test statistic for two hypotheses: Equality of regression functions and shifted regression functions. Neither markovian behavior nor Brownian motion error of the processes are assumed. A detailed simulation study finds the size of the new test near the nominal level and a good power for a variety of parametric models. The two-sample result serves to test for mean reversion of the diffusion drift in several examples. The interest rates Euribor, Libor as well as T-Bond yields do not show that stylized feature often modelled for interest rates. --