Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables

Given a response $Y$ and a vector $X = (X^1, \dots, X^d)$ of $d$ predictors, we investigate the problem of inferring direct causes of $Y$ among the vector $X$. Models for $Y$ that use all of its causal covariates as predictors enjoy the property of being invariant across different environments or interventional settings. Given data from such environments, this property has been exploited for causal discovery. Here, we extend this inference principle to situations in which some (discrete-valued) direct causes of $Y$ are unobserved. Such cases naturally give rise to switching regression models. We provide sufficient conditions for the existence, consistency and asymptotic normality of the MLE in linear switching regression models with Gaussian noise, and construct a test for the equality of such models. These results allow us to prove that the proposed causal discovery method obtains asymptotic false discovery control under mild conditions. We provide an algorithm, make available code, and test our method on simulated data. It is robust against model violations and outperforms state-of-the-art approaches. We further apply our method to a real data set, where we show that it does not only output causal predictors, but also a process-based clustering of data points, which could be of additional interest to practitioners.Comment: 46 pages, 14 figures; real-world application added in Section 5.2; additional numerical experiments added in the Appendix

Response Surface Methodology and Its Application in Optimizing the Efficiency of Organic Solar Cells

Response surface methodology (RSM) is a ubiquitous optimization approach used in a wide variety of scientific research studies. The philosophy behind a response surface method is to sequentially run relatively simple experiments or models in order to optimize a response variable of interest. In other words, we run a small number of experiments sequentially that can provide a large amount of information upon augmentation. In this dissertation, the RSM technique is utilized in order to find the optimum fabrication condition of a polymer solar cell that maximizes the cell efficiency. The optimal device performance was achieved using 10.25 mg/ml polymer concentration, 0.42 polymer-fullerene ratio, and 1624 rpm of active layer spinning speed. The cell efficiency at the optimum stationary point was found to be 5.23% for the Poly(diketopyrrolopyrrole-terthiophene) (PDPP3T)/PC60BM solar cells. Secondly, we explored methods for constructing a confidence region for the stationary point in RSM. In particular, we developed methods for constructing simultaneous confidence intervals for the coordinates of a stationary point in a quadratic response surface model. The methods include Bonferroni adjustment, a plug-in approach based on the asymptotic distribution of maximum likelihood estimators, and bootstrapping. The simultaneous coverage probabilities of the proposed methods are assessed via simulation. The coverage probabilities for the Bonferroni and plug-in approaches are pretty close to the nominal levels of 0.95 for large sample sizes. The metaheuristic method is also considered in order to search for an alternative solution to the design matrix that may be near to the optimal solution. Finally, we explored recent developments in RSM including generalized linear models and the case of multivariate response variables

Likelihood-based inference for max-stable processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes

Estimating the turning point location in shifted exponential model of time series

We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we provide a formula for computing the distribution of the turning point location and consequently to estimate a confidence interval for the location. We test this formula in simulated data series having a trend with asymmetric minimum, investigating the coverage rate as a function of a bandwidth parameter. The method is applied to estimate the confidence interval of the minimum location of the time series of RT intervals extracted from the electrocardiogram recorded during the exercise test. We discuss the connection with stochastic ordering

Transformation techniques for the parameter estimation of discrete-time transfer functions

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Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Testing for two-regime threshold cointegration in the parallel and official markets for foreign currency in Greece

This paper models the short-run as well as the long-run relationship between the parallel and official markets for US dollars in Greece in a threshold VECM framework. Modeling exchange rates within this context can be motivated by the fact that the transition mechanism is controlled by the parallel market premium. The results show that linearity is rejected in favour of a TVECM specification, which forms statistically an adequate representation of the data. Two regimes are implied by the model; the “typical” regime, which applies most of the time and the “unusual” one associated with economic and political events t hat took place in Greece during the 1980s. Another implication is that in the parallel exchange rate there are strong asymmetries between the two regimes in the speed of adjustment to the long-run equilibrium. Finally, Granger causality runs from the official to the parallel market in both regimes but not vice versa.Parallel market premium, nonlinearity, threshold cointegration, regime switching,