In this paper, a robust analysis of nitrogen dioxide (NO2) concentration measurements taken at Belisario station (Quito, Ecuador) was performed. The data used for the analysis constitute a set of ...measurements taken from 1 January 2008 to 31 December 2019. Furthermore, the analysis was carried out in a robust way, defining variables that represent years, months, days and hours, and classifying these variables based on estimates of the central tendency and dispersion of the data. The estimators used here were classic, nonparametric, based on a bootstrap method, and robust. Additionally, confidence intervals based on these estimators were built, and these intervals were used to categorize the variables under study. The results of this research showed that the NO2 concentration at Belisario station is not harmful to humans. Moreover, it was shown that this concentration tends to be stable across the years, changes slightly during the days of the week, and varies greatly when analyzed by months and hours of the day. Here, the precision provided by both nonparametric and robust statistical methods served to comprehensively proof the aforementioned. Finally, it can be concluded that the city of Quito is progressing on the right path in terms of improving air quality, because it has been shown that there is a decreasing tendency in the NO2 concentration across the years. In addition, according to the Quito Air Quality Index, most of the observations are in either the desirable level or acceptable level of air pollution, and the number of observations that are in the desirable level of air pollution increases across the years.
We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the ...selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.
We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to ...perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso regularization path, because, as it turns out, selection events for these procedures can be expressed as polyhedral constraints on y. The p-values associated with these tests are exactly uniform under the null distribution, in finite samples, yielding exact Type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. The R package
selectiveInference
, freely available on the CRAN repository, implements the new inference tools described in this article. Supplementary materials for this article are available online.
We present a (selective) review of recent frequentist high-dimensional inference methods for constructing p-values and confidence intervals in linear and generalized linear models. We include a ...broad, comparative empirical study which complements the viewpoint from statistical methodology and theory. Furthermore, we introduce and illustrate the R-package hdi which easily allows the use of different methods and supports reproducibility.
There are three common types of confidence interval (CI) in structural equation modeling (SEM): Wald-type CI, bootstrapping CI, and likelihood-based CI (LBCI). LBCI has the following advantages: (1) ...it has better coverage probabilities and Type I error rate compared to Wald-type CI when the sample size is finite; (2) it correctly tests the null hypothesis of a parameter based on likelihood ratio chi-square difference test; (3) it is less computationally intensive than bootstrapping CI; and (4) it is invariant to transformations. However, LBCI is not available in many popular SEM software packages. We developed an R package, semlbci, for forming LBCI for parameters in models fitted by lavaan, a popular open-source SEM package, such that researchers have more options in forming CIs for parameters in SEM. The package supports both unstandardized and standardized estimates, derived parameters such as indirect effect, multisample models, and the robust LBCI proposed by Falk.
We study the coverage properties of Bayesian confidence intervals for the smooth component functions of generalized additive models (GAMs) represented using any penalized regression spline approach. ...The intervals are the usual generalization of the intervals first proposed by Wahba and Silverman in 1983 and 1985, respectively, to the GAM component context. We present simulation evidence showing these intervals have close to nominal ' across-the-function' frequentist coverage probabilities, except when the truth is close to a straight line/plane function. We extend the argument introduced by Nychka in 1988 for univariate smoothing splines to explain these results.The theoretical argument suggests that close to nominal coverage probabilities can be achieved, provided that heavy oversmoothing is avoided, so that the bias is not too large a proportion of the sampling variability. The theoretical results allow us to derive alternative intervals from a purely frequentist point of view, and to explain the impact that the neglect of smoothing parameter variability has on confidence interval performance. They also suggest switching the target of inference for component-wise intervals away from smooth components in the space of the GAM identifiability constraints.
Arguing for a Negligible Effect Rainey, Carlisle
American journal of political science,
October 2014, Letnik:
58, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Political scientists often theorize that an explanatory variable should have "no effect" and support this claim by demonstrating that its coefficient's estimate is not statistically significant. This ...empirical argument is quite weak, but I introduce applied researchers to simple, powerful tools that can strengthen their arguments for this hypothesis. With several supporting examples, I illustrate that researchers can use 90% confidence intervals to argue against meaningful effects and provide persuasive evidence for their hypothesis.
We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, ...and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the U.S. excess deaths data from 2017 to 2020. The
supplementary material
, which contains the proofs of our theoretical results, is available online.
A great deal of interest has recently focused on conducting inference on the parameters in a high-dimensional linear model. In this paper, we consider a simple and very naïve two-step procedure for ...this task, in which we (i) fit a lasso model in order to obtain a subset of the variables, and (ii) fit a least squares model on the lasso-selected set. Conventional statistical wisdom tells us that we cannot make use of the standard statistical inference tools for the resulting least squares model (such as confidence intervals and p-values), since we peeked at the data twice: once in running the lasso, and again in fitting the least squares model. However, in this paper, we show that under a certain set of assumptions, with high probability, the set of variables selected by the lasso is identical to the one selected by the noiseless lasso and is hence deterministic. Consequently, the naïve two-step approach can yield asymptotically valid inference. We utilize this finding to develop the naïve confidence interval, which can be used to draw inference on the regression coefficients of the model selected by the lasso, as well as the naïve score test, which can be used to test the hypotheses regarding the full-model regression coefficients.
In recent years, the photovoltaic generation installed capacity has been steadily growing thanks to its inexhaustible and non-polluting characteristics. However, solar generators are strongly ...dependent on intermittent weather parameters, increasing power systems' uncertainty level. Forecasting models have arisen as a feasible solution to decreasing photovoltaic generators' uncertainty level, as they can produce accurate predictions. Traditionally, the vast majority of research studies have focused on the development of accurate prediction point forecasters. However, in recent years some researchers have suggested the concept of prediction interval forecasting, where not only an accurate prediction point but also the confidence level of a given prediction are computed to provide further information. This paper develops a new model for predicting photovoltaic generators' output power confidence interval 10 min ahead, based on deep learning, mathematical probability density functions and meteorological parameters. The model's accuracy has been validated with a real data series collected from Spanish meteorological stations. In addition, two error metrics, prediction interval coverage percentage and Skill score, are computed at a 95% confidence level to examine the model's accuracy. The prediction interval coverage percentage values are greater than the chosen confidence level, which means, as stated in the literature, the proposed model is well-founded.
•The model predicts future generation through involved meteorological parameters.•The forecaster relies on the combination of deep learning and mathematical functions.•Reliability and sharpness metrics are calculated to test model's accuracy.•The accuracy of predicted intervals reduces photovoltaic generators' uncertainty.
PDF
