Package com.imsl.stat.distributions

Class MaximumLikelihoodEstimation

java.lang.Object

com.imsl.stat.distributions.MaximumLikelihoodEstimation

All Implemented Interfaces:

Serializable, Cloneable

public class MaximumLikelihoodEstimation
extends Object
implements Serializable, Cloneable

Maximum likelihood parameter estimation.

See Also:

• Example 1
• Example 2
• Example 3
• Example 4
• Example 5
• Example 6
• Example 7
• Example 8
• Example 9
• Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	MaximumLikelihoodEstimation.OptimizationMethod	Indicates which optimization method to use in maximizing the likelihood.

Constructor Summary

Constructors

Constructor	Description
MaximumLikelihoodEstimation(double[] x, ProbabilityDistribution pd, double... guess)	Constructor for maximum likelihood estimation

Method Summary

Modifier and Type	Method	Description
void	compute()	Computes the maximum likelihood estimates.
void	compute(MaximumLikelihoodEstimation.OptimizationMethod optMethod)	Computes the maximum likelihood estimates with the specified optimization method.
double[]	getEstimates()	Returns the parameter estimates.
double[][]	getHessian()	Returns the Hessian of the log-likelihood function evaluated at the current parameter estimates.
double	getLogLikelihood(double[] x, double... params)	Returns the log-likelihood.
double	getMinusLogLikelihood()	Returns minus the log-likelihood evaluated at the parameter estimates.
double[]	getStandardErrors()	Returns the approximate standard errors of the maximum likelihood estimates.
double[][]	getVarCov()	Returns the approximate variance-covariance matrix of the maximum likelihood estimates.
void	setClosedForm(boolean cf)	Sets the flag indicating whether or not the closed form solution should be used.
void	setExact(boolean exact)	Deprecated. use setUseAnalytic(boolean) instead
void	setGuess(double... guess)	Sets the guess or starting values of the parameters.
void	setMaxIterations(int maxIterations)	Sets the maximum number of iterations for the solver to use.
final void	setRandomObject(Random r)	Sets the random object to be used in the Nelder-Mead method.
void	setSample(double[] x)	Sets the sample data to use in the estimation procedure.
void	setUseAnalytic(boolean useAnalytic)	Sets the flag indicating whether or not the PDF supplies the analytic gradient and Hessian.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

MaximumLikelihoodEstimation

public MaximumLikelihoodEstimation(double[] x,
 ProbabilityDistribution pd,
 double... guess)

Constructor for maximum likelihood estimation

Parameters:

x - a double array containing the sample observations

pd - an instance of ProbabilityDistribution

guess - a double array or a comma-separated list of doubles giving the starting values for the parameters

Note: The argument guess is a variable length argument list (varargs).

Method Details

getLogLikelihood

public double getLogLikelihood(double[] x,
 double... params)

Returns the log-likelihood.

Note that this method is for convenience and does not use any of the member data or parameters. The user supplies the arguments.

Parameters:

x - a double array containing sample data

params - a double array or comma separated list of doubles containing the parameter values

Returns:

a double, the log-likelihood evaluated at the given data and parameter values

compute

public void compute()
             throws MinConNLP.ConstraintEvaluationException,
MinConNLP.ObjectiveEvaluationException,
MinConNLP.WorkingSetSingularException,
MinConNLP.QPInfeasibleException,
MinConNLP.PenaltyFunctionPointInfeasibleException,
MinConNLP.LimitingAccuracyException,
MinConNLP.TooManyIterationsException,
MinConNLP.BadInitialGuessException,
MinConNLP.IllConditionedException,
MinConNLP.SingularException,
MinConNLP.LinearlyDependentGradientsException,
MinConNLP.NoAcceptableStepsizeException,
MinConNLP.TerminationCriteriaNotSatisfiedException

Computes the maximum likelihood estimates.

The method returns closed form solutions if usedClosedForm is true and closed form solutions are available for the likelihood. Otherwise, the default OptimizationMethod.MINCONNLP is used to numerically find the estimates.

Throws:

MinConNLP.ConstraintEvaluationException - Constraint evaluation returns an error with current point.

MinConNLP.ObjectiveEvaluationException - Objective evaluation returns an error with current point.

MinConNLP.WorkingSetSingularException - Working set is singular in dual extended QP.

MinConNLP.QPInfeasibleException - QP problem seemingly infeasible.

MinConNLP.PenaltyFunctionPointInfeasibleException - Penalty function point infeasible.

MinConNLP.LimitingAccuracyException - Limiting accuracy reached for a singular problem.

MinConNLP.TooManyIterationsException - Maximum number of iterations exceeded.

MinConNLP.BadInitialGuessException - Penalty function point infeasible for original problem. Try new initial guess.

MinConNLP.IllConditionedException - Problem is singular or ill-conditioned.

MinConNLP.SingularException - Problem is singular.

MinConNLP.LinearlyDependentGradientsException - Working set gradients are linearly dependent.

MinConNLP.NoAcceptableStepsizeException - No acceptable stepsize in [SIGMA,SIGLA].

MinConNLP.TerminationCriteriaNotSatisfiedException - Termination criteria are not satisfied.

compute

public void compute(MaximumLikelihoodEstimation.OptimizationMethod optMethod)
             throws MinConNLP.ConstraintEvaluationException,
MinConNLP.ObjectiveEvaluationException,
MinConNLP.WorkingSetSingularException,
MinConNLP.QPInfeasibleException,
MinConNLP.PenaltyFunctionPointInfeasibleException,
MinConNLP.LimitingAccuracyException,
MinConNLP.TooManyIterationsException,
MinConNLP.BadInitialGuessException,
MinConNLP.IllConditionedException,
MinConNLP.SingularException,
MinConNLP.LinearlyDependentGradientsException,
MinConNLP.NoAcceptableStepsizeException,
MinConNLP.TerminationCriteriaNotSatisfiedException

Computes the maximum likelihood estimates with the specified optimization method.

The method returns closed form solutions if usedClosedForm is true and closed form solutions are available for the likelihood.

Parameters:

optMethod - an OptimizationMethod

Throws:

MinConNLP.ConstraintEvaluationException - Constraint evaluation returns an error with current point.

MinConNLP.ObjectiveEvaluationException - Objective evaluation returns an error with current point.

MinConNLP.WorkingSetSingularException - Working set is singular in dual extended QP.

MinConNLP.QPInfeasibleException - QP problem seemingly infeasible.

MinConNLP.PenaltyFunctionPointInfeasibleException - Penalty function point infeasible.

MinConNLP.LimitingAccuracyException - Limiting accuracy reached for a singular problem.

MinConNLP.TooManyIterationsException - Maximum number of iterations exceeded.

MinConNLP.BadInitialGuessException - Penalty function point infeasible for original problem. Try new initial guess.

MinConNLP.IllConditionedException - Problem is singular or ill-conditioned.

MinConNLP.SingularException - Problem is singular.

MinConNLP.LinearlyDependentGradientsException - Working set gradients are linearly dependent.

MinConNLP.NoAcceptableStepsizeException - No acceptable stepsize in [SIGMA,SIGLA].

MinConNLP.TerminationCriteriaNotSatisfiedException - Termination criteria are not satisfied.

setUseAnalytic

public void setUseAnalytic(boolean useAnalytic)

Sets the flag indicating whether or not the PDF supplies the analytic gradient and Hessian.

Parameters:

useAnalytic - a boolean. When true, the method expects the pdf to supply the analytic gradient and Hessian calculation. If pd is an instance of class DiscreteUniformPD, then exclusively the analytical derivatives are used, that is, useAnalytic is always set to true, and this method is ignored.

Default: useAnalytic = false.

setExact

public void setExact(boolean exact)

Deprecated.

use setUseAnalytic(boolean) instead

Sets the flag indicating whether or not the PDF supplies the exact gradient and Hessian.

Parameters:

exact - a boolean. When true, the function expects the pdf to supply the analytic gradient and Hessian calculation. If pd is an instance of class DiscreteUniformPD, then exclusively the exact derivatives are used, that is, exact is always set to true, and this method is ignored.

Default: exact = false.

setClosedForm

public void setClosedForm(boolean cf)

Sets the flag indicating whether or not the closed form solution should be used.

Parameters:

cf - a boolean. When true, the compute() method returns the closed form solution if the ProbabilityDistribution is a ClosedFormMaximumLikelihoodInterface object. The option is ignored if that is not the case. If pd is an instance of class DiscreteUniformPD, then exclusively the closed form solution is computed, that is, cf is always set to true, and this method is ignored.

Default: cf = false.

setGuess

public void setGuess(double... guess)

Sets the guess or starting values of the parameters.

Parameters:

guess - a double array of the same length as the parameters containing proper starting values for the optimization. guess may also be a comma separated list of doubles giving the parameter values.

Note: The argument guess is a variable length argument list (varargs).

setRandomObject

public final void setRandomObject(Random r)

Sets the random object to be used in the Nelder-Mead method.

Parameters:

r - a Random object to be used in the computation of the complex vertices in the Nelder-Mead solver.

Specifying a seed for the Random object can produce repeatable/deterministic output.

setMaxIterations

public void setMaxIterations(int maxIterations)

Sets the maximum number of iterations for the solver to use.

Parameters:

maxIterations - an int, the maximum number of iterations for the solver to use. The default is maxIterations=400.

setSample

public void setSample(double[] x)

Sets the sample data to use in the estimation procedure.

Parameters:

x - a double array containing sample observations of the random variable

getEstimates

public double[] getEstimates()

Returns the parameter estimates.

Returns:

a double array containing the parameter estimates

getMinusLogLikelihood

public double getMinusLogLikelihood()

Returns minus the log-likelihood evaluated at the parameter estimates.

This method returns the value of the objective function, the minimum of minus the log-likelihood.

Returns:

a double, minus the log-likelihood

getStandardErrors

public double[] getStandardErrors()
                           throws SingularMatrixException

Returns the approximate standard errors of the maximum likelihood estimates.

Returns:

a double array containing the standard errors

Throws:

SingularMatrixException - The matrix is singular.

getVarCov

public double[][] getVarCov()
                     throws SingularMatrixException

Returns the approximate variance-covariance matrix of the maximum likelihood estimates. The approximation is the negative inverse Hessian of the log-likelihood.

Returns:

a double matrix containing the approximate variance-covariance matrix

Throws:

SingularMatrixException - The matrix is singular.

getHessian

public double[][] getHessian()

Returns the Hessian of the log-likelihood function evaluated at the current parameter estimates.

Returns:

a double matrix containing the Hessian matrix