Multiple Choice Questions Flashcards
What is the primary objective of Functional Data Analysis (FDA)?
A. Analysing categorical data
B. Analysing data collected over a continuous domain
C. Studying only time-series data
D. Focusing on spatial data analysis
B. Analysing data collected over a continuous domain
Which statistical technique is commonly used in Functional Data Analysis for smoothing and summarizing data?
A. Functional Principal Component Analysis (FPCA)
B. Cluster Analysis
C. Linear Regression
D. Fourier Transform
A. Functional Principal Component Analysis (FPCA)
In FDA, what does the term ”functional data” refer to?
A. Data with missing values
B. Data collected from experiments
C. Data with repeated measures over a continuum
D. Categorical data
C. Data with repeated measures over a continuum
Which of the following is a key assumption in Functional Data Analysis?
A. Independence of observations
B. Homoscedasticity
C. Time-series stationarity
D. Functional smoothness
D. Functional smoothness
What role does the concept of a ”functional basis” play in Functional Data Analysis?
A. It defines the distribution of data points
B. It provides a set of functions to represent data
C. It measures the spread of data
D. It assesses outliers in the data
B. It provides a set of functions to represent data
Which of the following is not a characteristic of functional data?
A. Data are measurements of smooth processes over time
B. Often have multiple measurements of the same process
C. Must be equally spaced or perfect measurements
D. Curves with similar trends
C. Must be equally spaced or perfect measurements
Which of the following factors does not influence the selection of the smoothing parameter in functional data analysis?
A. Sample size
B. Noise level in the data
C. Type of basis functions used
D. Computational resources available
D. Computational resources available
What does the smoothing parameter λ in functional data analysis control?
A. The number of data points in the functional dataset
B. The degree of flexibility in the fitted curve
C. The range of values in the functional dataset
D. The significance level for hypothesis testing
B. The degree of flexibility in the fitted curve
Which of the following statements about the smoothing parameter λ is true?
A. The smoothing parameter only affects the mean of the functional dataset
B. The smoothing parameter does not affect the smoothness of the curve
C. A smaller smoothing parameter leads to a smoother curve
D. A larger smoothing parameter leads to a smoother curve
D. A larger smoothing parameter leads to a smoother curve
How does cross-validation help in selecting the smoothing parameter λ?
A. By minimising the sum of squared errors (SSE)
B. By maximising the variance of the functional dataset
C. By maximising the likelihood function
D. By minimising the number of data points in the functional dataset
A. By minimising the sum of squared errors (SSE)
Which of the following techniques is commonly used to select the smoothing parameter λ in func-tional data analysis?
A. Principal component analysis (PCA)
B. Singular value decomposition (SVD)
C. Maximum likelihood estimation (MLE)
D. Generalized Cross-Validation (GCV)
D. Generalized Cross-Validation (GCV)
What happens if the smoothing parameter λ is too small in functional data analysis?
A. Over-smoothing of the curve occurs
B. Under-smoothing of the curve occurs
C. No effect on the curve’s smoothness
D. The curve becomes discontinuous
B. Under-smoothing of the curve occurs
What happens if the smoothing parameter λ is too large in functional data analysis?
A. Over-smoothing of the curve occurs
B. Under-smoothing of the curve occurs
C. No effect on the curve’s smoothness
D. The curve becomes discontinuous
A. Over-smoothing of the curve occurs
What does the smoothing parameter λ control in Roughness Penalty Smoothing Method for functional data analysis?
A. The level of significance for hypothesis testing
B. The number of penalties applied to the model
C. The trade-off between smoothness and goodness of fit
D. The type of basis functions used in the analysis
C. The trade-off between smoothness and goodness of fit
What is the purpose of the smoothing parameter λ in functional data analysis?
A. To reduce noise in the data
B. To increase the number of data points
C. To adjust the scale of the functional dataset
D. To control the degree of smoothing in the fitted curve
D. To control the degree of smoothing in the fitted curve
What is the primary objective of Generalized Cross-Validation in determining the optimal smoothing parameter λ?
A. To maximize the bias of the fitted curve
B. To minimize the variance of the fitted curve
C. To select the smoothing parameter that generalizes best to unseen data
D. To estimate the number of basis functions needed for the analysis
C. To select the smoothing parameter that generalizes best to unseen data
What is the primary objective of Functional Data Analysis (FDA)?
A. Analysing categorical data
B. Analysing data collected over a continuous domain
C. Studying only time-series data
D. Focusing on spatial data analysis
B. Analysing data collected over a continuous domain
What is the role of basis functions in functional data analysis?
A. To transform the functional data into a matrix format
B. To model the relationship between the predictor and response variables
C. To represent the functional data in terms of a finite set of functions
D. To calculate the derivatives of the functional data
C. To represent the functional data in terms of a finite set of functions
What is the primary purpose of a roughness penalty in functional data analysis?
A. To increase the complexity of the model
B. To penalize the smoothness of the fitted curve
C. To minimize the computational time required for analysis
D. To enforce linearity in the relationship between variables
B. To penalize the smoothness of the fitted curve
What is the main objective of Functional Linear Regression Analysis (FLRA)?
A. To estimate the functional relationship between two or more functional variables
B. To model the relationship between a functional or scalar response variable and one or more functional or scalar predictors
C. To compute the mean value of a functional variable
D. To identify outliers in functional data
B. To model the relationship between a functional or scalar response variable and one or more functional or scalar predictors
Which of the following best describes the difference between Traditional Linear Regression Analysis and Functional Linear Regression Analysis (FLRA)?
A. Traditional linear regression involves scalar variables, while FLRA involves functional variables
B. Traditional linear regression only considers fixed values for regression coefficients, while FLRA allows coefficients to vary as functions of time
C. Traditional linear regression only allows for one predictor variable, while FLRA can handle multiple functional predictors
D. Traditional linear regression assumes linear relationships, while FLRA assumes non-linear relationships
A. Traditional linear regression involves scalar variables, while FLRA involves functional variables
When might the Permutation F -Test methodology be used in Functional Linear Regression Analysis?
A. To estimate the functional relationship between two scalar variables
B. To assess the goodness of fit of the Functional Linear Regression model
C. To evaluate the statistical significance of relationships among functional independent variables and dependent variables
D. To determine the linearity assumption of the Functional Linear Regression mode
C. To evaluate the statistical significance of relationships among functional independent variables and dependent variables
Which of the following scenarios is not included in Functional Linear Regression Analysis?
A. The response variable is scalar or multivariate, and the independent variable is functional
B. The response variable is functional, and the independent variable is scalar
C. Both the response and independent variables are functional
D. Both the response and independent variables are scalars
D. Both the response and independent variables are scalars
What is the main objective of Functional Principal Component Analysis (FPCA)?
A. To identify outliers in functional data
B. To estimate the relationship between functional variables and scalar outcomes
C. To reduce the dimensionality of functional data while preserving the most important variability
D. To assess the goodness of fit of functional regression models
C. To reduce the dimensionality of functional data while preserving the most important variability