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In this article we introduce a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long‐ and the short‐range dependency of the process. A cross‐validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

In this article, we propose a class of partial deconvolution kernel estimators for the nonparametric regression function when some covariates are measured with error and some are not. The estimation procedure combines the classical kernel methodology and the deconvolution kernel technique. According to whether the measurement error is ordinarily smooth or supersmooth, we establish the optimal local and global convergence rates for these proposed estimators, and the optimal bandwidths are also identified. Furthermore, lower bounds for the convergence rates of all possible estimators for the nonparametric regression functions are developed. It is shown that, in both the super and ordinarily smooth cases, the convergence rates of the proposed partial deconvolution kernel estimators attain the lower bound. The Canadian Journal of Statistics 48: 535–560; 2020 © 2020 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Length-biased data are often encountered in cross-sectional surveys and prevalent-cohort studies on disease durations. Under length-biased sampling subjects with longer disease durations have greater chance to be observed. As a result, covariate values linked to the longer survivors are favored by the sampling mechanism. When the sampled durations are also subject to right censoring, the censoring is informative. Modeling dependence structure without adjusting for these issues leads to biased results. In this article, we consider copulas for modeling dependence when the collected data are length-biased and account for both informative censoring and covariate bias that are naturally linked to length-biased sampling. We address nonparametric estimation of the bivariate distribution, copula function and its density, and Kendall and Spearman measures for right-censored length-biased data. The proposed estimator for the bivariate cdf is a Hadamard-differentiable functional of two MLEs (Kaplan–Meier and empirical cdf) and inherits their efficiency. Based on this estimator, we devise two estimators for copula function and a local-polynomial estimator for copula density that accounts for boundary bias. The limiting processes of the estimators are established by deriving their iid representations. As a by-product, we establish the oscillation behavior of the bivariate cdf estimator. In addition, we introduce estimators for Kendall and Spearman measures and study their weak convergence. The proposed method is applied to analyze a set of right-censored length-biased data on survival with dementia, collected as part of a nationwide study in Canada. [ABSTRACT FROM AUTHOR]

In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

In this work, we are concerned with nonparametric estimation of the distribution function when the data are possibly censored and satisfy the α -mixing condition, also called strong mixing. Among various mixing conditions used in the literature, α -mixing is reasonably weak and has many practical applications as it is fulfilled by many stochastic processes including some time series models. In practice the observed data can be complete or subject to censorship, so we deal with these different cases. More precisely, the rate of the almost complete convergence is established, under the α -mixing condition, for complete, singly censored and twice censored data. To lend further support to our theoretical results, a simulation study is carried out to illustrate the good accuracy of the studied method, for relatively small sample sizes. Finally, an application to censored dependent data is provided via the analysis of Chromium concentrations collected from two stations of the Niagara River in Canada. [ABSTRACT FROM AUTHOR]

Mapping Canada's forests is a significant challenge given their extent and the interprovincial differences in forest inventories. We created new sets of nationally consistent forest attribute maps for the years 2001 and 2011 by building upon previously published work with the objective to determine if sequential maps of forest attributes could be used to quantify changes over time. We first refined our previously published methodology of using the k nearest neighbors ( kNN) prediction method and MODIS spectral reflectance data as predictive variables. The maps were generated using an improved reference dataset and a new analytical kNN workflow. We then evaluated 2001 to 2011 changes in two key attributes, aboveground biomass and percent tree cover, on pixels identified from published sources as having undergone fire, harvest, or postdisturbance regrowth during that period. For all three change types, average changes in both aboveground biomass and percent tree cover between 2001 and 2011 matched expectations relative to the dynamics of Canadian forests. Our results support the use of sequential national maps of forest attributes for evaluating regionally aggregated disturbance-related changes in forest properties. The new forest attribute maps are available from ; doi: at . [ABSTRACT FROM AUTHOR]

In follow-up studies on chronic disease cohorts, individuals are often observed at irregular visit times that may be related to their previous disease history and other factors. This can produce bias in standard methods of estimation. Working in the context of multistate models, we consider a method of nonparametric estimation for state occupancy probabilities that adjusts for dependent follow-up through the use of inverse-intensity-of-visit weighted estimating functions and smoothing. The methodology is applied to the estimation of viral rebound probabilities in the Canadian Observational Cohort on HIV-positive persons. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the evolution of firm distributions for entrant manufacturing firms in Canada using nonparametric methods. These nonparametric methods use functional principal components to describe these densities over time. This method is applied to a novel administrative firm-level database from Statistics Canada to investigate the evolution of the 1985 and 1989 cohorts of new entrants. We find that firm leverage (debt-to-asset ratio) distributions have persistent deviations from the initial distributions. Bootstrap test statistics suggest that the distributions are different across all time periods. Firm size and labour productivity have transitory deviations and some of the distributions are the same across all time periods. Univariate finite mixture and stochastic dominance tests are used to conduct pairwise comparisons as robustness measures. We find that these static pairwise comparisons confirm the dynamic evolution of these densities. This method illustrates the efficacy of functional principal components to analyse firm distributions. [ABSTRACT FROM AUTHOR]

We propose a nonparametric method to assess the effects of one or more covariates on the cure rate for survival data with a cure fraction. The method extends the existing work on single sample and multiple sample cases and also allows for a continuous covariate. The proposed estimator is shown to be consistent and asymptotically normal. A simulation study shows that the proposed method estimates the covariate effect on cure rate with smaller biases than the existing semi-parametric cure models, particularly when the semi-parametric cure models mis-specify the effect. The proposed method is applied to a study for leukaemia patients to assess the effect of age on the chance of being cured after bone marrow transplantation. The Canadian Journal of Statistics 42: 1-17; 2014 © 2013 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Dementia is one of the world’s major public health challenges. The lifetime risk of dementia is the proportion of individuals who ever develop dementia during their lifetime. Despite its importance to epidemiologists and policy-makers, this measure does not seem to have been estimated in the Canadian population. Data from a birth cohort study of dementia are not available. Instead, we must rely on data from the Canadian Study of Health and Aging, a large cross-sectional study of dementia with follow-up for survival. These data present challenges because they include substantial loss to follow-up and are not representatively drawn from the target population because of structural sampling biases. A first bias is imparted by the cross-sectional sampling scheme, while a second bias is a result of stratified sampling. Estimation of the lifetime risk and related quantities in the presence of these biases has not been previously addressed in the literature. We develop and study nonparametric estimators of the lifetime risk, the remaining lifetime risk, and cumulative risk at specific ages, accounting for these complexities. In particular, we reveal the fact that estimation of the lifetime risk is invariant to stratification by current age at sampling. We present simulation results validating our methodology, and provide novel facts about the epidemiology of dementia in Canada using data from the Canadian Study of Health and Aging. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Incidence is an important epidemiological concept most suitably studied using an incident cohort study. However, data are often collected from the more feasible prevalent cohort study, whereby diseased individuals are recruited through a cross-sectional survey and followed in time. In the absence of temporal trends in survival, we derive an efficient nonparametric estimator of the cumulative incidence based on such data and study its asymptotic properties. Arbitrary calendar time variations in disease incidence are allowed. Age-specific incidence and adjustments for both stratified sampling and temporal variations in survival are also discussed. Simulation results are presented and data from the Canadian Study of Health and Aging are analysed to infer the incidence of dementia in the Canadian elderly population. [ABSTRACT FROM PUBLISHER]

There is considerable interest in measuring tax noncompliance using microeconomic data. One such method estimates income under-reporting by selfemployed households by assuming a known, parametric form of the Engel curve and making the further parametric assumption that self-employed households under-report their income by a constant fraction, independent of income. This paper proposes a nonparametric approach which avoids functional form restrictions and allows the form of the reporting function to be uncovered rather than being imposed a priori. The approach is illustrated by estimating the effect of the Canadian Goods and Services Tax on income under-reporting by a sample of self-employed households. [ABSTRACT FROM AUTHOR]

In clinical studies with time-to-event outcomes, the restricted mean survival time (RMST) has attracted substantial attention as a summary measurement for its straightforward clinical interpretation. When the data are subject to length-biased sampling, which is frequently encountered in observational cohort studies, existing methods to estimate the RMST are not applicable. In this article, we consider nonparametric and semiparametric regression methods to estimate the RMST under the setting of length-biased sampling. To assess the covariate effects on the RMST, a semiparametric regression model that directly relates the covariates and the RMST is assumed. Based on the model, we develop unbiased estimating equations to obtain consistent estimators of covariate effects by properly adjusting for informative censoring and length bias. Stochastic process theories are used to establish the asymptotic properties of the proposed estimators. We investigate the finite sample performance through simulations and illustrate the methods by analyzing a prevalent cohort study of dementia in Canada., (© 2017, The International Biometric Society.)