N-Consistent Semiparametric Regression: Partially Linear Models with Unit Roots

We develop unit root tests using additional stationary covariates as suggested in Hansen (1995). However, we allow for the covariates to enter the model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988). We retain a linear structure for the autoregressive component and show that the parameter is estimated at rate N even though part of the model is estimated nonparametrically. The limiting distribution of the unit root test statistic is a mixture of the standard normal and the Dickey-Fuller distribution. A Monte Carlo experiment is used to evaluate the performance of the tests under various linear and nonlinear specifications for the covariates. We find that the tests are powerful when there is a nonlinear effect and experience a minimal power loss when the covariates have a linear effect or no effect at all.

Second-order approximation for adaptive regression estimators.

We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second-order mean squared error. We examine both independent and time series regressors; we also extend our results to a t-statistic. Monte Carlo simulations confirm the second order theory and the usefulness of the bandwidth selection method.

Identification and characterization of novel glomerulus-associated genes and proteins

The kidney is responsible for sieving the circulating blood to eliminate water-soluble waste products and potentially toxic substances from the body. The filtration step occurs in specialized filtration units called glomeruli. Some renal diseases are related to specific glomerular defects, but it is highly likely that the present knowledge gained from previous studies only represents a small proportion of genes and proteins that have important roles for normal kidney function. To identify other genes with roles for glomerular filtration function, our group developed GlomBase, which is a glomerular transcript database in which over 300 genes are highly glomerulus specific. Among those genes, several genes with highest glomerular expression were chosen for further analysis, but this thesis is mainly based on studies on three of them, dendrin, adenylate cyclase type I (Adcy1), and Crumbs homolog 2 (Crb2). Dendrin is a cytosolic protein previously identified only in the brain. However, we localized dendrin in the kidney specifically to the glomerular podocytes. Furthermore, we generated a polyclonal antibody against this novel glomerular protein. We detected that the earliest dendrin expression during glomerular maturation is at the capillary loop stage, and that it is located in the cytoplasmic face of the podocyte slit diaphragm. Unexpectedly, inactivation of the dendrin gene in mouse did not generate any obvious phenotype. Dendrin -/- mice were born at an expected Mendelian ratio and macroscopically all organs appeared normal. By the age of 1.2 years, no signs of renal impairment have been observed in the dendrin-/- mice. Under kidney challenging conditions, dendrin -/- mice show no difference when compared with dendrin +/+ mice. Even though dendrin does not seem to be crucial for the integrity of the glomerular filtration barrier, we do find two proteins that interact with dendrin, and their biological role in podocyte is still under investigation. These results are out scope of this thesis. Adcy1 is one out of nine members of the adenylate cyclase protein family which catalyze the formation of the secondary messenger cAMP. cAMP is involved in a wide variety of cellular signaling processes, including regulation of actin cytoskeleton assembly through PKA. Adcy1 has previously been thought to be expressed only by certain neuronal cells in the brain, but we localized Adcy1 expression to the glomerular podocytes as well. During glomerulogenesis, the Adcy1 expression was detected first at the stage when maturing podocytes develop foot processes. To study the role of Adcy1 gene in the kidney in vivo, we analyzed the kidneys of Adcy1-/- mice (mice generatedby other investigators, that without severe phenotype except mild behavioral abnormalities). We found the glomerulogenesis to proceed normally in Adcy1-/- mice, and in mature mouse, no signs of renal impairment was detected. However, challenging of the kidney with albumin overload caused severe albuminuria in Adcy1-/- mice, whereas wild type mice showed only moderate albumin leakage to the urine. Thus, Adcy1 may in fact be a susceptibility gene for proteinuria. Crb2 is yet another novel podocyte specific protein we identified. Its Drosophila homologue Crumbs is an essential component for epithelial cells organizing apicalbasal polarity and adherent junctions. In the mouse, it is expressed only in brain, kidney and heart. In the kidney, it is specifically located in the glomerular podocyte slit diaphragm. Interestingly, inactivation of this gene led to arrest the embryonic development after E7.75 and embryonic lethality, which demonstrates the importance of this gene during early embryonic development. The Crb2-/- embryos show defects in neuroepithelium and epithelial mesenchymal transition (EMT) at the primitive streak. The function of Crb2 protein in the glomerulus will be explored later by my colleagues in studies of conditional knockout mice with podocyte specific inactivation of the Crb2 gene. In summary, the discovery and characterization of novel glomerular genes and proteins presented in this thesis has increased our knowledge of glomerular biology as well as on the role of a glomeral gene in early embryogenesis

Copula-based nonlinear quantile autoregression

Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.

Copula-Based Nonlinear Quantile Autoregression

Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.Quantile autoregression, Copula, Ergodic nonlinear Markov models

A Semiparametric Panel Model for Unbalanced Data with Application to Climate Change in the United Kingdom

This paper is concerned with developing a semiparametric panel model to explain the trend in UK temperatures and other weather outcomes over the last century. We work with the monthly averaged maximum and minimum temperatures observed at the twenty six Meteorological Office stations. The data is an unbalanced panel. We allow the trend to evolve in a nonparametric way so that we obtain a fuller picture of the evolution of common temperature in the medium timescale. Profile likelihood estimators (PLE) are proposed and their statistical properties are studied. The proposed PLE has improved asymptotic property comparing the the sequential two-step estimators. Finally, forecasting based on the proposed model is studied.Global warming; Kernel estimation; Semiparametric; Trend analysis

Efficient Regression in Time Series Partial Linear Models

This paper studies efficient estimation of partial linear regression in time series models. In particular, it combines two topics that have attracted a good deal of attention in econometrics, viz. spectral regression and partial linear regression, and proposes an efficient frequency domain estimator for partial linear models with serially correlated residuals. A nonparametric treatment of regression errors is permitted so that it is not necessary to be explicit about the dynamic specification of the errors other than to assume stationarity. A new concept of weak dependence is introduced based on regularity conditions on the joint density. Under these and some other regularity conditions, it is shown that the spectral estimator is root-n-consistent, asymptotically normal, and asymptotically efficient.Efficient estimation, Partial linear regression, Spectral regression, Kernel estimation, Nonparametric, Semiparametric, Weak dependence

Partially Linear Models with Unit Roots

This paper studies the asymptotic properties of a nonstationary partially linear regression model. In particular, we allow for covariates to enter the unit root (or near unit root) model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988). It is proven that the autoregressive parameter can be estimated at rate N even though part of the model is estimated nonparametrically. Unit root tests based on the semiparametric estimate of the autoregressive parameter have a limiting distribution which is a mixture of a standard normal and the Dickey-Fuller distribution. A Monte Carlo experiment is conducted to evaluate the performance of the tests for various linear and nonlinear specifications